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Interfacial superconductivity discovered in bilayer nickelate heterostructures opens new avenues for effective tunability and control. Here, we report the superconductor-insulator transition in La$_{2.85}$Pr$_{0.15}$Ni$_2$O$_7$/SrLaAlO$_4$ interfaces, with corresponding electronic structures revealed using synchrotron low-temperature X-ray absorption spectroscopy (XAS) and X-ray linear dichroism (XLD). In addition to the valence states of each element within the films determined by XAS, XLD at the O K edge pre-peak reveals hybridizations involving both 2p$_{z}$ and 2p$_{x}$/2p$_{y}$ orbitals, which are concomitantly suppressed upon oxygen loss. Intriguingly, such oxygen loss that eliminates superconductivity, induces a qualitative XLD change at the Ni L$_{2}$ edge, implying significant transformations among 3d$_{x^{2}}$ $_{-y^{2}}$ and 3d$_{z^{2}}$ energy bands near the Fermi level. Our findings establish an element- and orbital-resolved electronic framework for the origin of superconductivity., Comment: under review

The discovery of superconductivity in bilayer nickelate thin films under ambient pressure provides an opportunity to directly investigate characteristic energy scales of the superconducting state from electronic structure. Here, we successfully probe the energy gap and dispersion renormalization in one unit-cell La$_{2.85}$Pr$_{0.15}$Ni$_2$O$_7$ films epitaxially grown on SrLaAlO$_4$ substrates, by developing an ultra-high vacuum quenching technique for in-situ angle-resolved photoemission spectroscopy measurements. The energy gap is observed on the underlying Fermi surface without showing a node along the Brillouin zone diagonal. This gap exhibits particle-hole symmetric behavior and persists to a temperature higher than the superconducting transition temperature, indicating the existence of a pseudogap. An abrupt band renormalization is observed with a dispersion anomaly at ~70 meV below Fermi level, pointing to another energy scale besides the energy gap. These observations provide initial information on fundamental properties of the superconducting state in bilayer nickelates under ambient pressure.

The discovery of high-temperature superconductivity in FeSe/SrTiO3 has sparked significant interests in exploring new superconducting systems with engineered interfaces. Here, using molecular beam epitaxy growth, we successfully fabricate FeSe/PbOx heterostructures and discover superconductivities in three different monolayer FeSe-related interfaces. We observe superconducting gaps of 13~14 meV in the monolayer FeSe films grown on two different phases of PbOx. Moreover, we discover a new insulating Fe10Se9 phase with an ordered $\sqrt{5}\times\sqrt{5}$ Se-vacancy structure. Our first-principles calculation suggests that this new insulating phase originates from electronic correlation. Intriguingly, an additional monolayer FeSe film grown on the insulating Fe10Se9 also exhibits superconductivity with the gap size of 5 meV. Our results suggest that the work function differences between the monolayer FeSe and the substrates, which can induce band bending and charge transfer, are crucial for the interfacial superconductivity., Comment: 8 pages, 4 figures

Majorana zero modes in tunneling conductance are expected to manifest as robust zero bias peaks (ZBPs). While ZBPs alone are not conclusive evidence of Majorana modes due to alternative explanations, robust ZBPs remain a crucial and necessary first-step indicator in the search for topological states. Here, we report the observation of robust ZBPs in PbTe-Pb hybrid nanowires. The peak height can reach $2e^2/h$, though it does not yet form a quantized plateau. Importantly, these ZBPs can remain non-split over sizable ranges in both magnetic field and gate voltage scans, highlighting their robustness. We discuss possible interpretations based on Majorana zero modes as well as Andreev bound states.

Bilayer nickelate thin film superconductors discovered under ambient pressure enable vast possibilities for investigating electronic structures of the superconducting state. Here, we report angle-resolved photoemission spectroscopy (ARPES) measurements of heterointerfaces between 1, 2, and 3 unit-cell epitaxial La$_{2.85}$Pr$_{0.15}$Ni$_2$O$_7$ films and SrLaAlO$_4$ substates, through pure-oxygen in situ sample transportation. Evidence obtained using photons with distinct probing depths shows that conduction is localized primarily at the first unit cell near the interface. Scanning transmission electron microscopy (STEM), together with energy-dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS), indicates that interfacial Sr diffusion and pronounced oxygen 2p hybridization gradient may collectively account for the interfacial confinement of conduction. Fermi surface maps reveal hole doping compared to non-superconducting ambient-pressure bulk crystals. Measurements of dispersive band structures suggest the contributions from both Ni $d_{x^2-y^2}$ and $d_{z^2}$ orbitals at the Fermi level. Density functional theory (DFT) + U calculations capture qualitative features of the ARPES results, consistent with a hole-doped scenario. These findings constrain theoretical models of the superconducting mechanism and suggest pathways for enhancing superconductivity in nickelates under ambient pressure., Comment: under review

