Superconductivity and the quantum Hall effect are considered to be two cornerstones of condensed matter physics. The realization of hybrid structures where these two effects coexist has recently become an active field of research. In this work, we study a Josephson junction where a central region in the quantum Hall regime is proximitized with superconductors that can be driven to a topological phase with an external Zeeman field. In this regime, the Majorana modes that emerge at the ends of each superconducting lead couple to the chiral quantum Hall edge states. This produces distinguishable features in the Andreev levels and Fraunhofer patterns that could help in detecting not only the topological phase transition but also the spin degree of freedom of these exotic quasiparticles. The current phase relation and the spectral properties of the junction throughout the topological transition are fully described by a numerical tight-binding calculation. In pursuance of the understanding of these results, we develop a low-energy spinful model that captures the main features of the numerical transport simulations in the topological phase.

The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrization: (i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram and (ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy $K$. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.

We address the issue of whether it is possible to generate Majorana bound states at the magnetic-superconducting interface in two-dimensional topological insulators with hidden Dirac points in the spectrum. In this case, the Dirac point of edge states is located at the energies of the bulk states such that two types of states are strongly hybridized. Here, we show that well-defined Majorana bound states can be obtained even in materials with a hidden Dirac point provided that the width of the magnetic strip is chosen to be comparable with the localization length of the edge states. The obtained topological phase diagram allows one to extract precisely the position of the Dirac point in the spectrum. In addition to standard zero-bias peak features caused by Majorana bound states in transport experiments, we propose to supplement future experiments with measurements of charge and spin polarization. In particular, we demonstrate that both observables flip their signs at the topological phase transition, thus providing an independent signature of the presence of topological superconductivity. All features remain stable against substantially strong disorder.

High mobility InSb quantum wells with tunable carrier densities are investigated by transport experiments in magnetic fields tilted with respect to the sample normal. We employ the coincidence method and the temperature dependence of the Shubnikov–de Haas oscillations and find a value for the effective $g$ factor of $|g^{*}|=35\pm 4$ and a value for the effective mass of $m^{*}\approx 0.017m_e$, where $m_e$ is the free electron mass. Our measurements are performed in a magnetic field and a density range where the enhancement mechanism of the effective $g$ factor can be neglected. Accordingly, the obtained effective $g$ factor and the effective mass can be explained in a single-particle picture. Additionally, we explore the magnetotransport up to magnetic fields of 35 T and do not find features related to the fractional quantum Hall effect.

Adversarial machine learning is an emerging field that focuses on studying vulnerabilities of machine learning approaches in adversarial settings and developing techniques accordingly to make learning robust to adversarial manipulations. It plays a vital role in various machine learning applications and recently has attracted tremendous attention across different communities. In this paper, we explore different adversarial scenarios in the context of quantum machine learning. We find that, similar to traditional classifiers based on classical neural networks, quantum learning systems are likewise vulnerable to crafted adversarial examples, independent of whether the input data is classical or quantum. In particular, we find that a quantum classifier that achieves nearly the state-of-the-art accuracy can be conclusively deceived by adversarial examples obtained via adding imperceptible perturbations to the original legitimate samples. This is explicitly demonstrated with quantum adversarial learning in different scenarios, including classifying real-life images (e.g., handwritten digit images in the dataset MNIST), learning phases of matter (such as ferromagnetic/paramagnetic orders and symmetry protected topological phases), and classifying quantum data. Furthermore, we show that based on the information of the adversarial examples at hand, practical defense strategies can be designed to fight against a number of different attacks. Our results uncover the notable vulnerability of quantum machine learning systems to adversarial perturbations, which not only reveals another perspective in bridging machine learning and quantum physics in theory but also provides valuable guidance for practical applications of quantum classifiers based on both near-term and future quantum technologies.

We present a diagrammatic Monte Carlo method for quantum impurity problems with general interactions and general hybridization functions. Our method uses a recursive determinant scheme to sample diagrams for the scattering amplitude. Unlike in other methods for general impurity problems, an approximation of the continuous hybridization function by a finite number of bath states is not needed and accessing low temperatures does not incur an exponential cost. We test the method for the example of molecular systems, where we systematically vary temperature, interatomic distance, and basis set size. We further apply the method to an impurity problem generated by a self-energy embedding calculation of correlated antiferromagnetic $\mathrm{NiO}$. We find that the method is ideal for quantum impurity problems with a large number of orbitals but only moderate correlations.

