We study the effect of gate-induced electric fields on the properties of semiconductor-superconductor hybrid nanowires which represent a promising platform for realizing topological superconductivity and Majorana zero modes. Using a self-consistent Schrödinger-Poisson approach that describes the semiconductor and the superconductor on equal footing, we are able to access the strong tunneling regime and identify the impact of an applied gate voltage on the coupling between semiconductor and superconductor. We discuss how physical parameters such as the induced superconducting gap and Landé $g$ factor in the semiconductor are modified by redistributing the density of states across the interface upon application of an external gate voltage. Finally, we map out the topological phase diagram as a function of magnetic field and gate voltage for InAs/Al nanowires.

Hybrid superconductor-semiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we seek to fill in this gap and address the role of band bending and superconductor-semiconductor hybridization in such devices by analyzing a gated single Al-InAs interface using a self-consistent Schrödinger-Poisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductor-semiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$ factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductor-semiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.

The iron-based superconductors are characterized by multiple-orbital physics where all the five Fe $3d$ orbitals get involved. The multiple-orbital nature gives rise to various novel phenomena like orbital-selective Mott transition, nematicity, and orbital fluctuation that provide a new route for realizing superconductivity. The complexity of multiple-orbital physics also requires us to disentangle the relationship between orbital, spin, and nematicity, and to identify dominant orbital ingredients that dictate superconductivity. The bulk FeSe superconductor provides an ideal platform to address these issues because of its simple crystal structure and unique coexistence of superconductivity and nematicity. However, the orbital nature of the low-energy electronic excitations and its relation to the superconducting gap remain controversial. Here, we report direct observation of the highly anisotropic Fermi surface and extremely anisotropic superconducting gap in the nematic state of the FeSe superconductor by high-resolution laser-based angle-resolved photoemission measurements. We find that the low-energy excitations of the entire hole pocket at the Brillouin zone center are dominated by the single $d_{xz}$ orbital. The superconducting gap exhibits an anticorrelation relation with the $d_{xz}$ spectral weight near the Fermi level; i.e., the gap size minimum (maximum) corresponds to the maximum (minimum) of the $d_{xz}$ spectral weight along the Fermi surface. These observations provide new insights in understanding the orbital origin of the extremely anisotropic superconducting gap in the FeSe superconductor and the relation between nematicity and superconductivity in the iron-based superconductors.

The recent observation of a half-integer quantized thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity ${\kappa }_{xy}$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity, focusing on the edge theory. As an example, we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized, and we argue that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $\mathrm{\Delta }{\kappa }_{xy}/T\sim \mathrm{sign}(\mathrm{B})T^2$, arises from an intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.

It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. Here we address this issue for two different physical scenarios: (i) a conformally invariant $(2+1)d$ quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the $S=1/2$ antiferromagnetic Heisenberg and $XY$ models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-$D$) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-$D$ iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length $\xi (D)$ combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

Traditional computational methods for studying quantum many-body systems are “forward methods,” which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one’s perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational “inverse method,” the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function $|{\psi }_T⟩$ and produces as output Hamiltonians for which $|{\psi }_T⟩$ is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and, in this work, we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model. EHC gives an alternative inverse approach for studying quantum many-body phenomena.

We analyze the effect of quenched disorder on spin-$1/2$ quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-$1/2$ moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-$1/2$ magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin $1/2$ per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of ${\mathrm{YbMgGaO}}_4$, a recently discovered triangular lattice spin-$1/2$ insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on ${\mathrm{YbMgGaO}}_4$ and related materials.

We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensions $d<\infty$. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.

In bilayer graphene, electrostatic confinement can be realized by a suitable design of top and back gate electrodes. We measure electronic transport through a bilayer graphene quantum dot, which is laterally confined by gapped regions and connected to the leads via $p$-$n$ junctions. Single electron and hole occupancy is realized and charge carriers $n=1,2,\dots 50$ can be filled successively into the quantum system with charging energies exceeding 10 meV. For the lowest quantum states, we can clearly observe valley and Zeeman splittings with a spin g-factor of $g_s\approx 2$. In the low-field limit, the valley splitting depends linearly on the perpendicular magnetic field and is in qualitative agreement with calculations.