The recent discovery of ambient-pressure superconductivity in thin-film bilayer nickelates opens new possibilities for investigating electronic structures in this new class of high-transition temperature $T_C$ superconductors. Here, we construct a realistic multi-orbital Hubbard model for the thin-film system, by integrating ab initio calculations with scanning transmission electron microscopy (STEM) measurements, which reveal a higher-symmetry lattice. The interaction parameters are calculated with the constrained random phase approximation (cRPA). Density functional theory (DFT) plus cluster dynamical mean-field theory (CDMFT) calculations, with cRPA calculated on-site Coulomb repulsive $U$ and experimentally measured electron filling $n$, quantitatively reproduces Fermi surfaces from angle-resolved photoemission spectroscopy (ARPES) experiments. The distinct Fermi surface topology from simple DFT+$U$ results features the indispensable role of correlation effects. Based upon the correlated electronic structures, A modified random-phase-approximation (RPA) approach yields a pronounced $s^{\pm}$-wave pairing instability, due to the strong spin fluctuations originated from Fermi surface nesting between bands with predominantly $d_{z^{2}}$ characters. Our findings highlight the quantitative effectiveness of the DFT+cRPA+CDMFT approach that precisely determines correlated electronic structure parameters without fine-tuning. The revealed intermediate correlation effect may explain the same order-of-magnitude onset $T_C$ observed both in pressured bulk and strained thin film bilayer nickelates., Comment: 4 figures and 3 tables in main manuscript. 9 figures and 2 tables in supplementary material

We investigate the anisotropic behaviors in PbTe and PbTe-Pb hybrid nanowires. In previous studies on PbTe, wire-to-wire variations in anisotropy indicate poor device control, posing a serious challenge for applications. Here, we achieve reproducible anisotropy in PbTe nanowires through a substantial reduction of disorder. We then couple PbTe to a superconductor Pb, and observe a pronounced deviation in the anisotropy behavior compared to bare PbTe nanowires. This deviation is gate-tunable and attributed to spin-orbit interaction and orbital effect, controlled by charge transfer between Pb and PbTe. These results provide a guidance for the controlled engineering of exotic quantum states in this hybrid material platform.

The discovery of bilayer nickelate superconductors under high pressure has opened a new chapter in high-transition temperature (high-TC) superconductivity. Here, we report ambient-pressure superconductivity onset above the McMillan limit (40 K) in bilayer nickelate epitaxial ultrathin films. Three-unit-cell (3UC) thick La2.85Pr0.15Ni2O7 single-phase-crystalline films are grown using the gigantic-oxidative atomic-layer-by-layer epitaxy (GOALL-Epitaxy) on SrLaAlO4 substrates. Resistivity measurements and magnetic-field responses indicate onset TC = 45 K. The transition to zero resistance exhibits characteristics consistent with a Berezinskii-Kosterlitz-Thouless (BKT)-like behavior, with TBKT = 9 K. Meissner diamagnetic effect is observed at TM = 8.5 K via a mutual inductance setup, in agreement with the BKT-like transition. In-plane and out-of-plane critical magnetic fields exhibit anisotropy. Scanning transmission electron microscopy (STEM) images and X-ray reciprocal space mappings (RSMs) show that the films maintain a tetragonal phase with coherent epitaxial compressive strain ~2% in the NiO2 planes relative to the bulk. Our findings pave the way for comprehensive investigations of nickelate superconductors under ambient pressure conditions and for exploring superconductivity at higher transition temperature through strain engineering in heterostructures., Comment: under review

Many-body ground states of imbalanced Fermi gas have been studied both theoretically and experimentally for several decades because of their fundamental significance in condensed matter physics, cold atom physics and nuclear physics. The Sarma state, a gapless spin-polarized superfluid, is one of those long sought-after exotic ground states of spin imbalanced Fermi gas. Yet, an unambiguous experimental evidence of Sarma superfluid state has not been found. Here, we report the experimental discovery of the Sarma state in atomically thick FeSe films by a dilution-refrigerator scanning tunneling microscope under high magnetic fields. In the bilayer or trilayer FeSe films, we directly observe the key evidence of the entrance of the Sarma state: the inner Zeeman splitting coherence peaks cross the Fermi level under high in-plane magnetic fields. The angle dependent critical in-plane magnetic field of coherence peak crossing shows a two-fold symmetry due to the anisotropy of the in-plane g-factor of FeSe films. Moreover, in a superconducting FeSe monolayer of a lateral size of several hundred nanometers, the Sarma state can also be induced by strong out-of-plane magnetic fields. Our findings pave the way to explore the unusual physical properties and potential applications in superconducting spintronics of the spin-polarized Sarma superfluid state.

On the spin-valve-like ferromagnet/spin glass/ferromagnet (FM/SG/FM) structure, the tunneling current is dominated by resistance switch (RS) instead of the local density of states according to the conventional tunneling theory. Here we show lattice-site dependent RS behaviors in one-quintuple-layer Bi2Te3 deposited on single MnBi2Te4 septuple layer, which comes from the difference in the efficiency of tunneling electrons to induce focused current or phonons at different sites, switching remotely the spin valve by spin-transfer torque or spin-phonon interactions. These lead to the observation of the dynamic 2-state lattice when the tip scans across the surface as well as the ability of scanning tunneling microscope (STM) to reveal atomic-scale features of electron-phonon (EP) interactions. Our work demonstrates the possibility of the spin-switch STM to image lattice-site dependent EP interactions of any materials deposited on the FM/SG/FM structure., Comment: 21 pages, 10 figures, including the supplementary materials

