We study the in-gap states that appear at the boundaries of both one- and two-dimensional topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an $s$-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin polarized on either side of the topological phase boundary. We also demonstrate that the spatial position energy-level spacing and spin polarization of the VP states can be modified by the introduction of in-plane electric fields.

Precise measurements of the thermodynamic critical field ($B_{\mathrm{c}}$) in the type-I noncentrosymmetric superconductor BeAu were performed by means of the muon-spin rotation and relaxation technique. The temperature evolution of $B_{\mathrm{c}}$ cannot be described within the single-gap scenario and it requires the presence of at least two different types of superconducting order parameters. The self-consistent two-gap approach, adapted for analysis of $B_{\mathrm{c}}\left(T\right)$ behavior, suggests the presence of two superconducting energy gaps with the gap-to-$T_{\mathrm{c}}$ ratios $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}\simeq 4.52$ and $\simeq 2.37$ for the big gap and the small gap, respectively [$\mathrm{\Delta }=\mathrm{\Delta }(T=0)$ is the zero-temperature value of the gap and $k_{\mathrm{B}}$ is the Boltzmann constant]. This implies that the superconductivity in BeAu is unconventional and that the supercarrier pairing occurs at various energy bands.

The antiferromagnetic Ruddlesden-Popper ruthenate ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is a model polar metal, combining inversion symmetry breaking with metallic conductivity; however, its low-temperature ($T<48\mathrm{K}$) crystal structure and Fermi-surface topology remain ambiguous despite numerous measurements and theoretical studies. Here we perform both first-principles calculations with static correlations and angle-resolved photoelectron spectroscopy experiments to construct a complete model of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, reconciling inconsistencies among interpretations of electrical transport, thermopower measurements, and momentum- and energy-resolved band dispersions. The solution relies on treating the interplay among Coulomb repulsion, magnetic ordering, spin-orbit interactions, and the ${\mathrm{RuO}}_6$ octahedral degrees of freedom on equal footing. For temperatures $30<T<48\mathrm{K}$, we propose weak electron-electron interactions produce a symmetry-preserving metal-semimetal transition with Weyl nodes in proximity to the Fermi level, whereas an orthorhombic $Pn{2}_{1}a$ structure emerges for $T<30\mathrm{K}$, exhibiting charge- and spin-density waves from enhanced Coulombic interactions.

We investigate the emergence of an astonishingly long prethermal plateau in a classical phonon field, here, a harmonic chain with on-site pinning. Integrability is broken by a weak anharmonic on-site potential with strength $\lambda$. In the small $\lambda$ limit, the approach to equilibrium of a translation invariant initial state is described by kinetic theory. However, when the phonon band becomes narrow, we find that the (nonconserved) number of phonons relaxes on much longer timescales than kinetic. We establish rigorous bounds on the relaxation time and develop a theory that yields exact predictions for the dissipation rate in the limit $\lambda \to 0$. We compare the theoretical predictions with data from molecular-dynamics simulations and find good agreement. Our Rapid Communication shows how classical systems may exhibit phenomena which, at the first glance, appear to require quantization.

We report the numerical investigation of strain-induced superconductor-insulator quantum phase transition on a Lieb lattice. Based on a nonperturbative Monte Carlo technique, which retains the spatial fluctuations of the superconducting pairing field at all orders but neglects the temporal fluctuations, we show that in two dimensions, an $s$-wave superconductor undergoes transition to a highly correlated bosonic insulator under the influence of strain, applied as staggered hopping amplitudes. We further demonstrate a strain-induced BCS-BEC like crossover in the superconducting state, such that the superconductor-insulator transition takes place between a bosonic superconductor and a bosonic insulator. Our results suggest that it is the contribution of the dispersive bands towards the superconducting order that dictates this crossover. To the best of our knowledge, this is the first work to report a theoretical investigation of “disorder free” superconductor-insulator phase transition in systems with Lieb lattice structure. With the recent experimental realization of the Lieb lattice in ultracold atomic gases, photonic lattices as well as in solid state systems, we believe that the results presented in this paper would be of importance to initiate experimental investigation of such novel quantum phase transitions. We further discuss the fate of such systems at finite temperature, highlighting the effect of fluctuations on the superconducting pair formations, thermal scales, and quasiparticle behavior. Our nonperturbative numerical approach to the problem enables us to capture the thermal scales of the system accurately and provides us with mean-field estimates of the ground state properties. The high-temperature quasiparticle signatures discussed in this paper are expected to serve as benchmarks for experiments such as radio frequency and momentum resolved radio frequency spectroscopy measurements carried out on systems such as ultracold atomic gases.

