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Electron-magnon coupling at the interface between a normal metal and a magnetically ordered insulator modifies the electrical conductivity of the normal metal, an effect known as spin-Hall magnetoresistance. It can also facilitate magnon-mediated current drag, the nonlocal electric current response of two normal metal layers separated by a magnetic insulator. In this article, we present a theory of these two spintronic effects and their nonlinear counterparts for time-dependent applied electric fields $E(\omega)$, with driving frequencies $\omega$ up to the THz regime. We compare various mechanisms leading to a quadratic-in-$E$ response $-$ Joule heating, spin-torque diode effect, and magnonic unidirectional spin-Hall magnetoresistance $-$ and show how these can be disentangled by their characteristic dependences on $\omega$ and the magnetization direction., Comment: 22 + 6 pages, 9 figures

The van der Waals (vdW) heterostructure of emerging two-dimensional (2D) quantum materials, with control over their quantum geometries, crystal symmetries, spin-orbit coupling, and magnetic anisotropies, provides a new platform for generating unconventional nonlinear Hall effects, spin polarization and efficiently controlling the magnetization dynamics for non-volatile spin-based computing. However, so far, the generation of a large out-of-plane spin polarization is limited to achieve energy-efficient field-free magnetization switching and spin dynamics measurements in all-2D vdW heterostructure are so far missing, where the interplay between spins and magnetization dynamics should enable the design of ultrafast spintronic devices. Here, we demonstrate magnetization dynamics and energy-efficient field-free spin-orbit torque (SOT) switching of out-of-plane magnet Fe3GaTe2 due to unconventional Berry curvature-induced out-of-plane spin polarization from a topological Weyl semimetal TaIrTe4 in a vdW heterostructure at room temperature. We observed a large non-linear 2nd harmonic Hall signal at room temperature and evaluated the SOT-induced magnetization dynamics with a large damping-like torque. Deterministic field-free SOT magnetization switching in vdW heterostructure of TaIrTe4/Fe3GaTe2 is observed at room temperature with a low current and power density, which is an order of magnitude better than that of conventional systems. From the magnetization switching experiments, a large SOT efficiency and a very large spin Hall conductivity. These findings on all-vdW heterostructures offer a promising route to energy-efficient and external field-free ultrafast spintronic technologies.

Blue phosphorene -- two-dimensional, hexagonal-structured, semiconducting phosphorus -- has gained attention as it is considered easier to synthesize on metal surfaces than its allotrope, black phosphorene. Recent studies report different structures of phosphorene, for example, on Cu(111), but the underlying mechanisms of their formation are not known. Here, using a combination of in situ ultrahigh vacuum low-energy electron microscopy and in vacuo scanning tunneling microscopy, we determine the time-evolution of the surface structure and morphology during the deposition of phosphorus on single-crystalline Cu(111). We find that during early stages of deposition, phosphorus intermixes with Cu, resulting in copper phosphide structures. With increasing surface concentration of phosphorus, the phosphide phase disappears and a blue phosphorene layer forms, followed by self-assembly of highly ordered phosphorus clusters that eventually grow into multilayer islands. We attribute the unexpected transformation of stable phosphide to a phosphorene layer, and the previously unreported multilayer growth, to the presence of a large concentration of P2 dimers on the surface. Our results constitute direct evidence for a new growth mode leading to a phosphorene layer via an intermediary phase, which could underpin the growth of other 2D materials on strongly interacting substrates., Comment: 25 pages, 5 figures

Mercury telluride is an intriguing compound that is well known for the first realization of topological states. Despite being known for a long time, a quantitative understanding of its electronic properties remains challenging due to the presence of many concomitant subtle effects. By combining accurate first principles calculations and $k.p$ modelling, we investigate the topological phase diagram of mercury telluride as a function of strain. Our research demonstrates the significance of including the linearly $k$-dependent higher-order $C_4$ strain terms into the usual $k.p$ treatment. In particular, we report a unique $k$-dependence of the sub-band splitting, which arises from the interplay between strain and the standard bulk inversion asymmetry terms within our $k.p$ model. The impact of this phenomenon is explored in relation to the camel's back shape during the tensile strain phase and its implications for the Weyl semimetal state in the compressive strain case are discussed., Comment: 12 pages, 7 figures

Electronic flying qubits offer an interesting alternative to photonic qubits: electrons propagate slower, hence easier to control in real time, and Coulomb interaction enables direct entanglement between different qubits. While their coherence time is limited, picosecond-scale control would make them competitive in terms of number of possible coherent operations. The key challenge lies in achieving the dynamical regime, where the injected plasmonic pulse width is shorter than the quantum device dimensions. Here we reach this new regime in a quantum nanoelectronic system by injecting ultrashort single electron plasmonic pulses into a 14-micrometer-long Mach-Zehnder interferometer. Our findings reveal that quantum coherence is preserved for ultrashort plasmonic pulses, exhibiting enhanced contrast of coherent oscillations compared to the DC regime. Moreover, this coherence remains robust even under large bias voltages. This milestone demonstrates the feasibility of flying qubits as a promising alternative to localized qubit architectures, offering reduced hardware footprint, increased connectivity, and potential for scalable quantum information processing.

The observation of unexpected polarisation textures such as vortices, skyrmions and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180{\deg} domain walls of PbTiO3 have recently been reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquitous nature of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarisation in the 180{\deg} domain walls in PbTiO3/SrTiO3 superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centres of the 180{\deg} domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves further attention.