We report transport measurements of infinite-layer cuprate Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ films with controlled electron (by trivalent europium) and hole (by interstitial apical oxygen) carriers grown on SrTiO$_3$(001) with molecular beam epitaxy. An unusual enhancement of superconductivity upon moderate electron-hole coexistence in the films is found, which spans over the whole superconducting phase diagram and becomes more prominent in the underdoped regime. The superconductivity exhibits a two-dimensional nature with a thickness of approximately 5.2 nm, irrespective of the varying carriers, confirmed by angle-resolved magnetoresistance measurements and the Berzzinsky-Kosterlitz-Thouless transition. Nevertheless, the electron-hole coexistence enlarges the thermal activation energy of vortex motion that deviates obviously from the usual logarithmic evolution with the magnetic field. Our results offer a promising perspective to understand and enhance the high-temperature superconductivity in cuprates., Comment: 6 pages, 4 figures

We obtain in single van-der-Waals layer of MnBi2Te4 the spin-valve-like ferromagnet/spin glass (SG)/ferromagnet architecture, where the switch of individual spin states in the SG-like layer appears as the resistance switch behavior. The characteristic temperature of SG can be effectively tuned by fine-control of Bi-doping in the SG layer. A doping- and temperature-dependent phase diagram is established. We demonstrate the remote manipulation and detection of the states of individual Mn-layer spins by tunneling electrons in favor of the electron-phonon, spin-phonon, spin-transfer torque and spin-flip interactions among hot electrons, lattice and local spins, where the spin valve layer is even buried below two-quintuple-layer Bi2Te3. The integration of the SG state into spin valves opens the opportunity of realizing atomic-scale spintronics by integrating different degrees of freedom in two dimensional materials., Comment: totally 29 pages,18 figures

MnBi2Te4 (MBT) is a typical magnetic topological insulator with an A-type antiferromagnetic (AFM) ground state. Here we prepared ultra-thin MBT films with controlled anti-site defects and observed rich doping-dependent magnetic behaviors. We find in one-septuple-layer MBT films a ferrimagnetic ground state and in two-septuple-layer ones a kind of re-entrant ferromagnetism (FM) that disappears with increased Bi-on-Mn doping in the FM Mn-layers. This re-entrant behavior is attributed to a kind of symmetric exchange-bias effect that arises in the presence of both AFM and FM sub-systems due to the introduction of high-dense Mn-on-Bi anti-site defects. Furthermore, all MBT films display spin-glass-like behaviors. Our work demonstrates rich magnetic behaviors originating from the competing magnetic interactions between Mn spins at different lattice positions in MBT., Comment: 20 pages, 9 figures

Unconventional superconductors that spontaneously break space-group symmetries of their underlying crystal lattice are distinguished by spatial modulations of the superconducting order parameter. These states have recently captured significant attention in various strongly correlated materials, where the breaking of translational or intra-unit-cell symmetries results in the emergence of pair density waves with wavelengths extending across one or multiple unit cells. Here, we employ a spectroscopic-imaging scanning tunneling microscope to identify robust half-unit-cell modulations of the superconducting gap magnitude, coherence strength and subgap states in tunable 1T$^{\prime}$-MoTe$_2$ monolayer. The modulations are oriented perpendicular to the zigzag Mo chains and coexist with three-unit-cell primary pair density wave modulations along the Mo chains, both of which attenuate with increasing temperature and the application of external magnetic fields. Importantly, we find that the superconductivity modulations are strongly linked to unconventional electron pairing mechanisms, which significantly deviate from the Cooper pairing observed in traditional Bardeen-Cooper-Schrieffer superconductors. Our results advance the knowledge of Cooper-pair density modulations and the intricate interplay with other symmetry-breaking states in strongly correlated superconductors., Comment: 31 pages,4 figures

Two-dimensional (2D) superconductors that reside on substrates must be influenced by Rashba spin-orbit coupling (SOC). The intriguing effect of Rashba-type SOCs on iron-based superconductors (IBSs) has remained largely a mystery. In this work, we unveil modified Landau-level spectroscopy and the intricate band splitting of FeSe monolayers through the precision of scanning tunneling spectroscopy, which unequivocally demonstrates the presence of Rashba SOC. The discovery sheds light on a nonparabolic electron band at the X/Y point, displaying a distinctive Landau quantization behavior characterized by $E_n\propto(nB)^{4/3}$. The theoretical model aligns with our experimental insights, positing that the k$^4$-term of the electron band becomes predominant and profoundly reshapes the band structure. Our research underscores the pivotal role of the Rashba SOC effect on 2D superconductors and sets the stage to probe new quantum states in systems with remarkably low carrier concentrations., Comment: 21 pages, 5 figures

A conventional superconducting state may be replaced by another dissipationless state hosting Cooper pairs with a finite momentum, leaving thermodynamic footprints for such a phase transition. Recently, a novel type of finite momentum pairing, so-called orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, has been proposed to occur in spin-orbit coupled superconductors such as bilayer $2\mathrm{H-NbSe_{2}}$. So far, a thermodynamic demonstration, which is key for establishing this exotic phase, has been lacking. Here, we reveal a first-order quantum phase transition to the orbital FFLO state in tunneling spectroscopic measurements on multilayer $2\mathrm{H-NbSe_{2}}$. The phase transition manifests itself as a sudden enhancement of the superconducting gap at an in-plane magnetic field $B_{//}$ well below the upper critical field. Furthermore, this transition shows prominent hysteresis by sweeping $B_{//}$ back and forth and quickly disappears once the magnetic field is tilted away from the sample plane by less than one degree. We obtain a comprehensive phase diagram for the orbital FFLO state and compare it with the theoretical calculation that takes into account the rearrangement of Josephson vortices. Our work elucidates the microscopic mechanism for the emergence of the orbital FFLO state.