We study mechanisms of control of charge state and concentration of different point defects in doped insulating crystals. The approach is based on the density functional theory calculations. We apply it to the problem of obtaining of Ti-doped sapphire crystals with high figure of merit (FOM). The FOM of a given sample is defined as the ratio of the coefficient of absorption at the pump frequency to the coefficient of absorption at the working frequency of a Ti:sapphire laser. It is one of standard specifications of commercial Ti:sapphire laser crystals. It is believed that the FOM is proportional to the ratio of the concentration of isolated ${\mathrm{Ti}}^{3+}$ ions to the concentration of ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{4+}$ pairs. We find that generally this ratio is in inverse proportion to the concentration of ${\mathrm{Ti}}^{4+}$ isolated substitutional defects with the coefficient of proportionality that depends on the temperature at which the thermodynamic equilibrium concentration of defects is reached. We argue that in certain cases the inverse proportion between concentrations of ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{4+}$ and ${\mathrm{Ti}}^{4+}$ may be violated. The role of codoping in the control of the charge state of dopants is analyzed. We show that codopants that form positively (negatively) charged defects may decrease (increase) the concentration of positively charged defects formed by the main dopants. To evaluate the effect of codoping it is important to take into account not only isolated defects but defect complexes formed by codopants, as well. In particular, we show that codoping of Ti:sapphire with nitrogen results in an essential increase of the concentration of ${\mathrm{Ti}}^{4+}$ and in a decrease of the FOM, and, consequently, growth or annealing in the presence of nitrogen or its compounds is unfavorable for producing Ti:sapphire laser crystals. The approach developed can be used for determining appropriate growth and annealing conditions for obtaining doped crystals with the required characteristics.

High-throughput density functional calculations are used to investigate the effect of interstitial B, C, and N atoms on 21 alloys reported to crystallize in the cubic ${\mathrm{Cu}}_3\mathrm{Au}$ structure. It is shown that the interstitials can have a significant impact on the magnetocrystalline anisotropy energy (MAE), the thermodynamic stability, and the magnetic ground-state structure, making these alloys interesting for hard magnetic, magnetocaloric, and other applications. For 29 alloy-interstitial combinations the formation of stable alloys with interstitial concentrations above 5% is expected. In ${\mathrm{Ni}}_3\mathrm{Mn}$ interstitial N induces a tetragonal distortion with substantial uniaxial MAE for realistic N concentrations. ${\mathrm{Mn}}_{3}X{\mathrm{N}}_x$ ($X$ = Rh, Ir, Pt, and Sb) compounds are identified as alloys with strong magnetocrystalline anisotropy. For ${\mathrm{Mn}}_3\mathrm{Ir}$ we find a strong enhancement of the MAE upon N alloying in the most stable collinear ferrimagnetic state as well as in the noncollinear magnetic ground state. ${\mathrm{Mn}}_3\mathrm{Ir}$ and ${\mathrm{Mn}}_3\mathrm{IrN}$ also show interesting topological transport properties. The effects of N concentration and strain on the magnetic properties are discussed. Further, the huge impact of N on the MAE of ${\mathrm{Mn}}_3\mathrm{Ir}$ and a possible impact of interstitial N on amorphous ${\mathrm{Mn}}_3\mathrm{Ir}$, a material that is indispensable in today's data storage devices, are discussed in relation to the electronic structure. For ${\mathrm{Mn}}_3\mathrm{Sb}$, noncollinear, ferrimagnetic, and ferromagnetic states are very close in energy, making this material potentially interesting for magnetocaloric applications. For the investigated Mn alloys and competing phases, the determination of the magnetic ground state is essential for a reliable prediction of the phase stability.

We derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [Shi, Kato, and Kim, Ann. Phys., 168164 (2020)]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological $S$ matrix of an abstract anyon theory. We show that the $S$ matrix is unitary and that it recovers the fusion multiplicities of the underlying anyon theory through the Verlinde formula. Importantly, we rigorously prove the modularity of the theory, which further implies that the mutual braiding statistics of anyons are nontrivial. The key to the proof is a generalized quantum state merging technique, which generates a topology beyond that of any subsystem of the original physical system.

