We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define “persistence” critical exponents and study how they are related to those critical exponents usually considered.

We study the effects of various symmetry-breaking perturbations on the experimentally measurable signatures (such as conductance and Josephson response) of quasi-one-dimensional (quasi-1D) spin-triplet superconductors. In the first part of the paper, we numerically compute the zero and nonzero temperature conductances of the quasi-1D nanowires that host multiple Majorana zero modes. Following the discussion of the case of s-wave Rashba nanowires, we shift to the main focus, i.e., multi-channel spin-triplet superconductors. Applying gate voltages (which changes the symmetry of the spin-orbit coupling) as well as magnetic fields to the nanowire, tunes the system between different symmetry classes by splitting the multiple Majorana zero modes. We study how the conductance tracks the topological invariants and the spectra in all these cases. In the second part of the paper, we study the effects of the symmetry-induced spectrum-breaking on the Andreev spectra of Josephson junctions. Similar to the case of the conductance studies, we find that the spectrum shows multiple zero-energy Andreev bound states in the highly symmetric case with mirror and chiral symmetries.

We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from nontrivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the dissipationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.

High-order topological charge is of intensive interest in the field of topological matter. In real materials, a cubic Dirac point is rare, and the chiral charge of one Weyl point (WP) has never be found to exceed $\left|C\right|=3$ for spin-$\frac{1}{2}$ electronic systems. In this paper, we argue that a cubic Dirac point can result in one quadruple WP ($\left|C\right|=4$ with double band degeneracy) when time-reversal symmetry is broken, provided that this cubic Dirac point is away from the high-symmetry points and involves the coupling of eight bands, rather than the four bands that were thought to be sufficient to describe a Dirac point. The eight-band manifold can be realized in materials with screw symmetry. Near the zone boundary along the screw axis, the folded bands are coupled to their “parent” bands, resulting in doubling the dimension of the Hilbert space. Indeed, in $\varepsilon$-TaN (space group 194 with screw symmetry) we find a quadruple WP when applying a Zeeman field along the screw axis. This quadruple WP away from high-symmetry points is distinct from highly degenerate nodes at the high-symmetry points already reported. We further find that such a high chiral charge might be related to the parity mixing of bands with high degeneracy, which in turn alters the screw eigenvalues and the resulting chiral charge.

Controlling the magnetic anisotropy in magnetic oxides is critical for the development of oxide spintronics. Here we report on the finding of an emergent interfacial magnetism, with unique perpendicular magnetic anisotropy (PMA), at the interface of a half-doped manganite ${\mathrm{La}}_{1/2}{\mathrm{Sr}}_{1/2}\mathrm{Mn}{\mathrm{O}}_3$ film on $\mathrm{LaAl}{\mathrm{O}}_3$ substrate, through combined electron spin resonance measurements and density functional theory calculations. The interfacial magnetism can be explained by the $3d_{3z^2-r^2}$ orbital-mediated ferromagnetic exchange interaction between Mn ions near the interface, which is enhanced by the compressive strain from the substrate. Our results provide a useful PMA system for possible spintronic applications, as well as atomistic-level insight to the magnetic anisotropy in strained manganite oxide interfaces.

We investigate the high-temperature dynamical conductivity $\sigma \left(\omega \right)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusivelike transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\le 32$ sites for the XXZ spin model with the frequency resolution $\delta \omega \sim {10}^{-3}J$. Results for the XXZ chain reveal a fine structure of $\sigma \left(\omega \right)$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\mathrm{\Delta }$. Still, we do not find clear evidence for a diffusive component, at least not for commensurate values of $\mathrm{\Delta }$, particularly for $\mathrm{\Delta }=0.5$, as well as for $\mathrm{\Delta }\to 0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.

Quantum wells (QWs) based on mercury telluride (HgTe) thin films provide a large range of unusual physical properties, from an insulator via a two-dimensional Dirac semimetal to a three-dimensional topological insulator. These properties result from the dramatic change in the QW band structure with the HgTe film thickness. Despite being a key property, these energy dispersion relations cannot be reflected in experiments due to the lack of appropriate tools. Here we report an experimental and theoretical study of two HgTe QWs with an inverted energy spectrum in which two-dimensional semimetallic states are realized. Using magneto-optical spectroscopy at subterahertz frequencies we obtain information about electron and hole cyclotron masses at all relevant Fermi level positions and different charge densities. The outcome is also supported by a Shubnikov–de Haas analysis of capacitance measurements, which allows us to obtain information on the degeneracy of the active modes. From these data, it is possible to reconstruct electron and hole dispersion relations. A detailed comparative analysis of the energy dispersion relations with theoretical calculations demonstrates a good agreement, even reflecting several subtle features like band splitting, the second conduction band, and the overlaps between the first conduction and the first valence band. Our study demonstrates that cyclotron resonance experiments can be efficiently used to directly obtain the band structures of semimetallic two-dimensional materials.

Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed imaginary swap (iswap) gates, however, require tuning qubit energies into resonance and have limited fidelity due to charge noise. We present a photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iswap gates.

We investigate the Andreev reflection and the Josephson effect in the $\alpha -T_3$ lattice, which falls between graphene ($\alpha =0$) and the dice lattice ($\alpha =1$), by adjusting the parameter $\alpha$. In the regime of the specular Andreev reflection, when the incident energy of the electron is small, the probability of Andreev reflection decreases as the parameter $\alpha$ increases. On the contrary, when the incident energy is large, the probability of Andreev reflection increases as the parameter $\alpha$ increases. Interestingly, when the incident energy approaches the superconducting energy gap function, the Andreev reflection with approximate all-angle perfect transmission happens in the case of $\alpha =1$. In the regime of Andreev retroreflection, when the parameter $\alpha$ increases, the probability of Andreev reflection increases regardless of the value of incident energy. When the incident energy approaches the superconducting energy gap function, the Andreev reflection with approximate all-angle perfect transmission happens regardless of the value of $\alpha$. We also give the differential conductance in these two regimes and find that it increases as the parameter $\alpha$ increases generally. In addition, the $\alpha -T_3$ lattice-based Josephson current increases as $\alpha$ increases. When the length of the junction approaches zero, the critical Josephson currents in the different values of $\alpha$ approach the same value.

We report scattering-induced valley polarization enhancement in monolayer molybdenum disulfide. With thermally activated and charge doping-introduced scattering, our sample exhibits 7- and 12-fold of improvements, respectively. This counterintuitive effect is attributed to disruptions to valley pseudospin precession caused by rapid modulation of exciton momentum and concomitant local exchange-interaction field, at timescales much shorter than the precession period. In contrast, the valley coherence is improved by thermally activated scattering, but not by charge doping-induced scattering. We propose that this is due to anisotropic pseudospin scattering and generalize the Maialle-Silva-Sham model to quantitatively explain our experimental results. Our work illustrates that cleaner samples with minimal scattering, such as those carefully suspended or protected by hexagonal boron nitride, do not necessarily lead to good valley polarization. Well-controlled scattering can in fact provide an interesting approach for improving valleytronic devices.

We present a general microscopic first-principles method to study the Coulomb-interaction-mediated heat transfer in the near field. Using the nonequilibrium Green's function formalism, we derive Caroli formulas for heat transfers between materials with translational invariance. The central physical quantities are the screened Coulomb potential and the spectrum function of polarizability. Within the random phase approximation, we calculate the polarizability using the linear response density functional theory and obtain the screened Coulomb potential from a retarded Dyson equation. We show that the heat transfer mediated by the Coulomb interaction is consistent with that of the $p$-polarized evanescent waves which dominate the heat transfer in the near field. We adopt single-layer graphene as an example to calculate heat transfers between two parallel sheets separated by a vacuum gap $d$. Our results show a saturation of heat flux at the extreme near field which is different from the reported $1/d$ dependence for local response functions. The calculated heat flux is up to $5\times {10}^4$ times more than the blackbody limit, and a $1/d^2$ dependence is shown at large separations. From the spectrum of energy current density, we infer that the near-field enhancement of heat transfer stems from electron transitions around the Fermi energy. With a uniform strain, the heat flux increases for most of the distances, while a negative correlation is shown at the moderate field. Our method is valid for inhomogeneous materials in which the macroscopic response function used in conventional theory of fluctuational electrodynamics would fail at the subnanometer scale.

We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent $\alpha$. We numerically study various probes for quantum chaos and eigenstate thermalization on the level of eigenvalues and eigenstates. The level-spacing statistics yields a clear sign towards a Wigner-Dyson distribution and therefore towards quantum chaos across all values of $\alpha >0$. Yet, for $\alpha <1$ we find that the microcanonical entropy is nonconvex. This is due to the fact that the spectrum is organized in energetically separated multiplets for $\alpha <1$. While quantum chaotic behavior develops within the individual multiplets, many multiplets do not overlap and do not mix with each other, as we analytically and numerically argue. Our findings suggest that a small fraction of the multiplets could persist at low energies for $\alpha \ll 1$ even for large $N$, giving rise to ensemble inequivalence.