In twisted bilayer graphene (TBG) devices, local strains often coexist and entangle with the twist-angle dependent moir\'e superlattice, both of which can significantly affect the electronic properties of TBG. Here, using low-temperature scanning tunneling microscopy, we investigate the fine evolution of the electronic structures of a TBG device with continuous variation of twist angles from 0.32{\deg} to 1.29{\deg}, spanning the first (1.1{\deg}), second (0.5{\deg}) and third (0.3{\deg}) magic angles. We reveal the exotic behavior of the flat bands and remote bands in both the energy space and real space near the magic angles. Interestingly, we observe an anomalous spectral weight transfer between the two flat band peaks in the tunneling spectra when approaching the first magic angle, suggesting strong inter-flat-bands interactions. The position of the remote band peak can be an index for the twist angle in TBG, since it positively correlates with the twist angle but is insensitive to the strain. Moreover, influences of the twist angle gradient on symmetry breaking of the flat bands are also studied.

In designing material functionalities for transition metal oxides, lattice structure and d-orbital occupancy are key determinants. However, the modulation of these two factors is inherently limited by the need to balance thermodynamic stability, growth kinetics, and stoichiometry precision, particularly for metastable phases. We introduce a methodology, namely the gigantic-oxidative atomic-layer-by-layer epitaxy (GOALL-Epitaxy), enhancing oxidation power 3-4 orders of magnitude beyond conventional pulsed laser deposition (PLD) and oxide molecular beam epitaxy (OMBE), while ensuring atomic-layer-by-layer growth of designed complex structures. Thermodynamic stability is markedly augmented with stronger oxidation at elevated temperatures, whereas growth kinetics is sustained by laser ablation at lower temperatures. We demonstrate the accurate growth of complex nickelates and cuprates, especially an artificially designed structure with alternating single and double NiO2 layers possessing distinct nominal d-orbital occupancy, as a parent of high-temperature superconductor. The GOALL-Epitaxy enables material discovery within the vastly broadened growth parameter space.

The pairing mechanism behind the monolayer FeSe is one essential question for iron-based superconductors. In this work, we show the sublattice degree of freedoms of monolayer FeSe plays a special role in its pairing properties, namely the sublattice dichotomy. The high-quality monolayer FeSe samples with atomic flat $1\times1$ topography on the SrTiO$_3$(001) substrates are grown by molecular beam epitaxy. By comparing the tunneling spectra at $\alpha$ and $\beta$ Fe sublattices, we find the coherence peak of $\alpha$-Fe at the inner gap $+V_i$ is higher than $\beta$-Fe while the coherence peak of $\beta$-Fe at $-V_i$ is higher than $\alpha$-Fe with a similar amount. We also observed a reversed effect at the outer gap $\pm V_o$. We propose the $\eta$-pairing mechanism between $k$ and $-k+Q$ is the key mechanism for this unconventional sublattice dichotomy effect., Comment: 6 pages, 4 figures

Clean one-dimensional electron systems can exhibit quantized conductance. The plateau conductance doubles if the transport is dominated by Andreev reflection. Here, we report quantized conductance observed in both Andreev and normal-state transports in PbTe-Pb and PbTe-In hybrid nanowires. The Andreev plateau is observed at $4e^2/h$, twice of the normal plateau value of $2e^2/h$. In comparison, Andreev conductance in the best-optimized III-V nanowires is non-quantized due to mode-mixing induced dips (a disorder effect), despite the quantization of normal-state transport. The negligible mode mixing in PbTe hybrids indicates an unprecedented low-disorder transport regime for nanowire devices, beneficial for Majorana researches.

The intrinsic magnetic order, large topological-magnetic gap and rich topological phases make MnBi2Te4 a wonderful platform to study exotic topological quantum states such as axion insulator and Chern insulator. To realize and manipulate these topological phases in a MnBi2Te4 thin film, precise manipulation of the electric field across the film is essential, which requires a dual-gate structure. In this work, we achieve dual-gate tuning of MnBi2Te4 thin films grown with molecular beam epitaxy on SrTiO3(111) substrates by applying the substrate and an AlOx layer as the gate dielectrics of bottom and top gates, respectively. Under magnetic field of 9T and temperature of 20 mK, the Hall and longitudinal resistivities of the films show inversed gate-voltage dependence, for both top- and bottom-gates, signifying the existence of the dissipationless edge state contributed by Chern insulator phase in the ferromagnetic configuration. The maximum of the Hall resistivity only reaches 0.8 h/e2, even with dual-gate tuning, probably due to the high density of bulk carriers introduced by secondary phases. In the antiferromagnetic state under zero magnetic field, the films show normal insulator behavior. The dual-gated MnBi2Te4 thin films lay the foundation for developing devices based on electrically tunable topological quantum states., Comment: 24 pages, 4 figures

Vortices in superconductors can help identify emergent phenomena but certain fundamental aspects of vortices, such as their entropy, remain poorly understood. Here, we study the vortex entropy in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by measuring both magneto-resistivity and Nernst effect on ultrathin flakes ($\le$2 unit-cell). We extract the London penetration depth from the magneto-transport measurements on samples with different doping levels. It reveals that the superfluid phase stiffness $\rho_s$ scales linearly with the superconducting transition temperature $T_c$, down to the extremely underdoped case. On the same batch of ultrathin flakes, we measure the Nernst effect via on-chip thermometry. Together, we obtain the vortex entropy and find that it decays exponentially with $T_c$ or $\rho_s$. We further analyze the Nernst signal above $T_c$ in the framework of Gaussian superconducting fluctuations. The combination of electrical and thermoelectric measurements in the two-dimensional limit provides fresh insight into high temperature superconductivity.