Manifestations of quantum interference effects in macroscopic objects are rare. Weak localization is one of the few examples of such effects showing up in the electron transport through solid state. Here, we show that weak localization becomes prominent also in optical spectroscopy via detection of the electron spin dynamics. In particular, we find that weak localization controls the free electron spin relaxation in semiconductors at low temperatures and weak magnetic fields by slowing it down by almost a factor of two in $n$-doped GaAs in the metallic phase. The weak localization effect on the spin relaxation is suppressed by moderate magnetic fields of approximately 1 T, which destroy the interference of electron trajectories, and by increasing the temperature. The weak localization suppression causes an anomalous decrease of the longitudinal electron spin relaxation time $T_1$ with magnetic field, in stark contrast with the well-known magnetic-field-induced increase in $T_1$. This is consistent with transport measurements, which show the same variation of resistivity with magnetic field. Our discovery opens up a vast playground to explore quantum magnetotransport effects optically in the spin dynamics.

At ambient pressure, CrAs undergoes a first-order transition into a double-helical magnetic state at $T_N=265\mathrm{K}$, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of the coupled structural/helimagnetic order in this system. Here, we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure ($P$), that the combined order is suppressed at $P_c\approx 10\mathrm{kbar}$, near which bulk superconductivity develops with a maximal transition temperature $T_c\approx 2\mathrm{K}$. We further show that the coupled order is also completely suppressed by phosphorus doping in ${\mathrm{CrAs}}_{1-x}{\mathrm{P}}_x$ at a critical $x_c\approx 0.05$, above which inelastic neutron scattering evidenced persistent antiferromagnetic correlations, providing a possible link between magnetism and superconductivity. In line with the presence of antiferromagnetic fluctuations near $P_c(x_c)$, the $A$ coefficient of the quadratic temperature dependence of resistivity exhibits a dramatic enhancement as $P$ ($x$) approaches $P_c(x_c)$, around which $\rho (T)$ has a non-Fermi-liquid form. Accordingly, the electronic specific-heat coefficient of ${\mathrm{CrAs}}_{1-x}{\mathrm{P}}_x$ peaks around $x_c$. These properties provide clear evidence for quantum criticality, which we interpret as originating from a nearly second-order helimagnetic quantum phase transition that is concomitant with a first-order structural transition. Our findings in CrAs highlight the distinct characteristics of quantum criticality in bad metals, thereby bringing out new insights into the physics of unconventional superconductivity such as those occurring in the high-$T_c$ iron pnictides.

Recent experiments in graphene heterostructures have observed Chern insulators—integer and fractional quantum Hall states made possible by a periodic substrate potential. Here, we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by ${\mathrm{QED}}_3$-Chern-Simons theory. At these critical points, $N_f$ flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level $K$, and remarkably, the entire family (with any $N_f$ or $K$) can be realized at special values of the external magnetic field. Transitions between particle-hole conjugate Jain states realize “pure” ${\mathrm{QED}}_3$, in which multiple flavors of Dirac fermions interact with a Maxwell U(1) gauge field. The multiflavor nature of the critical point leads to an emergent $\mathrm{SU}(N_f)$ symmetry. Specifically, at the transition from a $\nu =1/3$ to $2/3$ quantum Hall state, the emergent SU(3) symmetry predicts an octet of charge density waves with enhanced susceptibilities, which is verified by DMRG numerical simulations on microscopic models applicable to graphene heterostructures. We propose experiments on Chern insulators that could resolve open questions in the study of ($2+1$)-dimensional conformal field theories and test recent duality inspired conjectures.

We use high-resolution resonant inelastic x-ray scattering (RIXS) to study a thin film of ${\mathrm{NdNiO}}_3$, a compound whose unusual spin- and bond-ordered electronic ground state has been of long-standing interest. Below the magnetic ordering temperature, we observe well-defined collective magnon excitations along different high-symmetry directions in momentum space. The magnetic spectra depend strongly on the incident photon energy, which we attribute to RIXS coupling to different local electronic configurations of the expanded and compressed ${\mathrm{NiO}}_6$ octahedra in the bond-ordered state. Both the noncollinear magnetic ground state and the observed site-dependent magnon excitations are well described by a model that assumes strong competition between the antiferromagnetic superexchange and ferromagnetic double-exchange interactions. Our study provides direct insight into the magnetic dynamics and exchange interactions of the rare-earth nickelates and demonstrates that RIXS can serve as a site-selective probe of magnetism in these and other materials.