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field time-dependent amplitude and its quantum fluctuations. In this work, we demonstrate a quantum sensor that exploits the phase of a single electron wavefunction, measured in an electronic Fabry-Perot interferometer, to detect a classical time-dependent electric field. The time resolution, limited by the temporal width of the electronic wavepacket, is a few tens of picoseconds. The interferometry technique provides a voltage resolution of a few tens of microvolts, corresponding to a few microwave photons. Importantly, our detector simultaneously probes the amplitude of the field from the phase of the measured interference pattern and its fluctuations from the interference contrast. This capability paves the way for on-chip detection of quantum radiation, such as squeezed or Fock states., Comment: Main (8 pages and 3 figures) and supplementary files (17 pages and 12 figures)

Magnetic 2D materials enable novel tuning options of magnetism. As an example, the van der Waals material FePS3, a zigzag-type intralayer antiferromagnet, exhibits very strong magnetoelastic coupling due to the different bond lengths along different ferromagnetic and antiferromagnetic coupling directions enabling elastic tuning of magnetic properties. The likely cause of the length change is the intricate competition between direct exchange of the Fe atoms and superexchange via the S and P atoms. To elucidate this interplay, we study the band structure of exfoliated FePS3 by mu m scale ARPES (Angular Resolved Photoelectron Spectroscopy), both, above and, for the first time, below the Neel temperature TN. We find three characteristic changes across TN. They involve S 3p-type bands, Fe 3d-type bands and P 3p-type bands, respectively, as attributed by comparison with density functional theory calculations (DFT+U). This highlights the involvement of all the atoms in the magnetic phase transition providing independent evidence for the intricate exchange paths.

Inducing superconducting correlations in chiral edge states is predicted to generate topologically protected zero energy modes with exotic quantum statistics. Experimental efforts to date have focused on engineering interfaces between superconducting materials, typically amorphous metals, and semiconducting quantum Hall or quantum anomalous Hall (QAH) systems. However, the strong interfacial disorder inherent can prevent the formation of isolated topological modes. An appealing alternative is to use low-density flat band materials where the ground state can be tuned between intrinsic superconducting and quantum anomalous Hall states using only the electric field effect. However, quantized transport and superconductivity have not been simultaneously achieved. Here, we show that rhombohedral tetralayer graphene aligned to a hexagonal boron nitride substrate hosts a quantized anomalous Hall state at superlattice filling $\nu = -1$ as well as a superconducting state at $\nu \approx -3.1$ at zero magnetic field. Remarkably, gate voltage can also be used to actuate nonvolatile switching of the chirality in the quantum anomalous Hall state, allowing arbitrarily reconfigurable networks of topological edge modes in locally gated devices. Thermodynamic compressibility measurements further reveal a topologically ordered fractional Chern insulator at $\nu = 2/3$, also stable at zero magnetic field, enabling proximity coupling between superconductivity and fractionally charged edge modes. Finally, we show that integrating an additional transition metal dichalcogenide layer to the heterostructure enhances the maximum superconducting critical temperature and nucleates new superconducting pockets, while leaving the topology of $\nu = -1$ the quantum anomalous Hall state intact. Our results pave the way for hybrid interfaces between superconductors and topological edge states in the low-disorder limit.

Materials with antiferromagnetic order have recently emerged as promising candidates in spintronics based on their beneficial characteristics such as vanishing stray fields and ultra-fast dynamics. At the same time more complex localized non-coplanar magnetic states as for instance skyrmions are in the focus of applications due to their intriguing properties such as the topological Hall effect. Recently a conceptual shift has occurred to envision the use of such magnetic defects not only in one-dimensional race track devices but to exploit their unique properties in two-dimensional networks. Here we use local strain in a collinear antiferromagnet to induce non-coplanar domain wall junctions, which connect in a very specific way to form extended networks. We combine spin-polarized scanning tunneling microscopy with density functional theory to characterize the different building blocks of the network, and unravel the origin of the handedness of triple-junctions and the size of the arising topological orbital moments., Comment: Marie Sk{\l}odowska-Curie Actions, H2020-MSCA-ITN-2020; Project acronym SPEAR; Grant Agreement No. 955671

Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moir\'e flat bands and Landau levels (LLs). For instance, like the lowest LL, topological exact flat bands with ideal quantum geometry can be constructed using the same holomorphic function structure, $\psi_{\mathbf{k}} = f_{\mathbf{k}-\mathbf{k}_0}(z) \psi_{\mathbf{k}_0}$, where $f_{\mathbf{k}}(z)$ is a holomorphic function. This holomorphic structure has been the foundation of existing knowledge on constructing ideal topological flat bands. In this Letter, we report a new family of ideal topological flat bands where the $f$ function does not need to be holomorphic. We provide both model examples and universal principles, as well as an analytic method to construct the wavefunctions of these flat bands, revealing their universal properties, including ideal quantum geometry and a Chern number of $C = \pm 2$ or higher.

The interplay between strong electron-electron interaction and symmetry breaking can have profound influence on the topological properties of materials. In magic angle twisted bilayer graphene (MATBG), the flat band with a single SU(4) flavor associated with the spin and valley degrees of freedom gains non-zero Chern number when C2z symmetry or C2zT symmetry is broken. Electron-electron interaction can further lift the SU(4) degeneracy, leading to the Chern insulator states. Here we report a complete sequence of zero-field Chern insulators at all odd integer fillings (v = +-1, +-3) with different chirality (C = 1 or -1) in hBN aligned MATBG which structurally breaks C2z symmetry. The Chern states at hole fillings (v = -1, -3), which are firstly observed in this work, host an opposite chirality compared with the electron filling scenario. By slightly doping the v = +-3 states, we have observed new correlated insulating states at incommensurate moir\'e fillings which is highly suggested to be intrinsic Wigner crystals according to our theoretical calculations. Remarkably, we have observed prominent Streda-formula violation around v = -3 state. By doping the Chern gap at v = -3 with notable number of electrons at finite magnetic field, the Hall resistance Ryx robustly quantizes to ~ h/e2 whereas longitudinal resistance Rxx vanishes, indicating that the chemical potential is pinned within a Chern gap, forming an incommensurate Chern insulator. By providing the first experimental observation of zero-field Chern insulators in the flat valence band, our work fills up the overall topological framework of MATBG with broken C2z symmetry. Our findings also demonstrate that doped topological flat band is an ideal platform to investigate exotic incommensurate correlated topological states., Comment: 28 pages. 5 figures