The discovery of high-mobility two-dimensional electron gas and low carrier density superconductivity in multiple SrTiO$_3$-based heterostructures has stimulated intense interest in the surface properties of SrTiO$_3$. The recent discovery of high-T$_c$ superconductivity in the monolayer FeSe/SrTiO$_3$ aroused the upsurge and underscored the atomic precision probe of the surface structure. By performing atomically resolved cryogenic scanning tunneling microscopy/spectroscopy characterization on dual-TiO$_{2}$-${\delta}$-terminated SrTiO$_3$(001) surfaces with ($\sqrt{13}$ $\times$ $\sqrt{13}$), c(4 $\times$ 2), mixed (2 $\times$ 1), and (2 $\times$ 2) reconstructions, we disclosed universally broken rotational symmetry and contrasting bias- and temperature-dependent electronic states for apical and equatorial oxygen sites. With the sequentially evolved surface reconstructions and simultaneously increasing equatorial oxygen vacancies, the surface anisotropy reduces, and the work function lowers. Intriguingly, unidirectional stripe orders appear on the c(4 $\times$ 2) surface, whereas local (4 $\times$ 4) order emerges and eventually forms long-range unidirectional c(4 $\times$ 4) charge order on the (2 $\times$ 2) surface. This work reveals robust unidirectional charge orders induced by oxygen vacancies due to strong and delicate electronic-lattice interaction under broken rotational symmetry, providing insights into understanding the complex behaviors in perovskite oxide-based heterostructures.

Superconductivity and long-range ferromagnetism hardly coexist in a uniform manner. The counter-example has been observed, in uranium-based superconductors for instance, with a coexisting temperature limited to about 1 K. Here, we report the coexistence of high temperature superconductivity and itinerant ferromagnetism in lithium intercalated FeSe flakes. In superconducting samples with transition temperature around 40 K, we observe the anomalous Hall effect with a hysteresis loop in transverse resistivity and a butterfly-like pattern of magneto-resistance. Intriguingly, such ferromagnetism persists down to a temperature at which the zero-field resistance fully vanishes. Furthermore, the superconductivity is enhanced under an in-plane magnetic field, suggestive of the participation of spin-polarized Cooper pairs. The surprising finding underscores a uniform coexistence of the two antagonistic phenomena on a record-high energy scale.

Anderson localization is anticipated to play a pivotal role in the manifestation of the quantum anomalous Hall effect, akin to its role in conventional quantum Hall effects. The significance of Anderson localization is particularly pronounced in elucidating the reasons behind the fragility of the observed quantum anomalous Hall state in the intrinsic magnetic topological insulator MnBi2Te4 with a large predicted magnetic gap. Here, employing varying sized MnBi2Te4 micro/nano-structures fabricated from a single molecular-beam-epitaxy-grown thin film, we have carried out a systematic size- and temperature-dependent study on the transport properties of the films regarding the quantum anomalous Hall states. The low-temperature transport properties of the finite-sized MnBi2Te4 samples can be quantitatively understood through Anderson localization, which plays an indispensable role in stabilizing the ground states. At higher temperatures, the failure of electron localization induced by an excessively short electronic dephasing length is identified as the cause of deviation from quantization. The work reveals that electronic dephasing and localization are non-negligible factors in designing high-temperature quantum anomalous Hall systems., Comment: 20 pages, 4 figures

Network structures by semiconductor nanowires hold great promise for advanced quantum devices, especially for applications in topological quantum computing. In this study, we created networks of PbTe nanowires arranged in loop configurations. Using shadow-wall epitaxy, we defined superconducting quantum interference devices (SQUIDs) using the superconductor Pb. These SQUIDs exhibit oscillations in supercurrent upon the scanning of a magnetic field. Most of the oscillations can be fitted assuming a sinusoidal current-phase relation for each Josephson junction. Under certain conditions, the oscillations are found to be skewed, suggesting possible deviation from a sinusoidal behavior. Our results highlight the potential of PbTe nanowires for building complex quantum devices in the form of networks.

Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This degeneracy and its tunable lifting were challenging to observe in previous nanowire experiments, possibly due to disorder. Numerical simulations can qualitatively capture our observation, shedding light on device parameters for future applications.

