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A plasma scenario with negative triangularity (NT) shaping is achieved on MAST-U for the first time. While edge localized modes (ELMs) are eventually suppressed as the triangularity is decreased below $\delta$ < -0.06, an extended period of H-mode operation with Type-III ELMs is sustained at less negative $\delta$ even through access to the second stability region for ideal ballooning modes is closed. This documents a qualitative difference from the ELM-free access conditions documented in NT scenarios on conventional aspect ratio machines. The electron temperature at the pedestal top drops across the transition to ELM-free operation, but a steady rise in core temperature as $\delta$ is decreased allows for similar normalized beta in the ELM-free NT and H-mode positive triangularity shapes.

The superconducting diode effect (SDE) is a magneto-electric phenomenon where an external magnetic field imparts a non-zero center-of-mass momentum to Cooper pairs, either facilitating or hindering the flow of supercurrent depending on its direction. We propose that quantum spin Hall insulator (QSHI)-based Josephson junctions can serve as versatile platforms for non-dissipative electronics exhibiting the SDE when triggered by a phase bias and an out-of-plane magnetic field. By computing the contributions from Andreev bound states and the continuum of quasi-particle states, we provide both numerical and analytical results scrutinizing various aspects of the SDE, including its quality Q-factor. The maximum value of the $Q$-factor is found to be universal at low (zero) temperatures, which ties its origin to underlying topological properties that are independent of the junction's specific details. As the magnetic field increases, the SDE diminishes due to the closing of the induced superconducting gap caused by orbital effects. To observe the SDE, the QSHI-based Josephson junction must be designed so that its edges are transport-wise non-equivalent. Additionally, we explore the SDE in a more exotic yet realistic scenario, where the fermionic ground-state parity of the Josephson junction remains conserved while driving a current. In this 4$\pi$-periodic situation, we predict an enhancement of the SDE compared to its 2$\pi$-periodic, parity-unconstrained counterpart., Comment: 11 pages, 9 figures

The spread of valence band Wannier functions in semiconductors and insulators is a characteristic property that gives a rough estimation of how insulating is the material. We elaborate that the gauge-invariant part of the spread can be extracted experimentally from optical conductivity and absorbance, owing to their equivalence to the quantum metric of the valence band states integrated over momentum. Because the quantum metric enters the matrix element of optical conductivity, the spread of valence band Wannier functions in the gapped 3D materials can be obtained from the frequency-integration of the imaginary part of the dielectric function. We demonstrate this practically for typical semiconductors like Si and Ge, and for topological insulators like Bi$_{2}$Te$_{3}$. In 2D materials, the spread of Wannier functions in the valence bands can be obtained from the absorbance divided by frequency and then integrated over frequency. Applying this method to graphene reveals a finite spread caused by intrinsic spin-orbit coupling, which may be detected by absorbance in the microwave range. The absorbance of twisted bilayer graphene in the millimeter wave range can be used to detect the formation of the flat bands and quantify their quantum metric. Finally, we apply our method to hexagonal transition metal dichalcogenides MX$_{2}$ (M = Mo, W; X = S, Se, Te) and demonstrate how other effects like substrate, excitons, and higher energy bands can affect the spread of Wannier function., Comment: 13 pages, 7 figures

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that enforces the physical constraints in a probabilistic manner. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC). QHMC is an efficient way to sample from a broad class of distributions. Unlike the standard Hamiltonian Monte Carlo algorithm in which a particle has a fixed mass, QHMC allows a particle to have a random mass matrix with a probability distribution. Introducing the QHMC method to the inequality and monotonicity constrained GP regression in the probabilistic sense, our approach improves the accuracy and reduces the variance in the resulting GP model. According to our experiments on several datasets, the proposed approach serves as an efficient method as it accelerates the sampling process while maintaining the accuracy, and it is applicable to high dimensional problems., Comment: 21 pages, 17 figures and 6 tables

Graphene-based van der Waals heterostructures take advantage of tailoring spin-orbit coupling (SOC) in the graphene layer by proximity effect. At long-wavelength -- saddled by the electronic states near the Dirac points -- the proximitized features can be effectively modelled by the Hamiltonian involving novel SOC terms and allow for an admixture of the tangential and radial spin textures -- by the so-called Rashba angle $\theta_{\text{R}}$. Taking such effective models we perform realistic large-scale magneto-transport calculations -- transverse magnetic focusing and Dyakonov-Perel spin relaxation -- and show that there are unique qualitative and quantitative features allowing for an unbiased experimental disentanglement of the conventional Rashba SOC from its novel radial counterpart, called here the radial Rashba SOC. Along with that, we propose a scheme for a direct estimation of the Rashba angle by exploring the magneto-response symmetries when swapping an in-plane magnetic field. To complete the story, we analyze the magneto-transport signatures in the presence of an emergent Dresselhaus SOC and also provide some generic ramifications about possible scenarios of the radial superconducting diode effect., Comment: 6 pages, 4 figures, comments are welcome