The origin of the planar Hall effect (PHE) in various nonmagnetic semimetals has become a subject of considerable interest, especially in regard to the chiral anomaly that several of these semimetals exhibit. Here, we report a large PHE that exceeds several mΩ cm over a wide range of temperature $T$ and magnetic field $B$ in micron-thick single-crystalline bismuth thin films grown by molecular beam epitaxy techniques. The angular dependence of the PHE and the related anisotropic magnetoresistance (AMR) show complex behaviors as a function of $B$ and $T$. At high temperatures and in modest magnetic fields, the PHE and AMR can be quantitatively explained by a semiclassical transport model based on the well-established elongated electron and hole pockets of the Fermi surface in bismuth. Although these results establish an anisotropic electronic orbital origin of the PHE, we find that when the electric current is oriented along the binary axis of bismuth, the PHE and AMR behaviors can be well described by a model based on the chiral anomaly in Weyl or Dirac semimetals. However, this model cannot account for these behaviors when the current is rather oriented along the bisectrix axis. Thus, the anisotropy of the PHE is a useful test to check on the validity of the chiral anomaly in semimetals.

Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that the ${\mathbb{Z}}_N$ Berry phase (Berry phase quantized into $2\pi /N$) is a useful tool to characterize the symmetry-protected topological states, whereas the experimental evidence is still elusive. Recently, topolectrical circuits have emerged as a simple yet very powerful platform for studying topological physics that are challenging to realize in condensed-matter systems. Here, we present an experimental observation of second-order corner states characterized by the ${\mathbb{Z}}_3$ Berry phase in topolectrical circuits. We demonstrate theoretically and experimentally that the localized second-order topological states are protected by a generalized chiral symmetry of tripartite lattices, and they are pinned to “zero energy.” By introducing extra capacitors within sublattices in the circuit, we are able to examine the robustness of the zero modes against both chiral-symmetry-conserving and breaking disturbances. Our Rapid Communication paves the way for testing exotic topological band theory by electrical-circuit experiments.

Currently there is a growing interest in studying the coherent interaction between magnetic systems and electromagnetic radiation in a cavity, prompted partly by possible applications in hybrid quantum systems. We propose a multimode cavity optomagnonic system based on antiferromagnetic insulators, where optical photons couple coherently to the two homogeneous magnon modes of the antiferromagnet. These have frequencies typically in the THz range, a regime so far mostly unexplored in the realm of coherent interactions, and which makes antiferromagnets attractive for quantum transduction from THz to optical frequencies. We derive the theoretical model for the coupled system, and show that it presents unique characteristics. In particular, if the antiferromagnet presents hard-axis magnetic anisotropy, the optomagnonic coupling can be tuned by a magnetic field applied along the easy axis. This allows us to bring a selected magnon mode into and out of a dark mode, providing an alternative for a quantum memory protocol. The dynamical features of the driven system present unusual behavior due to optically induced magnon-magnon interactions, including regions of magnon heating for a red-detuned driving laser. The multimode character of the system is evident in a substructure of the optomagnonically induced transparency window.

Internodal dynamics of quasiparticles in Weyl semimetals manifest themselves in hydrodynamic, transport, and thermodynamic phenomena and are essential for potential valleytronic applications of these systems. In an external magnetic field, coherent quasiparticle tunnelling between the nodes modifies the quasiparticle dispersion and, in particular, opens gaps in the dispersion of quasiparticles at the zeroth Landau level. We study magnetotransport in a Weyl semimetal taking into account mechanisms of quasiparticle scattering, both affected by such gaps and independent of them. We compute the longitudinal resistivity of a disordered Weyl semimetal with two nodes in a strong magnetic field microscopically and demonstrate that in a broad range of magnetic fields, it has a strong angular dependence, $\rho \left(\eta \right)\propto C_1+C_2{cos}^2\eta$, where $\eta$ is the angle between the field and the separation between the nodes in momentum space. The first term is determined by the coherent internodal tunnelling and is important only at angles $\eta$ close to $\pi /2$. This contribution depends exponentially on the magnetic field, $\propto exp\left(-B_0/B\right)$. The second term is weakly dependent on the absolute value of the magnetic field for realistic concentrations of the impurities in a broad interval of fields.