A spin-polarized current source using nonmagnetic layered materials is promising for next-generation all-electrical spintronic science and technology. Here we electrically created spin polarization in a layered semimetal $\mathrm{Ta}{\mathrm{Te}}_2$ via the charge-spin conversion process. Using a hybrid device of $\mathrm{Ta}{\mathrm{Te}}_2$ in a van der Waals heterostructure with graphene, the spin polarization in $\mathrm{Ta}{\mathrm{Te}}_2$ is efficiently injected and detected by nonlocal spin-switch, Hanle spin precession, and inverse spin Hall effect measurements. Systematic experiments at different bias currents and gate voltages in a vertical geometry prove the $\mathrm{Ta}{\mathrm{Te}}_2$ as a nonmagnetic spin source at room temperature. These findings demonstrate the possibility of making an all-electrical spintronic device in a two-dimensional van der Waals heterostructure, which can be essential building blocks in energy-efficient spin-orbit technology.

We show how $U\left(1\right)$ lattice gauge theories display key signatures of ergodicity breaking in the presence of a random charge background. We argue that, in such gauge theories, there is a cooperative effect of disorder and interactions in favoring ergodicity breaking: This is due to the confining nature of the Coulomb potential, which suppresses the number of available energy resonances at all distances. Such a cooperative mechanism reflects into very modest finite-volume effects: This allows us to draw a sharp boundary for the ergodic regime, and thus the breakdown of quantum chaos for sufficiently strong gauge couplings, at system sizes accessible via exact diagonalization. Our conclusions are independent on the value of a background topological angle, and are contrasted with a gauge theory with truncated Hilbert space, where instead we observe very strong finite-volume effects akin to those observed in spin chains.

Excitonic magnetism involving superpositions of singlet and triplet states is expected to arise for two holes in strongly correlated and spin-orbit-coupled $t_{2g}$ orbitals. However, uncontested material examples for its realization are rare. We apply the variational cluster approach to the square lattice to investigate excitonic antiferromagnetism and the impact of a crystal field. We give a phase diagram depending on spin-orbit coupling and crystal field and find excitonic magnetism to survive in the presence of substantial crystal-field-induced orbital order. We address the specific example of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ using ab initio modeling and conclude it to realize such excitonic magnetism despite its pronounced orbital polarization. We also reproduce magnetic excitations and show the maximum at momentum (0,0) to be related to the excitonic character of the magnetic order.

Probing the topological invariants of interacting systems stands as a grand and open challenge. Here we describe a dynamical method to characterize 1D chiral models, based on the direct observation of time-evolving bulk excitations. We present analytical and state-of-the-art numerical calculations on various flavors of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how measuring the mean chiral displacement allows us to distinguish between topological insulator, trivial insulator, and symmetry-broken phases. Finally, we provide a readily-feasible experimental blueprint for a model displaying these three phases and we describe how to detect those.

