Recently, there has been significant progress in solving quantum many-particle problems via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this paper, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, solving the highly frustrated spin-1/2 $J_1-J_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.

Spin resonance in the superconducting state of Fe-based materials within the multiorbital model with unequal anisotropic gaps on different Fermi surface sheets is studied. On the basis of the model gap function and the one calculated within the spin fluctuation theory of pairing, I show that the resonance peak shifts to higher frequencies with increasing the zero-amplitude gap magnitude. On the contrary, with increasing the gap anisotropy, it shifts to lower frequencies and loses some intensity.

The physics of a planar chiral $p\pm ip$ superconductor is studied for various vortex configurations. The occurrence of vortex quasiparticle bound states is exposed together with their ensuing collective properties, such as subgap bands induced by intervortex tunneling. A general method to diagonalize the Hamiltonian of a superconductor in the presence of a vortex lattice is developed that employs only smooth gauge transformations. It renders the Hamiltonian to be periodic (thus allowing the use of the Bloch theorem) and enables the treatment of systems with vortices of finite radii. The pertinent anomalous charge response $c_{xy}$ is calculated (using the Streda formula) and reveals that it contains a quantized contribution. This is attributed to the response to the nucleation of vortices from which we deduce the system's quantum phase.

We study the quantum criticality of the phase transition between the Dirac semimetal and the excitonic insulator in two dimensions. Even though the system has a semimetallic ground state, there are observable effects of excitonic pairing at finite temperatures and/or finite energies, provided that the system is in proximity to the excitonic insulating transition. To determine the quantum critical behavior, we consider three potentially important interactions, including the Yukawa coupling between Dirac fermions and the excitonic order parameter fluctuation, the long-range Coulomb interaction, and the disorder scattering. We employ the renormalization group technique to study how these interactions affect quantum criticality and also how they influence each other. We first investigate the Yukawa coupling in the clean limit, and show that it gives rise to typical non-Fermi liquid behavior. Adding random scalar potential to the system always turns such a non-Fermi liquid into a compressible diffusive metal. In comparison, the non-Fermi liquid behavior is further enhanced by random vector potential, but is nearly unaffected by random mass. Incorporating the Coulomb interaction may change the results qualitatively. In particular, the non-Fermi liquid state is protected by the Coulomb interaction for weak random scalar potential, and it becomes a diffusive metal only when random scalar potential becomes sufficiently strong. When random vector potential or random mass coexists with Yukawa coupling and Coulomb interaction, the system is a stable non-Fermi liquid state, with fermion velocities flowing to constants in the former case and being singularly renormalized in the latter case. These quantum critical phenomena can be probed by measuring observable quantities. We also find that, while the fermion velocity anisotropy is not altered by the excitonic quantum fluctuation, it may be driven by the Coulomb interaction to flow to the isotropic limit.

Spin-orbit coupling in magnetic systems lacking inversion symmetry can give rise to nontrivial spin textures. Magnetic thin films and heterostructures are potential candidates for the formation of skyrmions and other noncollinear spin configurations as inversion symmetry is inherently lost at their surfaces and interfaces. However, manganites, in spite of their extraordinarily rich magnetic phase diagram, have not yet been considered of interest within this context as their spin-orbit coupling is assumed to be negligible. We demonstrate here, by means of angular dependent x-ray linear dichroism experiments and theoretical calculations, the existence of a noncollinear antiferromagnetic ordering at the surface of ferromagnetic ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$ thin films whose properties can only be explained by an unexpectedly large enhancement of the spin-orbit interaction. Our results reveal that spin-orbit coupling, usually assumed to be very small in manganites, can be significantly enhanced at surfaces and interfaces adding a new twist to the possible magnetic orders that can arise in electronically reconstructed systems.

We used x-ray absorption spectroscopy to study the orbital symmetry and the energy band splitting of (111) ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ and ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3/{\mathrm{SrTiO}}_3$ heterostructures, hosting a quasi-two-dimensional electron system (q2DES), and of a Ti-terminated (111) ${\mathrm{SrTiO}}_3$ single crystal, also known to form a q2DES at its surface. We demonstrate that the bulk tetragonal Ti-3d ${\mathrm{D}}_{4h}$ crystal field is turned into a trigonal ${\mathrm{D}}_{3d}$ crystal field in all cases. The symmetry adapted ${\mathrm{a}}_{1g}$ and ${\mathrm{e}}_g^{\pi }$ orbitals are nondegenerate in energy and their splitting, $\mathrm{\Delta }$, is positive at the bare STO surface but negative in the heterostructures, where the ${\mathrm{a}}_{1g}$ orbital is lowest in energy. These results demonstrate that the interfacial symmetry breaking induced by epitaxial engineering of oxide interfaces has a dramatic effect on their electronic properties, and it can be used to manipulate the ground state of the q2DES.