In Josephson diodes the asymmetry between positive and negative current branch of the current-phase relation leads to a polarity-dependent critical current and Josephson inductance. The supercurrent nonreciprocity can be described as a consequence of the anomalous Josephson effect -- a $\varphi_0$-shift of the current-phase relation -- in multichannel ballistic junctions with strong spin-orbit interaction. In this work, we simultaneously investigate $\varphi_0$-shift and supercurrent diode efficiency on the same Josephson junction by means of a superconducting quantum interferometer. By electrostatic gating, we reveal a direct link between $\varphi_0$-shift and diode effect. Our findings show that the supercurrent diode effect mainly results from magnetochiral anisotropy induced by spin-orbit interaction in combination with a Zeeman field., Comment: 15 pages, 8 figures

Ex-so-tic van der Waals heterostructures take advantage of the electrically tunable layer polarization to swap proximity exchange and spin-orbit coupling in the electronically active region. Perhaps the simplest example is Bernal bilayer graphene (BBG) encapsulated by a layered magnet from one side and a strong spin-orbit material from the other. Taking WS$_2$/BBG/Cr$_2$Ge$_2$Te$_6$ as a representative ex-so-tronic device, we employ realistic \emph{ab initio}-inspired Hamiltonians and effective electron-electron interactions to investigate the emergence of correlated phases within the random phase approximation. We find that for a given doping level, exchange and spin-orbit coupling induced Stoner and intervalley coherence instabilities can be swapped, allowing to explore the full spectrum of correlated phases within a single device.

Studies of the formation of Landau levels based on the Schr\"odinger equation for electrons constrained to curved surfaces have a long history. These include as prime examples surfaces with constant positive and negative curvature, the sphere [Phys. Rev. Lett. 51, 605 (1983)] and the pseudosphere [Annals of Physics 173, 185 (1987)]. Now, topological insulators, hosting Dirac-type surface states, provide a unique platform to experimentally examine such quantum Hall physics in curved space. Hence, extending previous work we consider solutions of the Dirac equation for the pseudosphere for both, the case of an overall perpendicular magnetic field and a homogeneous coaxial, thereby locally varying, magnetic field. For both magnetic-field configurations, we provide analytical solutions for spectra and eigenstates. For the experimentally relevant case of a coaxial magnetic field we find that the Landau levels split and show a peculiar scaling $\propto B^{1/4}$, thereby characteristically differing from the usual linear $B$ and $B^{1/2}$ dependence of the planar Schr\"odinger and Dirac case, respectively. We compare our analytical findings to numerical results that we also extend to the case of the Minding surface.

Objectives: To examine sex differences in the associations between vascular risk factors and 6-year changes in the volume of white matter hyperintensities (WMH), and between changes in WMH volumes and changes in cognitive performance, in a cohort of non-demented older adults. Methods: WMH volumes at 3 time-points (baseline, and 2- and 6-year follow-up) were automatically quantified in participants of Sydney Memory and Ageing Study (N = 605; age range = 70-92 years; 54.78% female). Linear mixed models were applied to examine the effects of vascular risk factors and cognitive consequences of the progression of WMH, as well as the sex moderation effects in the associations. Results: Total (TWMH), periventricular (PVWMH), and deep (DWMH) WMH volumes increased by 9.47%, 7.70%, and 11.78% per year, respectively. No sex differences were found in WMH progression rates. After Bonferroni correction, increases in PVWMH volumes over time were associated with decline in global cognition, especially in visuospatial and memory domains. Men with more increases in PVWMH volumes over time had greater declines in visuospatial abilities. Moreover, higher average TWMH volumes across time-points were associated with poorer average performance in processing speed and executive function domains across time. Higher average PVWMH volumes across time-points were also associated with worse average performance in the executive function domain over time, among women but not men. Conclusion: The findings highlighted sex differences in the associations between WMH progression and cognition decline over time, suggesting sex-specific strategies in managing WMH accumulations in ageing. Keywords: Cerebral small vessel disease, white matter hyperintensities, sex differences, brain ageing, cognitive decline.