Electrical manipulation of spin-polarized current is highly desirable yet tremendously challenging in developing ultracompact spintronic device technology. Here we propose a scheme to realize the all-electrical manipulation of spin-polarized current in an altermagnetic bilayer. Such a bilayer system can host layer-spin locking, in which one layer hosts a spin-polarized current while the other layer hosts a current with opposite spin polarization. An out-of-plane electric field breaks the layer degeneracy, leading to a gate-tunable spin-polarized current whose polarization can be fully reversed upon flipping the polarity of the electric field. Using first-principles calculations, we show that CrS bilayer with C-type antiferromagnetic exchange interaction exhibits a hidden layer-spin locking mechanism that enables the spin polarization of the transport current to be electrically manipulated via the layer degree of freedom. We demonstrate that sign-reversible spin polarization as high as 87% can be achieved at room temperature. This work presents the pioneering concept of layer-spintronics which synergizes altermagnetism and bilayer stacking to achieve efficient electrical control of spin., Comment: 20 pages, 5 figures

Graphene is known to exhibit a pronounced photo-thermoelectric effect (PTE) in its in-plane carrier transport and attracting attention toward various optoelectronic applications. In this study, we demonstrate an out-of-plane PTE by utilizing electron tunneling across a barrier, namely, the tunneling photo-thermoelectric effect (TPTE). This was achieved in a monolayer graphene (MLG)/bilayer hexagonal boron nitride (h-BN)/bilayer graphene (BLG) asymmetric tunnel junction. MLG and BLG exhibit different cyclotron resonance (CR) optical absorption energies when their energies are Landau quantized under an out-of-plane magnetic field. We tuned the magnetic field under mid-infrared (MIR) irradiation to bring MLG into CR conditions, whereas BLG was not in CR. The CR absorption in the MLG generates an electron temperature difference between the MLG and BLG, and induces an out-of-plane TPTE voltage across the h-BN tunnel barrier. The TPTE exhibited a unique dependence on the Fermi energy of the MLG, which differed from that of the in-plane PTE of the MLG. The TPTE signal was large when the Fermi energy of the MLG was tuned near the phase transition between the quantum Hall state (QHS) and non-QHS, that is, the transition between carrier localization and delocalization. The TPTE provides another degree of freedom for probing the electronic and optoelectronic properties of two-dimensional material heterostructures., Comment: 18 pages, 4 figures

Non-Hermitian skin effects (NHSEs) have recently been investigated extensively at the single-particle level. When many-body interactions become dominant, novel non-Hermitian physical phenomena can emerge. In this work, we theoretically study NHSEs controlled by dissipation and interaction. We consider a 1D zigzag Bose-Hubbard lattice, subject to magnetic flux, staggered onsite single-particle loss, and uniform onsite two-particle loss. When the two-particle loss is small, two-body bound eigenstates (i.e., doublons) are all localized at the same boundary due to the interplay of the magnetic flux and staggered single-particle loss. While, for strong two-particle loss, the localization direction of doublons is unexpectedly reversed. This is attributed to the effective strong nonreciprocal hopping of doublons induced by the virtual second-order and third-order hopping processes of particle pairs with the combination of the magnetic flux, staggered single-particle loss, and strong two-particle loss. Moreover, a two-particle gain can induce the same skin-localization and reversal features of doublons, which can be utilized to dynamically observe the NHSE and its reversal of doublons controlled by interactions. Our results open up a new avenue for exploring novel non-Hermitian phenomena in many-body systems., Comment: 16 pages, 9 figures; Comments are welcome

The advent of two-dimensional van der Waals materials is a frontier of condensed matter physics and quantum devices. However, characterizing such materials remains challenging due to the limitations of bulk material techniques, necessitating the development of specialized methods. In this study, we investigate the superconducting properties of Bi2Sr2CaCu2O8+x flakes by integrating them with a hybrid superconducting microwave resonator. The hybrid resonator is significantly modified by the interaction with the flake while maintaining a high quality factor. We also observe a significant upshift of the resonator frequency with increasing temperature, as well as a positive nonlinearity. These effects originate from a presently unknown microscopic mechanism within the flake, and can be modeled as a two-level system bath interacting with resonant mode. Our findings open a path for high quality hybrid circuits with van der Waals flakes for exploring novel materials and developing new devices for quantum technology., Comment: 5 pages, 4 figures with a supplementary material of 7 pages and 7 figures

The interplay of electrons with a chiral medium has a diverse impact across science and technology, influencing drug separation, chemical reactions, and electronic transport. In particular, such electronchirality interactions can significantly affect charge and spin transport in chiral conductors, ranging from bulk semiconductors down to individual molecules. Consequentially, these interactions are appealing for spintronic manipulations. However, an atomistic mapping of the different electron chirality interactions and their potential for spintronics has yet to be reached. Here, we find that single molecule junctions based on helicene molecules behave as a combined magnetic diode and spin valve device. This dual functionality is used to identify the coexistence of different electron chirality interactions at the atomic scale. Specifically, we find that the magnetic diode behavior arises from an interaction between the angular momentum of electrons in a chiral medium and magnetic fields, whereas the spin valve functionality stems from an interaction between the electron spin and a chiral medium. The coexistence of these two interactions in the same atomic scale system is then used to identify the distinct properties of each interaction. This work uncovers the different electron chirality interactions available at the atomic level. The found concurrent existence of such interactions can broaden the available methods for spintronics by combining their peculiar functionalities.

In the present article, we explore the electron properties of magnetic semiconductors with strong Rashba spin-orbit coupling taking into account the presence of domain walls at the sample surface. We consider antiphase domain walls separating domains with both in-plane and out-of-plane magnetization as well as noncollinear domain walls. First, we propose the model and unveil general physical picture of phenomenon supported by analytical arguments. Further, we perform a comprehensive tight-binding numerical calculations to provide a profound understanding of our findings. A domain wall separating domains with any polarization directions is demonstrated to host a bound state. What is more interesting is that we predict that either of these domain walls also induces one-dimensional resonant state. The surface energy spectrum and spin polarization of the states are highly sensitive to the magnetization orientation in the adjacent domains. The spectral broadening and the spatial localization of the resonant state depend significantly on a relation between the Rashba splitting and the exchange one. Our estimation shows that chiral conducting channels associated with the long-lived resonant states can emerge along the magnetic domain walls and can be accessed experimentally at the surface of BiTeI doped with transition metal atoms.