The infinite-layer structure nickelate ${\mathrm{Ba}}_2{\mathrm{NiO}}_2{\left(\mathrm{AgSe}\right)}_2$ (BNOAS) with $d^8$ Ni ions and a peculiar susceptibility $\chi \left(T\right)$, synthesized at high pressure, is studied with correlated density functional methods. The overriding feature of the calculations is a violation of Hund's rule coupled with complete but unconventional spin-orbital polarization, leading to an unexpected low-spin ${}^1{B}_1$, “off-diagonal singlet” textured by an internal orbital structure of compensating $d_{x^2-y^2}^{\uparrow }$ and $d_{z^2}^{\downarrow }$ spins. This unconventional configuration has a lower energy than conventional high-spin or low-spin alternatives. An electronic transition is obtained at a critical Ni-O separation $d_c^{\text{Ni-O}}=2.03\text{Å}$, which corresponds closely to the observed critical value of 2.00–2.05 Å, above which Ni becomes magnetic in square planar ${\mathrm{NiO}}_2$ compounds. We propose scenarios for the signature of magnetic reconstruction in $\chi \left(T\right)$ at $T_m=130$ K without any Curie-Weiss background (no moment) that invokes ordering of Ni $d^8$ moieties that are largely this generalized Kondo singlet. Because hole states are primarily Se $4p$ rather than O $2p$, the usual issue of Mott insulator versus charge transfer insulator is supplanted by a character in which electrons and holes are separated in real space. The underlying physics of this system is modeled by a Kondo sieve spin model (two-dimensional Kondo necklace) of a “Kondo” $d_{z^2}$ spin on each site, coupled to a $d_{x^2-y^2}$ spin that is itself strongly coupled to neighboring like-spins within the layer. The observed magnetic order places BNOAS below the quantum critical point of the Kondo sieve model, providing a realization of the long-range ordered near-singlet weak antiferromagnetic phase. We propose electron doping experiments that would drive the system toward a $d^{9-\delta }$ configuration and possible superconductivity with a similarity to the recently reported hole-doped infinite-layer cuprate ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3.2}$ that superconducts at 73 K.

The Dirac mass of a two-dimensional QAH insulator is directly related to the parity anomaly of planar quantum electrodynamics, as shown initially by Niemi and Semenoff [Phys. Rev. Lett. 51, 2077 (1983)]. In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. We reveal that in the calculation of the effective action, before renormalization, the Newtonian mass acts similar to a parity-breaking element of a high-energy regularization scheme. This calculation allows us to derive the finite frequency correction to the DC Hall conductivity of a QAH insulator. We predict that the leading order AC correction contains a term proportional to the Chern number. This term originates from the Newtonian mass and can be measured via electrical or magneto-optical experiments. Moreover, we prove that the Newtonian mass significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene.

We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the noncommutative algebra between a flux operator and $C_n$ rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and the fractional corner charge. Second, we define a new entanglement property, dubbed “higher-order entanglement,” to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.

Lattice modulation spectroscopy is a powerful tool for probing low-energy excitations of interacting many-body systems. By means of bosonization we analyze the absorbed power in a one-dimensional interacting quantum gas of bosons or fermions, subjected to a periodic drive of the optical lattice. For these Tomonaga-Luttinger liquids we find a universal ${\omega }^3$ scaling of the absorbed power, which at very low-frequency turns into an ${\omega }^2$ scaling when scattering processes at the boundary of the system are taken into account. We confirm this behavior numerically by simulations based on time-dependent matrix product states. Furthermore, in the presence of impurities, the theory predicts an ${\omega }^2$ bulk scaling. While typical response functions of Tomonaga-Luttinger liquids are characterized by exponents that depend on the interaction strength, modulation spectroscopy of cold atoms leads to a universal power-law exponent of the absorbed power. Our findings can be readily demonstrated in ultracold atoms in optical lattices with current experimental technology.

Anisotropic magnetoresistance (AMR), originating from spin-orbit coupling (SOC), is the sensitivity of the electrical resistance in magnetic systems to the direction of spin magnetization. Although this phenomenon has been experimentally reported for several nanoscale junctions, a clear understanding of the physical mechanism behind it is still elusive. Here we discuss a concept based on orbital symmetry considerations to attain a significant AMR of up to 95% for a broad class of $\pi$-type molecular spin valves. It is illustrated at the benzene-dithiolate molecule connecting two monoatomic nickel electrodes. We find that SOC opens, via spin-flip events at the ferromagnet-molecule interface, a conduction channel, which is fully blocked by symmetry without SOC. Importantly, the interplay between two transport channels turns out to depend strongly on the magnetization direction in the nickel electrodes due to the tilting of molecular orbitals. Moreover, due to multiband quantum interference, appearing at the band edge of nickel electrodes, a transmission drop is observed just above the Fermi energy. Altogether, these effects lead to a significant AMR around the Fermi level, which even changes sign. Our theoretical understanding, corroborated in terms of ab initio calculations and simplified analytical models, reveals the general principles for an efficient realization of AMR in molecule-based spintronic devices.

The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an appropriate characterization of the distance to criticality felt by the quenched system. The subsequent long-time evolution, beyond the identified dynamical critical region, is also investigated by looking at the behavior of the density wavefront evolution and the corresponding phase ordering dynamics.