The development of reliable and flexible machine learning based interatomic potentials (ML-IPs) is becoming increasingly important in studying the physical properties of complex condensed matter systems. Besides the structure descriptor model for total energy decomposition, the trial-and-error approach used in the design of the training dataset makes the ML-IP hardly improvable and reliable for modeling materials with chemical bond hierarchy. In this work, a dual adaptive sampling (DAS) method with an on the fly ambiguity threshold was developed to automatically generate an effective training dataset covering a wide temperature range or a wide spectrum of thermodynamic conditions. The DAS method consists of an inner loop for exploring the local configuration space and an outer loop for covering a wide temperature range. We validated the developed DAS method by simulating thermal transport of complex materials. The simulation results show that even with a substantially small dataset, our approach not only accurately reproduces the energies and forces but also predicts reliably effective high-order force constants to at least fourth order. The lattice thermal conductivity and its temperature dependence were evaluated using the Green-Kubo simulations with ML-IP for $\mathrm{Co}{\mathrm{Sb}}_3$ with up to third-order phonon scattering, and those for ${\mathrm{Mg}}_3{\mathrm{Sb}}_2$ with up to fourth-order phonon scattering, and all show good agreements with experiments. Our work provides an avenue to effectively construct a training dataset for ML-IP of complex materials with chemical bond hierarchy.

In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev $\left(K\right)$ and $\mathrm{\Gamma }$, leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the $\mathrm{\Gamma }$ model remains controversial. In particular, the phase diagram of the $K\mathrm{\Gamma }$ model with ferromagnetic $K$ and antiferromagnetic $\mathrm{\Gamma }$ interactions has been intensively studied because of its relevance to candidate materials such as $\alpha \text{−}{\mathrm{RuCl}}_3$. Numerical studies also included the effects of tuning the bond strengths, i.e., $z$-bond strength different from the other bonds. However, no clear consensus on the overall phase diagram has been reached yet. Here we study the classical $K\mathrm{\Gamma }$ model with anisotropic bond strengths using Monte Carlo simulations to understand the phases that emerge out of competition between the two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations. We found various large unit cell phases due to the competing frustrations, and analyzed their intrinsic degeneracy based on the symmetry of the Hamiltonian. Using the linear spin wave theory we showed that the anisotropic bond strength enhances quantum fluctuations in the $\mathrm{\Gamma }$-dominant regime where a small reduced moment is observed. The implications of our findings in relation to the quantum model are also discussed.

We study the propagation of probe pulses carrying orbital angular momentum (OAM) in a crystal of molecular magnets characterized by a double-$\mathrm{\Lambda }$ light-matter coupling scheme. The model is based on the four-wave mixing (FWM) of applied fields interacting with the magnetic dipole moment of the molecular magnets. We consider the light-matter interaction under the situation where a weak probe field carries an optical vortex and investigate the exchange of optical vortices between different frequencies via the FWM in the microwave region. The propagation of OAM beams with nonzero radial indices is then explored. It is found that the conservation of both azimuthal and radial indices is satisfied over the swapping of OAM states of light. Superimposing two initially weak OAM modes with different topological charges creates specific vortex beams with a very characteristic form. The resulting beam contains a central vortex as well as several singly charged peripheral vortices distributed at the same radial distance from the center of the light beam. This complex pattern of vortices arises because the intensity radius of two interfering OAM modes is different. It is shown that the boundary region of intensity dominance of two OAM modes can be controlled by the molecular magnets parameters and strong cw electromagnetic fields. Our proposed scheme may provide a route to study the solid systems suitable for quantum technologies as well as for OAM exchange devices for quantum information processing.

We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multiorbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which coexists with nematicity. We analyze the angular dependence of the gap function and specific heat $C_v\left(T\right)$ of such a nematic superconductor. We specifically address three issues: (i) the angular dependence of the gap in light of the competition between the nematicity-induced $s-d$ mixture and the orbital transmutation of low-energy excitations in the nematic state, (ii) the effect of nematicity on the magnitude of the jump of the specific heat $C_v\left(T\right)$ at $T_c$ and the temperature dependence of $C_v\left(T\right)$ below $T_c$, and (iii) a potential transition at $T_{c1}<T_c$ from an $s+d$ state to an $s+e^{i\eta }d$ state that breaks time-reversal symmetry. We consider two scenarios for a nematic order: scenario A, in which this order develops between $d_{xz}$ and $d_{yz}$ orbitals on hole and electron pockets, and scenario B, in which there is an additional component of the nematic order for $d_{xy}$ fermions on the two electron pockets.

The magnetic field of moving vortices in anisotropic superconductors is considered in the framework of the time-dependent London approach. It is found that, at distances large relative to the core size, the field may change sign that alludes to a nontrivial intervortex interaction which depends on the crystal anisotropy and on the speed and direction of motion. These effects are caused by the electric fields and corresponding normal currents which appear due to the moving vortex magnetic structure. We find that the motion related part of the magnetic field attenuates at large distances as $1/r^3$ unlike the exponential decay of the static vortex field. The electric field induced by the vortex motion decreases as $1/r^2$.