Exploration of new dielectrics with large capacitive coupling is an essential topic in modern electronics when conventional dielectrics suffer from the leakage issue near breakdown limit. To address this looming challenge, we demonstrate that rare-earth-metal fluorides with extremely-low ion migration barriers can generally exhibit an excellent capacitive coupling over 20 $\mu$F cm$^{-2}$ (with an equivalent oxide thickness of ~0.15 nm and a large effective dielectric constant near 30) and great compatibility with scalable device manufacturing processes. Such static dielectric capability of superionic fluorides is exemplified by MoS$_2$ transistors exhibiting high on/off current ratios over 10$^8$, ultralow subthreshold swing of 65 mV dec$^{-1}$, and ultralow leakage current density of ~10$^{-6}$ A cm$^{-2}$. Therefore, the fluoride-gated logic inverters can achieve significantly higher static voltage gain values, surpassing ~167, compared to conventional dielectric. Furthermore, the application of fluoride gating enables the demonstration of NAND, NOR, AND, and OR logic circuits with low static energy consumption. Notably, the superconductor-to-insulator transition at the clean-limit Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ can also be realized through fluoride gating. Our findings highlight fluoride dielectrics as a pioneering platform for advanced electronics applications and for tailoring emergent electronic states in condensed matters., Comment: 33 pages, 5 figures

Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we resolve systematically individual transition-metal (Fe, Cr and Ni) impurities induced YSR multiplets as well as their Zeeman effects in K$_3$C$_{60}$ superconductor. The YSR multiplets show identical $d$ orbital-like wave functions that are symmetry-mismatched to the threefold K$_3$C$_{60}$(111) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets., Comment: 38 pages, 4 figures in the main text

Superconductivity in semiconductor nanostructures contains fascinating physics due to the interplay between Andreev reflection, spin, and orbital interactions. New material hybrids can access new quantum regimes and phenomena. Here, we report the realization of epitaxial indium thin films on PbTe nanowires.The film is continuous and forms an atomically sharp interface with PbTe.Tunneling devices reveal a hard superconducting gap.The gap size, 1.08 to 1.18 meV, is twice as large as bulk indium (around 0.5 meV), due to the presence of PbTe. A similar enhancement is also observed in the critical temperature of In on a PbTe substrate. Zero bias conductance peaks appear at finite magnetic fields. The effective g-factor (15 to 45) is notably enhanced compared to bare PbTe wires (less than 10) due to the presence of In, differing from Al-hybrids. Josephson devices exhibit gate-tunable supercurrents. The PbTe-In hybrid enhances the properties of both, the superconductivity of In and g-factors of PbTe, and thus may enable exotic phases of matter such as topological superconductivity.

Material challenges are the key issue in Majorana research where surface disorder constrains device performance. Here, we tackle this challenge by embedding PbTe nanowires within a lattice-constant-matched crystal. The wire edges are shaped by self-organized growth instead of lithography, resulting in nearly-atomic-flat facets along both cross-sectional and longitudinal directions. Quantized conductance is observed at zero magnetic field with channel lengths maximally reaching 1.7 $\mu$m, significantly surpassing the state-of-the-art of III-V nanowires (an order-of-magnitude improvement compared to InSb). Coupling PbTe to a Pb film unveils a flat interface spanning microns and a large superconducting gap of 1 meV. Our result not only represents a stride toward meeting the stringent low-disorder requirement for Majoranas, but may also open the door to various hybrid quantum devices requiring a low level of disorder.

The interface-enhanced superconductivity in monolayer iron selenide (FeSe) films on SrTiO3 has been actively pursued in the past decade. Although a synergistic effect between interfacial charge transfer and interfacial electron-phonon coupling (EPC) is proposed to be responsible for the mechanism, the microscopic nature of the interfacial EPC in the enhancement of superconductivity remains highly controversial. Herein we experimentally reveal that a coherent optical phonon mode at 4.2 THz from the SrTiO3 substrate couples to FeSe electrons and modulates the quasiparticle relaxations using ultrafast pump-probe spectroscopy. This mode originates from the antiferrodistortive (AFD) transition in SrTiO3 and is significantly stronger in the presence of monolayer FeSe than that in purely FeTe-capped Nb-doped SrTiO3. Pump fluence and temperature-dependent spectroscopy measurements suggest that SrTiO3 substrate facilitates the stabilization of FeSe structure and possibly prevents the occurrence of nematic phase transition, supporting that SrTiO3 substrate modifies the electronic structure of monolayer FeSe through a strong interfacial EPC strength as large as 0.77. Our results provide unprecedented direct evidence that the strong coupling of SrTiO3 coherent phonon to FeSe electrons is indeed responsible for the high-temperature superconductivity in monolayer FeSe and SrTiO3 heterostructure.

In this study, we investigate intrinsic magnetic topological insulator MnBi2Te4 thin films grown by molecular beam epitaxy. We observe a reentrant quantum anomalous Hall effect when the Fermi energy enters the valance band and magnetic field equals zero, indicating the emergence of the Chern Anderson insulator state. The discovery opens a new avenue for realizing the QAH effect and underscores the fundamental role of both Berry curvature and Anderson localization., Comment: 15 pages, 4 figures

The interfacial FeSe/TiO$_{2-\delta}$ coupling induces high-temperature superconductivity in monolayer FeSe films. Using cryogenic atomically resolved scanning tunneling microscopy/spectroscopy, we obtained atomic-site dependent surface density of states, work function, and pairing gap in the monolayer FeSe on SrTiO$_3$(001)-($\sqrt{13} \times \sqrt{13}$)-33.7${\deg}$ surface. Our results disclosed the out-of-plane Se-Fe-Se triple layer gradient variation, switched DOS for Fe sites on and off TiO$_{5\square}$, and inequivalent Fe sublattices, which gives global spatial modulation of pairing gap contaminant with the ($\sqrt{13} \times \sqrt{13}$) pattern. Moreover, the coherent lattice coupling induces strong inversion asymmetry and in-plane anisotropy in the monolayer FeSe, which is demonstrated to correlate with the particle-hole asymmetry in coherence peaks. The strong atomic-scale correlations in lattice and electronic structure, and pairing gap in particular, put constraints on exploring the unconventional high-temperature superconductivity emerging from interface coupling, e.g., strong demand for atomic-scale interface engineering and characterization.