There is strong interest in designing and realizing optically-active semiconductor nanostructures of greater complexity for applications in fields ranging from biomedical engineering to quantum computing. While these increasingly complex nanostructures can implement progressively sophisticated optical functions, the presence of more material constituents and interfaces also leads to increasingly complex exciton dynamics. In particular, the rates of carrier trapping and detrapping in complex heterostructures are critically important for advanced optical functionality, but they can rarely be directly measured. In this work, we develop a model that includes trapping and release of carriers by optically inactive states. The model explains the widely observed biexponential decay of the photoluminescence signal from neutral excitons in low dimensional semiconductor emitters. The model also allows determination of likelihood intervals for all the transition rates involved in the emission dynamics, without the use of approximations. Furthermore, in cases for which the high temperature limit is suitable, the model leads to specific values of such rates, outperforming reduced models previously used to estimate those quantities. We demonstrate the value of this model by applying it to time resolved photoluminescence measurements of CdSeTe/CdS heterostructures. We obtain values not only for the radiative and nonradiative lifetimes, but also for the delayed photoluminescence originating in trapping and release.

The determination of material parameters is significantly important in material science, which is often a challenging task. Recently, advancements have shown that magnetic parameters, such as the Dzyaloshinskii-Moriya interaction (DMI), can be estimated from a magnetic domain image using machine learning (ML). This development suggests a potential shift in how magnetic parameters are determined, moving away from traditional measurement techniques to more innovative methods involving image-based inputs processed by ML. In previous studies, the test images used for estimation always matched the training images in size. However, since image size is contingent on the microscopy technique used, the ability to accurately estimate parameters from images of varying sizes is essential. Here, we investigated the feasibility of estimating the DMI constant and saturation magnetization from magnetic domain images of different sizes using ML. We successfully demonstrated that it is possible to estimate these parameters even when the imaging sizes differ between training and test datasets. Additionally, our comparison of the estimation accuracy for the DMI constant and saturation magnetization revealed that the tolerance for differences in image size varies depending on the specific parameter being estimated. These findings could have a significant impact on the future methods of determining magnetic parameters.

Arrays of coupled nanomagnets have wide-ranging fundamental and practical applications in artificial spin ices, neuromorphic computing and spintronics. However, lacking in these fields are nanomagnets with perpendicular magnetic anisotropy with sufficient magnetostatic interaction. This would not only open up new possibilities for artificial spin ice geometries but also enable novel coupling methods for applications. Here we demonstrate a method to engineer the energy landscape of artificial spin lattices with perpendicular magnetic anisotropy. With this, we are able to realize for the first time magnetostatically-coupled 2D lattices of out-of-plane Ising spins that spontaneously order at room temperature on timescales that can be precisely engineered. We show how this property, together with straightforward electrical interfacing, make this system a promising platform for reservoir computing. Our results open the way to investigate the thermodynamics of out-of-plane magnetostatically coupled nanomagnet arrays with novel spin ice geometries, as well as to exploit such nanomagnet arrays in unconventional computing, taking advantage of the adjustable temporal dynamics and strong coupling between nanomagnets.

The optical properties of graphene (Gr)-covered CsPbBr$_3$ quantum dots (QDs) were investigated using micro-photoluminescence spectroscopy, revealing a remarkable three-orders-of-magnitude enhancement in photoluminescence (PL) intensity compared to bare CsPbBr$_3$ QDs. To elucidate the underlying mechanisms, we combined experimental techniques with density functional theory (DFT) calculations. DFT simulations showed that the graphene layer generates interfacial electrostatic potential barriers when in contact with the CsPbBr$_3$ surface, impeding carrier leakage from perovskite to graphene and enhancing radiative recombination. Additionally, graphene passivates CsPbBr$_3$ surface defect states, suppressing nonradiative recombination of photo-generated carriers. Our study also revealed that graphene becomes n-doped upon contact with CsPbBr$_3$ QDs, activating its plasmon mode. This mode resonantly couples with photo-generated excitons in the perovskite. The momentum mismatch between graphene plasmons and free-space photons is resolved through plasmon scattering at Gr/CsPbBr$_3$ interface corrugations, facilitating the observed super-bright emission. These findings highlight the critical role of graphene as a top contact in dramatically enhancing CsPbBr$_3$ QDs' PL. Our work advances the understanding of graphene-perovskite interfaces and opens new avenues for designing high-efficiency optoelectronic devices. The multifaceted enhancement mechanisms uncovered provide valuable insights for future research in nanophotonics and materials science, potentially leading to breakthroughs in light-emitting technologies., Comment: 33 pages

Rare-earth-ion (REI) ensembles in crystals have remarkable optical and spin properties characterized by narrow homogeneous linewidths relative to the inhomogeneous ensemble broadening. This makes it possible to precisely tailor the ensemble spectral density and therefore the absorption profile by applying narrow-linewidth radiation to transfer population into auxiliary levels, a process broadly known as spectral hole burning (SHB). REI-doped crystals find applications in information processing, both classical (pattern recognition, filtering, spectral analysis) and quantum (photon storage), all protocols requiring suitable ensemble preparation by SHB as a first step. In Er$^{3+}$-doped materials, the longest reported hole lifetime is one minute, and longer lifetimes are desirable. Here, we report SHB and accumulated echo measurements in a scheelite crystal of CaWO$_4$ by pumping the electron spin transition of Er$^{3+}$ ions at microwave frequencies and millikelvin temperatures, with nuclear spin states of neighboring $^{183}$W atoms serving as the auxiliary levels. The lifetime of the holes and accumulated echoes rises steeply as the sample temperature is decreased, exceeding a month at 10 mK. Our results demonstrate that millikelvin temperatures can be beneficial for signal processing applications requiring long spectral hole lifetimes.