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing \emph{ab initio}-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr$_2$Ge$_2$Te$_6$ (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement field and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a \textit{spin-valley-coherent} phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magneto-correlation effect -- strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

The DCELANM-Net structure, which this article offers, is a model that ingeniously combines a Dual Channel Efficient Layer Aggregation Network (DCELAN) and a Micro Masked Autoencoder (Micro-MAE). On the one hand, for the DCELAN, the features are more effectively fitted by deepening the network structure; the deeper network can successfully learn and fuse the features, which can more accurately locate the local feature information; and the utilization of each layer of channels is more effectively improved by widening the network structure and residual connections. We adopted Micro-MAE as the learner of the model. In addition to being straightforward in its methodology, it also offers a self-supervised learning method, which has the benefit of being incredibly scaleable for the model.

Superconducting systems that simultaneously lack space-inversion and time-reversal symmetries have recently been the subject of a flurry of experimental and theoretical research activities. Their ability to carry supercurrents with magnitudes depending on the polarity (current direction) - termed supercurrent diode effect - might be practically exploited to design dissipationless counterparts of contemporary semiconductor-based diodes. Magnetic Josephson junctions realized in the two-dimensional electron gas (2DEG) within a narrow quantum well through proximity to conventional superconductors perhaps belong to the most striking and versatile platforms for such supercurrent rectifiers. Starting from the Bogoliubov-de Gennes approach, we provide a minimal theoretical model to explore the impact of the spin-orbit coupling and magnetic exchange inside the 2DEG on the Andreev bound states and Josephson current-phase relations. Assuming realistic junction parameters, we evaluate the polarity-dependent critical currents to quantify the efficiency of these Josephson junctions as supercurrent diodes, and discuss the tunability of the Josephson supercurrent diode effect in terms of spin-orbit coupling, magnetic exchange, and transparency of the nonsuperconducting weak link. Furthermore, we demonstrate that the junctions might undergo current-reversing $ 0 $-$ \pi $-like phase transitions at large enough magnetic exchange, which appear as sharp peaks followed by a sudden suppression in the supercurrent-diode-effect efficiency. The characteristics of the Josephson supercurrent diode effect obtained from our model convincingly reproduce many unique features observed in recent experiments, validating its robustness and suitability for further studies., Comment: 12+2 pages, 9 figures

Nonreciprocal phenomena in the normal state are well established and key to many commercial applications. In contrast, superconducting analogs, such as the superconducting diode effect (SDE), are only starting to be experimentally explored and pose significant challenges to their theoretical understanding. In this work we put forth a phenomenological picture of the SDE based on the generalized Ginzburg-Landau free energy, which includes a Lifshitz invariant as the hallmark of noncentrosymmetric helical phase of the finite-momentum Cooper pairs. We reveal that such a Lifshitz invariant drives the SDE in quasi-two-dimensional systems in an applied magnetic field and cannot be removed by a gauge transformation, due to the inherently inhomogeneous magnetic response. For a thin film, the SDE scales with the square of its thickness and nonlinearly with the strength of the in-plane magnetic field. We derive an explicit formula that relates the SDE at small magnetic fields to the strength of Rashba spin-orbit coupling, g-factor, and Fermi energy. For a noncentrosymmetric Josephson junction, we self-consistently obtain generalized anharmonic current-phase relation which support the SDE. The transparency of our approach, which agrees well with experimentally-measured SDE, offers an important method to study nonreciprocal phenomena, central to superconducting spintronics and topological superconductivity., Comment: 4+3 pages, 2 figures

The recent discovery of intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that nonreciprocal supercurrents naturally emerge when both space- and time-inversion symmetries are broken. In Josephson junctions, nonreciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here, we demonstrate a sign reversal of the supercurrent diode effect, in both its AC and DC manifestations. In particular, the AC diode effect -- i.e., the asymmetry of the Josephson inductance as a function of the supercurrent -- allows us to probe the current-phase relation near equilibrium. Using a minimal theoretical model, we can then link the sign reversal of the AC diode effect to the so-called 0-$\pi$-like transition, a predicted, but still elusive feature of multi-channel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions., Comment: 13 pages, 6 figures