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two dimensional electron gases (InAs, InSb, InAsSb and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of the superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrent and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection, wherein phase bias and tunneling spectroscopy are applicable.

Josephson tunneling in twisted cuprate junctions provides a litmus test for the pairing symmetry, which is fundamental for understanding the microscopic mechanism of high temperature superconductivity. This issue is rekindled by experimental advances in van der Waals stacking and the proposal of an emergent d+id-wave. So far, all experiments have been carried out on Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) with double CuO$_2$ planes but show controversial results. Here, we investigate junctions made of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+y}$ (Bi-2201) with single CuO$_2$ planes. Our on-site cold stacking technique ensures uncompromised crystalline quality and stoichiometry at the interface. Junctions with carefully calibrated twist angles around 45{\deg} show strong Josephson tunneling and conventional temperature dependence. Furthermore, we observe standard Fraunhofer diffraction patterns and integer Fiske steps in a junction with a twist angle of 45.0$\pm$0.2{\deg}. Together, these results pose strong constraints on the d or d+id-wave pairing and suggest an indispensable isotropic pairing component., Comment: 32 pages, 5 figures

Disorder is the primary obstacle in current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of $2e^2/h$ are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires, as none of the previously studied SAG nanowires (InSb or InAs) exhibit zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

Semiconductor nanowires coupled to a superconductor provide a powerful testbed for quantum device physics such as Majorana zero modes and gate-tunable hybrid qubits. The performance of these quantum devices heavily relies on the quality of the induced superconducting gap. A hard gap, evident as vanishing subgap conductance in tunneling spectroscopy, is both necessary and desired. Previously, a hard gap has been achieved and extensively studied in III-V semiconductor nanowires (InAs and InSb). In this study, we present the observation of a hard superconducting gap in PbTe nanowires coupled to a superconductor Pb. The gap size ($\Delta$) is $\sim$ 1 meV (maximally 1.3 meV in one device). Additionally, subgap Andreev bound states can also be created and controlled through gate tuning. Tuning a device into the open regime can reveal Andreev enhancement of the subgap conductance, suggesting a remarkable transparent superconductor-semiconductor interface, with a transparency of $\sim$ 0.96. These results pave the way for diverse superconducting quantum devices based on PbTe nanowires.

Learning the electron scattering around atomic impurities is a fundamental step to fully understand the basic electronic transport properties of realistic conducting materials. Although many efforts have been made in this field for several decades, atomic scale transport around single point-like impurities has yet been achieved. Here, we report the direct visualization of the electric current induced dipoles around single atomic impurities in epitaxial bilayer graphene by multi-probe low temperature scanning tunneling potentiometry as the local current density is raised up to around 25 A/m, which is considerably higher than that in previous studies. We find the directions of these dipoles which are parallel or anti-parallel to local current are determined by the charge polarity of the impurities, revealing the direct evidence for the existence of the carrier density modulation effect proposed by Landauer in 1976. Furthermore, by $in$ $situ$ tuning local current direction with contact probes, these dipoles are redirected correspondingly. Our work paves the way to explore the electronic quantum transport phenomena at single atomic impurity level and the potential future electronics toward or beyond the end of Moore's Law.

Majorana bound states (MBSs) are building blocks for topological quantum computing. They can be generated via the combination of electronic topology and superconductivity. To achieve logic operations via Majorana braiding, positional control of the MBS must be established. To this end, exotic co-existing phases or collective modes in an intrinsic topological superconductor can provide a tuning knob to manipulate the MBS. Here we report the observation of a striped surface charge order coexisting with superconductivity and its controllable tuning of the MBS in the topological superconductor 2M-WS2 using low-temperature scanning tunneling microscopy. By applying an out-of-plane magnetic field, we observe that MBS is absent in vortices in the region with strong stripe order. This is in contrast to adjacent underlaying layers without charge order where vortex-bound MBSs are observed. Via theoretical simulations, we show that the surface stripe order does not destroy the bulk topology, but it can effectively modify the spatial distribution of MBS, i.e., it pushes them downward away from the 2M-WS2 surface. Our findings demonstrate that the interplay of charge order and topological superconductivity can be used to manipulate the positions of the MBS, and to explore of new states of matter., Comment: 20 pages, 4 figures