Majorana bound states (MBSs) are quasiparticles which are their own antiparticles. They are predicted to emerge as zero-energy modes localized at the boundary of a topological superconductor. No intrinsic topological superconductor is known to date. However, by interfacing conventional superconductors and semiconductors with strong spin--orbit coupling it is possible to create a system hosting topological states. Hence epitaxial superconductors and semiconductors have emerged as an attractive materials system with atomically sharp interfaces and broad flexibility in device fabrications incorporating Josephson junctions. We discuss the basics of topological superconductivity and provide insight on how to go beyond current state-of-the-art experiments. We argue that the ultimate success in realizing MBS physics requires the observation of non-Abelian braiding and fusion experiments.

Coulomb drag is a powerful tool to study interactions in coupled low-dimensional systems. Historically, Coulomb drag has been attributed to a frictional force arising from momentum transfer whose direction is dictated by the current flow. However recent findings in one-dimensional systems have also identified a rectified contribution that is independent of the current flow direction. In this work, we present Coulomb drag measurements between vertically coupled GaAs/AlGaAs quantum wires separated vertically by a hard barrier only 15 nm wide where both momentum transfer and rectified Coulomb drag signals are observed simultaneously, and whose relative magnitude are temperature and gate tunable. Our study opens up the possibility of studying the physical mechanisms behind the onset of both momentum transfer and charge rectification drag simultaneously in a single device, ultimately leading to a better understanding of Luttinger liquids in multi-channel wires and paving the way for the creation of energy harvesting devices., Comment: 9 pages, 5 figures

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of eigenvalues and eigenvectors of a Hamiltonian--a large, sparse matrix--relative to system properties poses a significant challenge, especially for arbitrary systems. Superconducting quantum circuits offer substantial flexibility in Hamiltonian design, making them an ideal platform for this task. In this work, we present a comprehensive framework for the gradient-based optimization of superconducting quantum circuits, leveraging the SQcircuit software package. By addressing the challenge of calculating the gradient of the eigensystem for large, sparse Hamiltonians and integrating automatic differentiation within SQcircuit, our framework enables efficient and precise computation of gradients for various circuit properties or custom-defined metrics, streamlining the optimization process. We apply this framework to the qubit discovery problem, demonstrating its effectiveness in identifying qubit designs with superior performance metrics. The optimized circuits show improvements in a heuristic measure of gate count, upper bounds on gate speed, decoherence time, and resilience to noise and fabrication errors compared to existing qubits. While this methodology is showcased through qubit optimization and discovery, it is versatile and can be extended to tackle other optimization challenges in superconducting quantum hardware design., Comment: 23 pages, 10 figures. Accompanying SQcircuit package on https://sqcircuit.org/

Ideal $C=1$ Chern bands exhibit a Landau level correspondence: they factorize as a lowest Landau levels and a spinor wavefunction that spans the layer index. We demonstrate that, in single Dirac moir\'e models, the spinor develops generally a Skyrme texture in real space with an associated Berry phase which compensates exactly the magnetic phase of the Landau level. For ideal bands with higher Chern numbers $C>1$, we find that $C$ color Landau levels are carried by $C$ spinors with Skyrme textures. We identify a SU(C) gauge symmetry in the color space of spinors and an emergent non-Abelian connection in real space intimately linked to the Pontryagin winding index of the layer skyrmions. They result in a total real-space Chern number of $-1$, screening the magnetic phase, irrespective of $C$ and of the number of layers. The topologically robust Skyrme texture remains remarkably intact in twisted bilayer graphene, even far from the chiral limit, and for realistic values of corrugation, making it an experimentally testable feature. We verify our predictions at the first magic angle of twisted bilayer, trilayer, and monolayer-bilayer graphene., Comment: 8+13 pages, 6 figures

The Kondo problem, which describes the interaction of a spin $s$ magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in $1/s$ with the renormalization group. We study both the case of an impurity interacting with a single channel $K=1$ of fermions in the $s \rightarrow \infty$ limit and the case with $K$ channels in the double-scaling limit $K \rightarrow \infty$, $s \to \infty$, $K/s$ fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large $s$ and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime $K > 2s$ we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.

Tailoring the losses of optical systems within the frame of non-Hermitian physics has appeared very fruitful in the last few years. In particular, the description of exceptional points (EPs) with coupled resonators have become widespread. The on-chip realization of these functionalities is highly significant for integrated nanophotonics, but requires fine control techniques of the nanodevice properties. Here, we demonstrate pump-controlled directional emission of two coupled nanolasers that distantly interact via an integrated waveguide. This coupling scheme unusually enables both frequency- and loss-couplings between two cavities, which can be advantageously exploited to reach EPs by either detuning the cavities or controlling the gain of nanolasers. The system can be readily reconfigured from bidirectional to unidirectional emission by adjusting the pump power.

Incorporating valley as a degree of freedom into quantum anomalous Hall systems offers a novel approach to manipulating valleytronics in electronic transport. Using the Kane-Mele monolayer as a concrete model, we comprehensively explore the various topological phases in the presence of inequivalent exchange fields and reveal the roles of the interfacial Rashba effect and external electric field in tuning topological valley-polarized states. We find that valley-polarized states can be realized by introducing Kane-Mele spin-orbit coupling and inequivalent exchange fields. Further introducing Rashba spin-orbit coupling and an electric field into the system can lead to diverse topological states, such as the valley-polarized quantum anomalous Hall effect with $\mathcal{C}=~\pm 1,\pm 2$ and valley-contrasting states with $\mathcal{C}=0$. Remarkably, different valley-polarized topological states can be continuously tuned by varying the strength and direction of the external electric field in a fixed system. Our work demonstrates the tunability of topological states in valley-polarized quantum anomalous Hall systems and provides an ideal platform for applications in electronic transport devices in topological valleytronics.