We report a topological semimetal ${\mathrm{W}}_2{\mathrm{As}}_3$ with a space group $C2/m$. Based on the first-principles calculations, band crossings are partially gapped when spin-orbit coupling is included. The $Z_2$ indices at the electron filling are [1;111], characterizing a strong topological insulator and topological surface states. From the magnetotransport measurements, nearly quadratic field dependence of magnetoresistance (MR) ($B\parallel \left[200\right]$) at 3 K indicates an electron-hole compensated compound whose longitudinal MR reaches 11 500% at 3 K and 15 T. In addition, multiband features are detected from the high-magnetic-field Shubnikov–de Haas (SdH) oscillation, Hall resistivity, and band calculations. A nontrivial $\pi$ Berry's phase is obtained, suggesting the topological feature of this material. A two-band model can fit well the conductivity and Hall coefficient. Our experiments manifest that the transport properties of ${\mathrm{W}}_2{\mathrm{As}}_3$ are in good agreement with the theoretical calculations.

We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the nonlinear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger liquids which is governed by the spin-charge separation of the elementary collective excitations.

We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of the underlying topological phases change between noninteracting fermions and a bosonic system in the strong coupling limit, the symmetry-protection argument enforces a gap closing and thereby predicts a breakdown of the topological pumping. We also demonstrate that, even in the weakly interacting regime where the bulk topological pumping is still robust, the interaction effects manifest themselves in the edge density profiles, leading to a unique feature of the pumping in open boundary conditions. Furthermore, an extension of the above results indicates that an analog of an interaction-induced phase of Weyl semimetals can be realized in the setup of the topological pumping. Our results provide a systematic understanding for the stability of topological pumping against strong interactions, to which the conventional perturbative argument cannot be applied.

The role of classical dynamics in spin transport is an intriguing problem from the point of view of classical-quantum correspondence, as spin is a purely relativistic quantum mechanical variable with no classical counterpart. Nevertheless, due to spin-orbit coupling (generally referred to as the relativistic interaction of a particle's spin with its motion inside a potential) and because the orbital motion does have a classical correspondence, the nature of the classical dynamics can affect spin. A basic transport structure is quantum dots, whose geometrical shape can be chosen to lead to characteristically distinct classical behaviors ranging from integrable dynamics to chaos. Whether and how classical chaos can affect spin transport and if the effect can be exploited for applications in spintronics are thus issues of both fundamental and practical interest. Here we report results from systematic, full quantum computations of spin transport through quantum dots hosting different types of classical dynamics. Our main finding is that chaos can play orthogonal roles in affecting spin polarization, depending on the relative strength of the spin-orbit coupling. For weak coupling with a characteristic interaction length much larger than the system size, chaos can be beneficial to preserving spin polarization. In the strong coupling regime where the interaction length is smaller than the system dimension, chaos typically destroys spin polarization. We develop a semiclassical theory to understand these phenomena and point out their implications and potential applications in developing spintronic devices.

We use a variational technique to study the many-body phase diagram of electrons and holes in $n$-doped and $p$-doped monolayer transition metal dichalcogenides (TMDs). We find a total of four different phases. (i) A fully spin polarized and valley polarized ferromagnetic state. (ii) A state with no global spin polarization but with spin polarization in each valley separately, i.e., spin-valley locking. (iii) A state with spin polarization in one of the valleys and little to no spin polarization in the other valley. (iv) A paramagnetic state with no valley polarization. These phases are separated by first-order phase transitions and are determined by the particle density and the dielectric constant of the substrate. We find that in the presence of a perpendicular magnetic field the four different phases persist. In the case of $n$-doped ${\mathrm{MoS}}_2$, a fifth phase, which is completely valley polarized but not spin polarized, appears for magnetic fields larger than 7 T and for magnetic fields larger than 23 T completely replaces the second phase.

Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously to surface energies. Despite a radical reduction in atomic coordination numbers, the 2D and three-dimensional (3D) vacancy formation energies and work functions are nearly the same for each metal. Finally, static polarizabilities reveal a clear cubic dependence on bond length. These trends provide useful insights when moving towards reality with elemental 2D metals.