Proximity-induced fine features and spin-textures of the electronic bands in graphene-based van der Waals heterostructures can be explored from the point of tailoring a twist angle. Here we study spin-orbit coupling and exchange coupling engineering of graphene states in the proximity of 1T-TaS$_2$ not triggering the twist, but a charge density wave in 1T-TaS$_2$-a realistic low-temperature phase. Using density functional theory and effective model we found that the emergence of the charge density wave in 1T-TaS$_2$ significantly enhances Rashba spin-orbit splitting in graphene and tilts the spin texture by a significant Rashba angle-in a very similar way as in the conventional twist-angle scenarios. Moreover, the partially filled Ta $d$-band in the charge density wave phase leads to the spontaneous emergence of the in-plane magnetic order that transgresses via proximity from 1T-TaS$_2$ to graphene, hence, simultaneously superimposing along the spin-orbit also the exchange coupling proximity effect. To describe this intricate proximity landscape we have developed an effective model Hamiltonian and provided a minimal set of parameters that excellently reproduces all the spectral features predicted by the first-principles calculations. Conceptually, the charge density wave provides a highly interesting knob to control the fine features of electronic states and to tailor the superimposed proximity effects-a sort of twistronics without twist.

Most quantum gravity theories quantize space time on the order of Planck length (lp). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over travelling particles at astronomical length distances. However, reports on LIV are controversial, and space discreetness could still be compatible with Lorentz invariance. Here, it is tested whether space quantization on the order of Planck length could still be compatible with Lorentz invariance through the application of a covariant geometric uncertainty principle (GeUP) as a constraint over geodesics in FRW geometries. Space time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann Lemaitre Robertson Walker solution to General Relativity (FLRW or FRW metric). A generic expression for the quadratic proper space time line element is derived, proportional to Planck length squared, and dependent on two contributions. The first is associated to the energy time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories, and within experimental constraints on putative LIV., Comment: The manuscript was accepted in Axioms

Most of 2D superconductors are of type II, i.e., they are penetrated by quantized vortices when exposed to out-of-plane magnetic fields. In presence of a supercurrent, a Lorentz-like force acts on the vortices, leading to drift and dissipation. The current-induced vortex motion is impeded by pinning at defects, enabling the use of superconductors to generate high magnetic fields without dissipation. Usually, the pinning strength decreases upon any type of pair-breaking. Here we show that in Rashba superconductors the application of an in-plane field leads, instead, to an unexpected enhancement of pinning. When rotating the in-plane component of the field with respect to the current direction, the vortex inductance turns out to be highly anisotropic. We explain this phenomenon as a manifestation of Lifshitz invariant terms in the Ginzburg-Landau free energy, which are enabled by inversion and time-reversal symmetry breaking and lead to an elliptic squeezing of vortex cores. Our experiment provides access to a fundamental property of Rashba superconductors and offers an entirely new approach to vortex manipulation., Comment: 23 pages, 9 figures

Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction leads to a possible violation of the $I(\varphi)=-I(-\varphi)$ equality for the current-phase relation. This is known as anomalous Josephson effect and it produces a phase shift $\varphi_0$ in sinusoidal current-phase relations. In ballistic Josephson junctions with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy of Josephson inductance. In this work, we present measurements of both effects on arrays of Josephson junctions defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the magnetochiral anisotropy, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips., Comment: 9 pages, 4 figures

Bilayer graphene has two non-equivalent sublattices and, therefore, the same adatom impurity can manifest in spectrally distinct ways-sharp versus broad resonances near the charge neutrality-depending on the sublattice it adsorbs at. Employing Green's function analytical methods and the numerical Kwant package we investigate the spectral and transport interplay between the resonances and superconducting coherence induced in bilayer graphene by proximity to an s-wave superconductor. Analyzing doping and temperature dependencies of quasi-particle spin-relaxation rates, energies of Yu-Shiba-Rusinov states, Andreev spectra and the supercurrent characteristics of Josephson junctions we find unique superconducting signatures discriminating between resonant and off-resonant regimes. Our findings are in certain aspects going beyond the superconducting bilayer graphene and hold for generic s-wave superconductors functionalized by the resonant magnetic impurities., Comment: Main text 16 pages and 8 figures; SM 6 pages and 4 figures

$\text{BaBiO}_{3}$ compound is known as an archetype example of a three-dimensional Holstein model with the realization of the charge density wave state at half-filling and the superconducting state when doped. Although many works are devoted to the study of the electron-phonon interaction in $\text{BaBiO}_{3}$, the influence of the electron-electron Hubbard interaction on the electronic structure in this system is still under quest. In our work, we obtain an analytical expression for the screened Coulomb potential, and along with the basis of \textit{ab initio}-computed maximally localized Wannier orbitals, we quantitatively estimate the magnitude of the effective on-site Hubbard potential scrutinizing the effects of distortion of the crystal lattice. We show that a proper inclusion of the electron-electron interactions into the Holstein model significantly lowers the value of the underlying electron-phonon coupling. Finally, we find that the amplitudes of the repulsive electron-electron potential and its attractive counterpart mediated by the electron-phonon coupling are rather comparable. This may open a way for a realization of the intermediate phase of $\text{BaBiO}_{3}$ in terms of the Holstein-Hubbard model.