Circuit-based quantum devices rely on keeping electrons at millikelvin temperatures. Improved coherence and sensitivity as well as discovering new physical phenomena motivate pursuing ever lower electron temperatures, accessible using on-chip cooling techniques. Here we show that a two-dimensional electron gas (2DEG), manipulated using gate voltages, works as an on-chip heat sink only limited by a fundamental phonon heat-leak. A single-shot 2DEG cooler can reduce the electron temperature by a factor of two with a hold time up to a second. Integrating an array of such coolers to obtain continuous cooldown in will allow reaching down to microkelvin device temperatures., Comment: 7 pages, 3 figures, 1 table

Synchronization of coupled oscillators is a fundamental phenomenon that has been observed in many natural and engineered systems, ranging from biological cells to electronic circuits. In recent years, spin torque nano-oscillators (STNOs) have emerged as a promising platform for a variety of applications in nanoscale systems such as neuromorphic computing, due to their compact size, low power consumption, and tunable properties. However, achieving synchronization in a large array of STNOs remains a challenge, for the complexity of the interactions between the oscillators. To address this challenge, we report on the achievement of synchronization across a 2D array of STNOs. We designed a honeycomb model that created a network of interactions among the oscillators that only involved nearest neighbors. Using micromagnetic simulations, we demonstrated the effectiveness of our design and observed that global synchronization across the whole array. Such global synchronization can also be tuned by enable/disenable next-nearest neighbor interactions. We also found that our design enables synchronization at room temperature, which is crucial for practical applications. Our work contributes to the growing body of research on the synchronization of coupled oscillators in spintronics and could pave the way for the development of new types of spintronic devices and potential applications.

Lanthanide atoms show long magnetic lifetimes because of their strongly localized 4f electrons, but electrical control of their spins has been difficult because of their closed valence shell configurations. We achieved electron spin resonance of individual lanthanide atoms using a scanning tunneling microscope to probe the atoms bound to a protective insulating film. These atoms were prepared in the monovalent state with an unpaired 6s electron, enabling tunnel current to access their 4f electrons. Europium spectra display a rich array of transitions among the 54 combined electron and nuclear spin states. In contrast, samarium's ground state is a Kramers doublet with an extraordinarily large g-factor of nearly 5. These results demonstrate that all-electronic sensing and control of individual lanthanide spins is possible for quantum devices and spin-based electronics by using their rarely-observed monovalent cation state., Comment: 63 pages, 5 main text figures, 15 supplementary information figures

The use of single-photon sources (SPSs) is central to numerous systems and devices proposed amidst a modern surge in quantum technology. However, manufacturing schemes remain imperfect, and single-photon emission purity must often be experimentally verified via interferometry. Such a process is typically slow and costly, which has motivated growing research into whether SPS quality can be more rapidly inferred from incomplete emission statistics. Hence, this study is a sequel to previous work that demonstrated significant uncertainty in the standard method of quality estimation, i.e. the least-squares fitting of a physically motivated function, and asks: can machine learning (ML) do better? The study leverages eight datasets obtained from measurements involving an exemplary quantum emitter, i.e. a single InGaAs/GaAs epitaxial quantum dot; these eight contexts predominantly vary in the intensity of the exciting laser. Specifically, via a form of `transfer learning', five ML models, three linear and two ensemble-based, are trained on data from seven of the contexts and tested on the eighth. Validation metrics quickly reveal that even a linear regressor can outperform standard fitting when it is tested on the same contexts it was trained on, but the success of transfer learning is less assured, even though statistical analysis, made possible by data augmentation, suggests its superiority as an early estimator. Accordingly, the study concludes by discussing future strategies for grappling with the problem of SPS context dissimilarity, e.g. feature engineering and model adaptation., Comment: The data and software that supports the findings of this study are openly available at https://github.com/UTS-CASLab/sps-quality

We predict "intrinsic" spin relaxation times ($T_{1}$) of graphite due to spin-orbit-phonon interaction, i.e., the combination of spin-orbit coupling and electron-phonon interaction, using our developed first-principles density-matrix approach. We obtain ultralong $T_{1}$, e.g., $\sim$600 ns at 300 K, which leads to ultralong in-plane spin diffusion length $\sim$110 $\mu$m within the drift-diffusion model. Our prediction sets the upper bound of $T_{1}$ of graphite at each given temperature and Fermi level. The anisotropy ratios of $T_{1}$ or values of $T_{1z}/T_{1x}$ are found small and around 0.6. We examine the applicability of the well-known Elliot-Yafet (EY) relation, which declares that spin relaxation rate $T_{1\alpha}^{-1}$ ($\alpha=x,y,z$) is proportional to the product of the ensemble average of spin mixing parameter $\left\langle b_{\alpha}^{2}\right\rangle $ and carrier relaxation rate $\tau_{p}^{-1}$. Our numerical tests suggest that the EY relation works qualitatively if the degeneracy threshold $t^{\mathrm{deg}}$ for evaluating $b_{\alpha}^{2}$ is elatively large (not much smaller than or comparable to $k_{B}T$), e.g., $10^{-3}$ eV or larger, but fails if $t^{\mathrm{deg}}$ is too tiny (much smaller than $k_{B}T$), e.g., $10^{-6}$ eV or smaller., Comment: 9 pages, 4 figures

A tight-binding model for $e_g$ orbitals on a simple cubic lattice with finite thickness is investigated. The hopping integrals for nearest-neighboring sites are considered. We examine the electronic band structures for systems with (001), (110), and (111) surfaces. Electronic states well localized around the surfaces are found for the (110) and (111) surfaces. In particular, the surface state is flat and extends in the entire Brillouin zone for the (111) surface, provided the bulk band projected onto the surface Brillouin zone is gapped. We also find that these surface states possess octupole moments in both the (110) and (111) surface cases., Comment: 7 pages, 10 figures. arXiv admin note: text overlap with arXiv:2404.00823