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard data sets including the Bars and Stripes random binary patterns and the MNIST handwritten digits to illustrate the abilities, features, and drawbacks of our model over popular generative models such as the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.

A remarkable feature of typical ground states of strongly correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant upper bound on the entanglement entropy, called the area law. However, the known bound exists only in a hypothetical limit, rendering its physical relevance highly questionable. In this paper, we give a simple proof of the area law for entanglement entropy in one dimension under the condition of exponentially decaying correlations. Our proof dramatically reduces the previously known bound on the entanglement entropy, bringing it into a realistic regime for the first time. The proof is composed of several simple and straightforward steps based on elementary quantum information tools. We discuss the underlying physical picture, based on a renormalization-like construction underpinning the proof, which transforms the entanglement entropy of a continuous region into a sum of mutual information in different length scales and the entanglement entropy at the boundary.

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6-GHz acoustic resonance to a wavelength-scale volume of less than 1 cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate $g/2\pi \approx 1.6\mathrm{MHz}$ and a mechanical quality factor $Q_m\approx 3\times {10}^4$, leading to a cooperativity $C\sim 4$ when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.

In the Dirac-Weyl semimetal, the chiral anomaly appears as an “axial” current arising from charge pumping between the lowest (chiral) Landau levels of the Weyl nodes, when an electric field is applied parallel to a magnetic field $\mathbf{B}$. Evidence for the chiral anomaly was obtained from the longitudinal magnetoresistance (LMR) in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi. However, current-jetting effects (focusing of the current density $\mathbf{J}$) have raised general concerns about LMR experiments. Here, we implement a litmus test that allows the intrinsic LMR in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi to be sharply distinguished from pure current-jetting effects (in pure Bi). Current jetting enhances $J$ along the mid-line (spine) of the sample while decreasing it at the edge. We measure the distortion by comparing the local voltage drop at the spine (expressed as the resistance $R_{\text{spine}}$) with that at the edge ($R_{\text{edge}}$). In Bi, $R_{\text{spine}}$ sharply increases with $B$, but $R_{\text{edge}}$ decreases (jetting effects are dominant). However, in ${\mathrm{Na}}_3\mathrm{Bi}$ and GdPtBi, both $R_{\text{spine}}$ and $R_{\text{edge}}$ decrease (jetting effects are subdominant). A numerical simulation allows the jetting distortions to be removed entirely. We find that the intrinsic longitudinal resistivity ${\rho }_{xx}(B)$ in ${\mathrm{Na}}_3\mathrm{Bi}$ decreases by a factor of 10.9 between $B=0$ and 10 T. A second litmus test is obtained from the parametric plot of the planar angular magnetoresistance. These results considerably strengthen the evidence for the intrinsic nature of the chiral-anomaly-induced LMR. We briefly discuss how the squeeze test may be extended to test ${\mathrm{ZrTe}}_5$.

The spin-$1/2$ triangular lattice antiferromagnet ${\mathrm{YbMgGaO}}_4$ has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of ${\mathrm{YbMgGaO}}_4$ to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged $g$ factors and exchange interactions. Our results paint ${\mathrm{YbMgGaO}}_4$ as an easy-plane $XXZ$ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained $g$ factors are substantially different from previous reports. This work establishes the hierarchy of exchange interactions in ${\mathrm{YbMgGaO}}_4$ from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in $1+1\mathrm{D}$ bosonic systems, there is no nontrivial topological order, while in $2+1\mathrm{D}$ bosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in $3+1\mathrm{D}$ the classification is much simpler than it was thought to be; we propose a partial classification of topological orders for $3+1\mathrm{D}$ bosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair $(G,{\omega }_4)$: a finite group $G$ and its group 4-cocycle ${\omega }_4\in {\mathcal{H}}^4[G;U(1)]$ (up to group automorphisms). Furthermore, all such $3+1\mathrm{D}$ topological orders can be realized by Dijkgraaf-Witten gauge theories.

We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe, in a region in parameter space, the onset of antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their buildup associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations, taking into account experimental imperfections measured at the single-particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their buildup in time.