Electronic liquid-crystal phases are observed in numerous strongly-correlated systems including high-temperature superconductors. However, identifying these exotic phases and understanding their interplay with superconductivity in topological materials remain challenging. Here we employ a cryogenic scanning tunneling microscopy to discover a smectic (stripe) charge order (CO) and a primary pair-density-wave (PDW) in topological monolayer 1T$^\prime$-MoTe$_2$. The two orders are spatially modulated unidirectionally at the same wavevector, but have a marked spatial phase difference of about 2$\pi$/5. Importantly, the primary PDW state features a two-gap superconductivity below the transition temperature of 6.0 K and induces another unique particle-hole-symmetric CO at twice the PDW wavevector. Combining these results and our density functional calculations, we reveal that the two smectic orders are primarily driven by nesting behaviors between electron and hole pockets. Our findings establish monolayer 1T$^\prime$-MoTe$_2$ as a topological paradigm for exploring electronic smecticity, which intertwines with multiple preexisting symmetry-breaking states., Comment: 16 pages, 4 figures, Supplementary materials

PbTe nanowires coupled to a superconductor have recently been proposed as a potential Majorana platform. The hallmark of the one-dimensional nature of ballistic nanowires is their quantized conductance. Here, we report the observation of conductance plateaus at multiples of the quantized value $2e^2/h$ in PbTe nanowires at finite magnetic fields. The quantized plateaus, as a function of source-drain bias and magnetic field, allow for the extraction of the Land\'e $g$-factor, sub-band spacing and effective mass. The coefficient of 2 in the plateau conductance indicates the presence of valley degeneracy arising from the crystal orientation of the nanowires, which are grown on a (001) substrate. Occasionally, this degeneracy can be lifted by a gate voltage that breaks the mirror symmetry. Our results demonstrate the one-dimensionality of PbTe nanowires and fulfill one of the necessary conditions for the realization of Majorana zero modes., Comment: Raw data and processing codes within this paper are available at: https://doi.org/10.5281/zenodo.7848599

Motivated by the discovery of superconductivity in the infinite-layer nickelate family, we report an experimental endeavor to clean the surface of nickelate superconductor Pr0.8Sr0.2NiO2 films by Ar+ ion sputtering and subsequent annealing, and we study their electronic structures by cryogenic scanning tunneling microscopy and spectroscopy. The annealed surfaces are characterized by nano-sized clusters and Coulomb staircases with periodicity inversely proportional to the projected area of the nanoclusters, consistent with a double-barrier tunneling junction model. Moreover, the dynamical Coulomb blockade effects are observed and result in well-defined energy gaps around the Fermi level, which correlate closely with the specific configuration of the junctions. These Coulomb blockade-related phenomena provide an alternative plausible cause of the observed gap structure that should be considered in the spectroscopic understanding of nickelate superconductors with the nano-clustered surface., Comment: 7 pages, 5 figures

We explore topology-localization phase diagram by simulating one-dimensional Su-Schrieffer-Heeger (SSH) model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed new light on the investigation of the topological and localization phenomena in condensed-matter physics., Comment: 5 pages, 4 figures

There is a heated debate on the Josephson effect in twisted Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes. Recent experimental results suggest the presence of either anomalously isotropic pairing or exotic $d$+i$d$-wave pairing, in addition to the commonly believed $d$-wave one. Here, we address this controversy by fabricating ultraclean junctions with uncompromised crystalline quality and stoichiometry at the junction interfaces. In the optimally doped regime, we obtain prominent Josephson coupling (2-4 mV) in multiple junctions with the twist angle of 45$^\circ$, in sharp contrast to a recent report that shows two orders of magnitude suppression around 45$^\circ$ from the value at 0$^\circ$. We further extend this study to the previously unexplored overdoped regime and observe pronounced Josephson tunneling at 45$^\circ$ together with Josephson diode effect up to 50 K. Our work helps establish the persistent presence of an isotropic pairing component across the entire superconducting phase diagram., Comment: 6 pages, 5 figures

Interest in superconducting proximity effect has been revived by the exploitation of Andreev states and by the possible emergence of Majorana bound states at the interface. Spectroscopy of these states has been so far restricted to just a handful of superconductor-metal systems in the diffusion regime, whereas reports in otherwise clean superconductor-superconductor heterojunctions are scarce. Here, we realize molecular beam epitaxy growth of atomically sharp planar heterojunctions between Pb and a topological superconductor candidate RhPb2 that allows us to spectroscopically image the proximity effect in the clean limit. The measured energy spectra of RhPb2 vary with the spatial separation from proximal Pb, and exhibit unusual modifications in the pairing gap structure and size that extend over a distance far beyond the coherence length. This anomalously long-range proximity (LRP) effect breaks the rotational symmetry of Cooper pair potential in real space and largely deforms the Abrikosov vortex cores. Our work opens promising avenues for fundamental studies of the Andreev physics and extraordinary states in clean superconducting heterojunctions., Comment: 8 pages, 4 figures

Semiconductor-superconductor hybrid nanowires are a leading material platform for the realization of Majorana zero modes. The semiconductors in previous studies are dominantly InAs or InSb. In this work, we show the induced superconductivity in a PbTe nanowire epitaxially coupled to a superconductor Pb. The Josephson junction device based on this hybrid reveals a gate-tunable supercurrent in the open regime and a hard superconducting gap in the tunneling regime. By demonstrating the superconducting proximity effect, our result can enable Majorana searches and other applications like gate-tunable qubits in a new semiconductor system., Comment: Raw data and processing codes within this paper are available at: https://doi.org/10.5281/zenodo.7398019