The classical uncertainty principle inequalities were imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle was reformulated in terms of proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This reformulation confirmed the need for a minimum length of space-time line element in the geodesic, which depended on a Lorentz-covariant geodesic-derived scalar. In agreement with quantum gravity theories, GeUP imposed a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity., Comment: The link to the published paper is: https://www.mdpi.com/2624-8174/3/3/49/htm

Transport is called nonreciprocal when not only the sign, but also the absolute value of the current, depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, e.g., by the interplay of spin-orbit coupling and magnetic field. So far, observation of nonreciprocity was always tied to resistivity, and dissipationless nonreciprocal circuit elements were elusive. Here, we engineer fully superconducting nonreciprocal devices based on highly-transparent Josephson junctions fabricated on InAs quantum wells. We demonstrate supercurrent rectification far below the transition temperature. By measuring Josephson inductance, we can link nonreciprocal supercurrent to the asymmetry of the current-phase relation, and directly derive the supercurrent magnetochiral anisotropy coefficient for the first time. A semi-quantitative model well explains the main features of our experimental data. Nonreciprocal Josephson junctions have the potential to become for superconducting circuits what $pn$-junctions are for traditional electronics, opening the way to novel nondissipative circuit elements., Comment: 16 pages, 11 figures

Strong gate control of proximity-induced spin-orbit coupling was recently predicted in bilayer graphene/transition metal dichalcogenides (BLG/TMDC) heterostructures, as charge carriers can easily be shifted between the two graphene layers, and only one of them is in close contact to the TMDC. The presence of spin-orbit coupling can be probed by weak antilocalization (WAL) in low field magnetotransport measurements. When the spin-orbit splitting in such a heterostructure increases with the out of plane electric displacement field $\bar D$, one intuitively expects a concomitant increase of WAL visibility. Our experiments show that this is not the case. Instead, we observe a maximum of WAL visibility around $\bar D=0$. This counterintuitive behaviour originates in the intricate dependence of WAL in graphene on symmetric and antisymmetric spin lifetimes, caused by the valley-Zeeman and Rashba terms, respectively. Our observations are confirmed by calculating spin precession and spin lifetimes from an $8\times 8$ model Hamiltonian of BLG/TMDC., Comment: Accepted by Phys Rev B

Unique electronic band structure of graphene with its semi-metallic features near the charge neutrality point is sensitive to impurity effects. Using the Lifshitz and Anderson impurity models, we study in detail the disorder induced spectral phenomena in the electronic band structure of graphene, namely, the formation of resonances, quasi-gaps, bound states, impurity sub-bands, and their overall impact on the electronic band restructuring and the associated Mott-like metal-insulator transitions. We perform systematic analytical and numerical study for realistic impurities, both substitutional and adsorbed, focusing on those effects that stem from the impurity adatoms locations (top, bridge, and hollow positions), concentration, host sublattice occupation, perturbation strengths, etc. Possible experimental and practical implications are discussed as well., Comment: 20 pages (including appendices), 17 figures

We present a detailed theoretical study of chiral topological superconductor phases in proximity-superconducting graphene systems based on an effective model inspired by DFT simulations. Inducing s-wave superconductivity to quantum anomalous Hall effect systems leads to chiral topological superconductors. For out-of-plane magnetization we find topological superconducting phases with even numbers of chiral Majorana fermions per edge which is correlated to the opening of a nontrivial gap in the bulk system in the $\mathrm{ K}$-points and their connection under particle-hole symmetry. We show that in a quantum anomalous Hall insulator with in-plane magnetization and nontrivial gap opening at $\mathrm{M}$, the corresponding topological superconductor can be tuned to host only single chiral Majorana states at its edge which is promising for proposals exploiting such states for braiding operations.

We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number $C=1$. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing to control topological phase transitions. We also propose, using density functional theory, a material platform---graphene on Ising antiferromagnet MnPSe$_3$---to realize staggered exchange (pseudospin Zeeman) coupling.