Thermoelectric power ($S$) and Hall effect ($R_{\mathrm{H}}$) measurements on the paramagnetic superconductor ${\mathrm{UTe}}_2$ with the magnetic field applied along the hard magnetization $b$ axis are reported. The first-order nature of the metamagnetic transition at $H_{\mathrm{m}}=H_{\mathrm{c}2}^b=35$ T leads to drastic consequences on $S$ and $R_{\mathrm{H}}$. In contrast to the field dependence of the specific heat in the normal state through $H_{\mathrm{m}}$, $S\left(H\right)$ is not symmetric with respect to $H_{\mathrm{m}}$. This implies a strong interplay between ferromagnetic fluctuations and a Fermi-surface reconstruction at $H_{\mathrm{m}}$. $R_{\mathrm{H}}$ is very well described by incoherent skew scattering above the coherence temperature $T_{\mathrm{m}}$ corresponding roughly to the temperature of the maximum in the susceptibility $T_{{\chi }_{\max }}$ and coherent skew scattering at lower temperatures. The discontinuous field dependence of both $S\left(H\right)$ and the ordinary Hall coefficient $R_0$, at $H_{\mathrm{m}}$ and at low temperature, provides evidence of a change in the band structure at the Fermi level.

Recent experiments have examined the impact of a magnetic field on ferroquadrupolar orders in the intermetallic Kondo material $\mathrm{Pr}{\mathrm{Ti}}_2{\mathrm{Al}}_{20}$. Motivated by this, we use extensive Monte Carlo simulations to study a diamond lattice $XY$ model of non-Kramers pseudospin-$1/2$ ${\mathrm{Pr}}^{3+}$ moments which crucially incorporates three-spin interactions. This model supports a thermal $Z_3$ Potts ordering transition upon cooling from the paramagnetic phase into the ferroquadrupolar phase. An applied magnetic field along the [110] direction leads to a thermal Ising transition out of the quadrupolar ordered phase. A magnetic field along the [001] direction leads to only thermal crossovers, but supports a spinodal transition out of metastable domains which could be strongly pinned by coupling to elastic lattice deformations. We propose noise measurements as a potential probe to “hear” the spinodal transition. Our work highlights the importance of multispin interactions in Kondo materials near the small-to-large Fermi surface transition.

Metallic $\mathrm{Li}\mathrm{Os}{\mathrm{O}}_3$ undergoes a continuous ferroelectric-like structural phase transition below $T_c=140\mathrm{K}$ to realize a polar metal. To understand the microscopic interactions that drive this transition, we study its critical behavior above $T_c$ via electromechanical coupling—distortions of the lattice induced by short-range dipole-dipole correlations arising from Li off-center displacements. By mapping the full angular distribution of second harmonic electric-quadrupole radiation from $\mathrm{Li}\mathrm{Os}{\mathrm{O}}_3$ and performing a simplified hyper-polarizable bond model analysis, we uncover subtle symmetry-preserving lattice distortions over a broad temperature range extending from $T_c$ up to around 230 K, characterized by nonuniform changes in the short and long Li-O bond lengths. Such an extended region of critical fluctuations may explain anomalous features reported in specific heat and Raman scattering data and suggests the presence of competing interactions that are not accounted for in existing theoretical treatments. More broadly, our results showcase how electromechanical effects serve as a probe of critical behavior near inversion symmetry-breaking transitions in metals.

The 2D electron gas (2DEG) formed at the surface of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$(001) has attracted great interest because of its fascinating physical properties and potential as a novel electronic platform, but up to now has eluded a comprehensible way to tune its properties. Using angle-resolved photoemission spectroscopy with and without spin detection, we here show that the band filling can be controlled by growing thin $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ films on Nb-doped $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$(001) substrates. This results in a single spin-polarized 2D Fermi surface, which bears potential as a platform for Majorana physics. Based on our results, it can furthermore be concluded that the 2DEG does not extend more than two unit cells into the film and that its properties depend on the amount of $\mathrm{Sr}{\mathrm{O}}_x$ at the surface and possibly the dielectric response of the system.