A spin valve represents a well-established device concept in magnetic memory technologies, whose functionality is determined by electron transmission being controlled by the relative alignment of magnetic moments of the two ferromagnetic layers. Recently, the advent of valleytronics has conceptualized a valley spin valve (VSV) - a device that utilizes the valley degree of freedom and spin-valley locking to achieve a similar valve effect without relying on magnetism. In this study, we propose a non-volatile VSV (n-VSV) based on a two-dimensional (2D) ferroelectric semiconductor where the resistance of the n-VSV is controlled by the ferroelectric domain wall between the two uniformly polarized domains. Focusing on the 1T'' phase of MoS2, which is known to be ferroelectric down to a monolayer and using density functional theory (DFT) combined with the quantum-transport calculations, we demonstrate that switching between the uniformly polarized state and the state with oppositely polarized domains separated by a domain wall results in resistance change of as high as 10^7. This giant VSV effect occurs due to transmission being strongly dependent on matching (mismatching) the valley-dependent spin polarizations in the two domains with the same (opposite) ferroelectric polarization orientations, when the chemical potential of 1T''-MoS2 lies within the spin-split valleys. Our work paves a new route for realizing high-performance nonvolatile valleytronics., Comment: 6 pages, 4 figures

Spin qubits in gate-defined quantum dots are emerging as a leading technology due to their scalability and long coherence times. However, maintaining these qubits at ultra-low temperatures typically requires complex cryogenic systems. This paper proposes a novel gate-defined double quantum dot (DQD) cooling system using microwave-induced state depopulation and phonon filtering to achieve local temperatures below 10 mK at a bath temperature of 1 K. The system utilizes microwave-induced state depopulation and phonon filtering, combined with fast cyclic detuning of the quantum dot on-site energies and Rabi oscillations, to efficiently transfer thermal populations to the ground state, thereby surpassing natural thermal transition rates. The cooling cycle involves adjusting gate potentials to drive the system through adiabatic and diabatic transitions, complemented by microwave pulses resonant with specific energy level differences. This mechanism continuously pumps the population from excited states into the ground state, effectively reducing the system's temperature. Numerical calculations demonstrate the feasibility of achieving these low local temperatures, with detailed analysis showing the sensitivity of cooling performance to detuning energy, magnetic field strength, and diabatic return time.

While fractional quantum Hall systems provide the best experimental evidence yet of (abelian) anyons plausibly necessary for future fault-tolerant quantum computation, like all strongly-coupled quantum systems their physics is not deeply understood. However, generally a promising approach is to (holographically) realize such systems on branes in string/M-theory; and specifically an old argument by Hellerman & Susskind gives a sketch of fractional quantum Hall states arising via discrete light cone quantization of M5/M9-brane intersections. Here we present a rigorous derivation of abelian anyon quantum states on M5$\perp$MO9-branes ("open M5-branes") on the discrete light cone, after globally completing the traditional local field content on the M5-worldvolume via a flux-quantization law compatible with the ambient 11d supergravity, specifically taken to be in the unstable co-Homotopy cohomology ("Hypothesis H"). The main step in the proof uses a theorem of Okuyama to identify co-Homotopy moduli spaces with configuration spaces of strings with charged endpoints, and identifies their loop spaces with cobordism of framed links that, under topological light cone quantization, turn out to be identified with the regularized Wilson loops of abelian Chern-Simons theory., Comment: 22 pages

It is well-known that the cornerstone of the proximity effect in superconductor/ferromagnet heterostructures is a generation of triplet Cooper pairs from singlet Cooper pairs inherent in a conventional superconductor. This proximity effect brought a lot of new exciting physics and gave a powerful impulse to development of superconducting spintronics. Nowadays a new direction of spintronics is actively developing, which is based on antiferromagnets and their heterostructures. It is called antiferromagnetic spintronics. By analogy with an important role played by triplet Cooper pairs in conventional superconducting spintronics based on ferromagnets the question arises: does the triplet proximity effect exist in superconductor/antiferromagnet heterostructures and, if so, what are the properties of the induced triplet correlations and the prospects for use in superconducting spintronics? Recent theoretical findings predict that despite the absence of a net magnetization, the Neel magnetic order of the antiferromagnet does give rise to specific spin-triplet correlations at superconductor/antiferromagnet interfaces. They were called Neel triplet correlations. The goal of this review is to discuss the current understanding of the fundamental physics of these Neel triplet correlations and their physical manifestations.

Recent experiments on multilayer rhombohedral graphene have unearthed a number of interesting phenomena in the regime where Integer and Fractional Quantum Anomalous Hall phenomena were previously reported. Specifically at low temperature ($T$) and low applied currents, an "Extended" Integer Quantum Anomalous Hall (EIQAH) is seen over a wide range of the phase diagram. As the current is increased, at low $T$, the EIQAH undergoes a phase transition to a metallic state at generic fillings, and to the fractional quantum anomalous Hall (FQAH) state at the Jain fillings. Increasing temperature at the Jain fillings also leads to an evolution out of the EIQAH to the Jain state. Here we provide an interpretation of these observations. We describe the EIQAH as a crystalline state (either of holes doped into the $\nu = 1$ state, or an Anomalous Hall Crystal of electrons) that breaks moir\'e translation symmetry. At generic fillings, we show how an electric current-induced depinning transition of the crystalline order leads to peculiar non-linear current-voltage curves consistent with the experiment. At Jain fillings, we propose that the depinning transition is pre-empted by an equilibrium transition between EIQAH and Jain FQAH states. This transition occurs due to the large polarizability of the Jain FQAH states which enables them to lower their energy effectively in an applied electric field compared to the crystal states. We also discuss the finite temperature evolution in terms of the relative entropies of the crystalline and FQAH states., Comment: 8+3 pages, 3 figures

Low-noise amplifiers are of great importance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SIGIS) junction coupled to a superconducting microwave cavity. The strong non-linearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency $\omega_\mathrm{r}$. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of $T_\mathrm{N} = 1.4$ K. Our theoretical modelling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system., Comment: 9 pages, 5 figures