Recently, giant planar Hall effect originating from chiral anomaly has been predicted in nonmagnetic Dirac/Weyl semimetals. $\mathrm{ZrT}{\mathrm{e}}_5$ is considered to be an intriguing Dirac semimetal at the boundary of weak topological insulators and strong topological insulators, although this claim still remains controversial. Here, we report the observation in $\mathrm{ZrT}{\mathrm{e}}_{5-\delta }$ of the giant planar Hall resistivity that shows two different magnetic-field dependences as predicted by theory and a maximum at the Lifshitz transition temperature. We found that the giant planar Hall resistivity fades out with decreasing the thickness of $\mathrm{ZrT}{\mathrm{e}}_{5-\delta }$ nanoplates, which may be ascribed to the vanishing of the 3D nature of the samples. In addition, we have observed a nontrivial Berry phase, chiral-anomaly-induced negative longitudinal magnetoresistance, and a giant in-plane anisotropic magnetoresistance in these $\mathrm{ZrT}{\mathrm{e}}_{5-\delta }$ nanoplates. All the experimental observations demonstrated coherently that $\mathrm{ZrT}{\mathrm{e}}_{5-\delta }$ is a Dirac semimetal.

We introduce a laser control scenario to transiently transform an insulating heterojunction into a conducting one on a femtosecond timescale. The scenario is based on opening Landau-Zener quantum tunneling channels for electron transfer between two adjacent semiconductors via Stark shifts induced by nonresonant lasers of intermediate intensity (nonperturbative but nonionizing). Through quantum dynamics simulations we demonstrate the robustness of the approach and its utility for controlling electron dynamics at interfaces.

We predict conductance oscillations in a quantum anomalous Hall two-dimensional strip having a superconducting region of length $L_x$ with a chiral Majorana mode. These oscillations require a finite transverse extension of the strip $L_y$ of a few microns or less. Measuring the conductance periodicity with $L_x$ and a fixed bias, or with bias and a fixed $L_x$, yields the speed of the chiral Majorana mode. The physical mechanism behind the oscillations is the interference between backscattered chiral modes from the second to first interface of the normal-superconductor-normal double junction. The interferometer effect is enhanced by the presence of side barriers.

The charge density is among the most fundamental solid state properties determining bonding, electrical characteristics, and adsorption or catalysis at surfaces. While atomic-scale charge densities have as yet been retrieved by solid state theory, we demonstrate both charge density and electric field mapping across a mono-/bilayer boundary in 2D ${\mathrm{MoS}}_2$ by momentum-resolved scanning transmission electron microscopy. Based on consistency of the four-dimensional experimental data, statistical parameter estimation and dynamical electron scattering simulations using strain-relaxed supercells, we are able to identify an AA-type bilayer stacking and charge depletion at the Mo-terminated layer edge.

We report a systematic lattice dynamics study of the technologically important ${\mathrm{Fe}}_3\mathrm{Si}$/GaAs heterostructure for ${\mathrm{Fe}}_3\mathrm{Si}$ layer thicknesses of 3, 6, 8, and 36 monolayers. The Fe-partial phonon density of states obtained by nuclear inelastic scattering exhibits up to a twofold enhancement of the low-energy phonon states compared to the bulk material for layer thicknesses of 8 monolayers and below. First-principles calculations explain the observed effect by interface-specific phonon states originating from the significantly reduced atomic force constants and allow for achieving a comprehensive understanding of the lattice dynamics of epitaxial strain-free interfaces.

We report the relationship between the surface superstructure of ${\mathrm{SrTiO}}_3$(001) (STO) substrates and the superconducting properties of single unit cell (1-UC) FeSe films using scanning tunneling microscopy/spectroscopy (STM/STS). Under reflection high-energy-electron diffraction observation, we controlled the periodicity of the STO surface to $2\times 1$ and $\sqrt{2}\times \sqrt{2}$ and grew high-quality FeSe films. We found that the substrate periodicity can be imaged through the 1-UC FeSe from high-resolution STM observations and obtained clear evidence that the superconducting gap size depends on the surface periodicity (10–15 meV on $2\times 1$, 12–17 meV on $\sqrt{2}\times \sqrt{2}$, and 9–13 meV for $2\times 1$ domains on the $\sqrt{2}\times \sqrt{2}$ surface). Our results strongly suggest the important role of the film/substrate interface on high-temperature superconductivity.

We performed tunneling spectroscopy measurements of graphene coupled to niobium/niobium-nitride superconducting electrodes. Due to the proximity effect, the graphene density of states depends on the phase difference between the superconductors and exhibits a hard induced gap at zero phase, consistent with a continuum of Andreev bound states. At energies larger than the superconducting gap, we observed phase-dependent energy levels displaying the Coulomb blockade effect, which are interpreted as arising from spurious quantum dots, presumably embedded in the heterostructures and coupled to the proximitized graphene.