Recent experimental and theoretical development in the Quantum Hall effect in monolayer graphene showed that the previous model of the valley-anisotropy interaction is incomplete, as it was assumed to be ultra-short range (USR). In this work, we use exact diagonalization to go beyond the ultra-short range to find the different phases for $\nu=2/3$. We model the interaction as Yukawa so that we can control the range as a proof of concept. Even in this simple setting, we discovered how dropping the USR condition shifts the transition borders in favour of certain phases, leads to a new bond-ordered phase appearing, and breaks the ferromagnetic phase in two competing states as a result of lifting the USR-driven degeneracy., Comment: 13 pages and 5 figures

The nitrogen-vacancy (NV) center in diamond is a solid-state spin defect that has been widely adopted for quantum sensing and quantum information processing applications. Typically, experiments are performed either with a single isolated NV center or with an unresolved ensemble of many NV centers, resulting in a trade-off between measurement speed and spatial resolution or control over individual defects. In this work, we introduce an experimental platform that bypasses this trade-off by addressing multiple optically resolved NV centers in parallel. We perform charge- and spin-state manipulations selectively on multiple NV centers from within a larger set, and we manipulate and measure the electronic spin states of 10 NV centers in parallel. Further, we show that the high signal-to-noise ratio of the measurements enables the detection of shot-to-shot pairwise correlations between the spin states of 10 NV centers, corresponding to the simultaneous measurement of 45 unique correlation coefficients. We conclude by discussing how our platform can be scaled to parallel experiments with thousands of individually resolved NV centers. These results enable high-throughput experiments with individual spin defects, and provide a natural platform for the application of recently developed correlated sensing techniques., Comment: Main text: 12 pages, 4 figures, 54 references. Methods: 18 pages, 8 extended data figures, 1 extended data table, 5 additional references. Supplemental files: 3 movies composed of camera images from pulsed ESR and Rabi experiments performed on 10 NV centers in parallel are uploaded as separate animated GIFs, please see the main text and methods sections for details

Magnetic adatoms on s-wave superconductors induce bound states inside the superconducting gap, called Yu-Shiba-Rusinov states (YSR). The anisotropy of the Fermi surface determines the spatial extension of bound states in a quasi-two-dimensional superconductor. This is especially important in the diluted impurity limit since the orbital overlap determines the coupling of YSR states of neighboring atoms and the formation of the collective YSR system. Here, we build diluted arrays of Mn atoms with different dimensionalities on the surface of $\beta$-Bi$_2$Pd, and we measure the evolution of their YSR spectra with the structure. We detect the coupling as a split of YSR peaks in subgap spectra and find that the split size increases with the number of atoms. The orientation of the structures along different directions of the \bipd substrate modulates the split and particle-hole asymmetry of the YSR states due to the anisotropic character of the Fermi surface, captured by the Green function model. With the aid of the model, we found multiple YSR excitations in an extended 2D array of 25 Mn atoms, and we identified that their spatial distribution reflects a chiral LDOS., Comment: 10 pages, 5 figures

Nodal loop semimetals are topological materials with drumhead surface states characterized by reduced kinetic energy. If the Fermi energy of such a system is near these nondispersive states interaction among charge carriers substantially impacts their electronic structure. The emergence of magnetism in these surface states is one of the possible consequences. Ca3P2 an already synthesized material possesses a remarkably large nodal loop which is situated exactly at the Fermi level of the bulk system. In the present work, we investigate how surface magnetism is impacted by surface reconstruction and lattice termination in finite slabs in this material. We show that a slight deviation from the stoichiometric occupation of Ca sites results in the stabilization of magnetic patterns.

Single nitrogen vacancy (NV) centers in diamond have been used extensively for high-sensitivity nanoscale sensing, but conventional approaches use confocal microscopy to measure individual centers sequentially, limiting throughput and access to non-local physical properties. Here we design and implement a multiplexed NV sensing platform that allows us to read out many single NV centers simultaneously using a low-noise camera. Using this platform, we coherently manipulate and read out the spin states of hundreds of individual NV centers in parallel, achieving comparable magnetic field sensitivity to confocal measurements. We also implement a parallelized version of spin-to-charge-conversion readout for low NV center spin state readout noise and use it to demonstrate multiplexed covariance magnetometry, in which we measure six two-point magnetic field correlators from four NV centers simultaneously. The number of correlators we can measure is limited only by the available laser power, opening the door to massively multiplexed covariance magnetometry. Our platform significantly increases the throughput and broadens the applications of nanoscale sensing using diamond quantum sensors.

Exploring the non-Hermitian properties of semiconductor materials for optical applications is at the forefront of photonic research. However, the selection of appropriate systems to implement such photonic devices remains a topic of debate. In this work, we demonstrate that a perovskite crystal, characterized by its easy and low-cost manufacturing, when placed between two distributed Bragg reflectors with an air gap, can form a natural double microcavity. This construction shows promising properties for the realisation of novel, tunable non-Hermitian photonic devices through strong light-matter coupling. We reveal that such a system exhibits double-coupled polariton modes with dispersion including multiple inflection points. Owing to its non-Hermiticity, our system exhibits nonreciprocal properties and allows for the observation of exceptional points. Our experimental studies are in agreement with the theoretical analysis based on coupled mode theory and calculations based on transfer matrix method., Comment: Accepted manuscript (AM)

The Berry curvature dipole (BCD) serves as a one of the fundamental contributors to emergence of the nonlinear Hall effect (NLHE). Despite intense interest due to its potential for new technologies reaching beyond the quantum efficiency limit, the interplay between BCD and NLHE has been barely understood yet in the absence of a systematic study on the electronic band structure. Here, we report NLHE realized in NbIrTe4 that persists above room temperature coupled with a sign change in the Hall conductivity at 150 K. First-principles calculations combined with angle-resolved photoemission spectroscopy (ARPES) measurements show that BCD tuned by the partial occupancy of spin-orbit split bands via temperature is responsible for the temperature-dependent NLHE. Our findings highlight the correlation between BCD and the electronic band structure, providing a viable route to create and engineer the non-trivial Hall effect by tuning the geometric properties of quasiparticles in transition-metal chalcogen compounds.

As a short topical review, this article reports progress on the generalization and applications of entanglement in non-Hermitian quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various applications, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions., Comment: a short review. 15p, 1figures