In many unconventional superconductors, nematic quantum fluctuations are strongest where the critical temperature is highest, inviting the conjecture that nematicity plays an important role in the pairing mechanism. Recently, ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Ni}}_2{\mathrm{As}}_2$ has been identified as a tunable nematic system that provides an ideal testing ground for this proposition. We therefore propose several sharp empirical tests, supported by quantitative calculations in a simple model of ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Ni}}_2{\mathrm{As}}_2$. The most stringent predictions concern experiments under uniaxial strain, which has recently emerged as a powerful tuning parameter in the study of correlated materials. Since uniaxial strain so precisely targets nematic fluctuations, such experiments may provide compelling evidence for nematic-mediated pairing, analogous to the isotope effect in conventional superconductors.

The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read out by measuring the mean chiral displacement of a single-particle wave function that is connected to a fully localized one via a unitary and translation-invariant map. Remarkably, this implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases. We confirm experimentally these results in a quantum walk of structured light.

The celebrated Dyson singularity signals the relative delocalization of single-particle wave functions at the zero-energy symmetry point of disordered systems with a chiral symmetry. Here we show that analogous zero modes in interacting quantum systems can fully localize at sufficiently large disorder, but do so less strongly than nonzero modes, as signified by their real-space and Fock-space localization characteristics. We demonstrate this effect in a spin-1 Ising chain, which naturally provides a chiral symmetry in an odd-dimensional Hilbert space, thereby guaranteeing the existence of a many-body zero mode at all disorder strengths. In the localized phase, the bipartite entanglement entropy of the zero mode follows an area law, but is enhanced by a system-size-independent factor of order unity when compared to the nonzero modes. Analytically, this feature can be attributed to a specific zero-mode hybridization pattern on neighboring spins. The zero mode also displays a symmetry-induced even-odd and spin-orientation fragmentation of excitations, characterized by real-space spin-correlation functions, which generalizes the sublattice polarization of topological zero modes in noninteracting systems, and holds at any disorder strength.

Recent advances in tuning electronic, magnetic, and topological properties of two-dimensional (2D) magnets have opened a new frontier in the study of quantum physics and promised exciting possibilities for future quantum technologies. In this study, we find that the dual-gate technology can well tune the electronic and topological properties of antiferromagnetic (AFM) even septuple-layer (SL) ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ thin films. Under an out-of-plane electric field that breaks $\mathcal{PT}$ symmetry, the Berry curvature of the thin film could be engineered efficiently, resulting in a huge change of anomalous Hall (AH) signal. Beyond the critical electric field, the double-SL ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ thin film becomes a Chern insulator with a high Chern number of 3. We further demonstrate that such 2D material can be used as an AFM switch via electric-field control of the AH signal. These discoveries inspire the design of low-power memory prototypes for future AFM spintronic applications.

Scanning tunneling microscopy (STM) is a notoriously slow technique; data-recording is serial, which renders complex measurement tasks, such as quasiparticle interference (QPI) mapping, impractical. However, QPI could provide insight into band-structure details of quantum materials that can be inaccessible to angle-resolved photoemission spectroscopy. Here we use compressed sensing (CS) to fundamentally speed-up QPI mapping. We reliably recover the QPI information from a fraction of the usual local density of state measurements. The requirement of CS is naturally fulfilled for QPI, since CS relies on sparsity in a vector domain, here given by few nonzero coefficients in Fourier space. We exemplify CS on a simulated Cu(111) surface using random sampling of uniform and varying probability density. The latter improves QPI recovery and mitigates Fourier artifacts. We further simplify the motion of the STM tip through an open traveling salesman's problem for greater efficiency and use the tip-path for drift correction. We expect that the implications of our CS approach will be transformative for the exploration of two-dimensional quantum materials.

Quantum batteries, composed of quantum cells, are expected to outperform their classical analogs. The origin of such advantages lies in the role of quantum correlations, which may arise during the charging and discharging processes performed on the battery. In this theoretical work, we introduce a systematic characterization of the relevant quantities of quantum batteries, i.e., the capacity and the power, in relation to such correlations. For these quantities, we derive upper bounds for batteries that are a collection of noninteracting quantum cells with fixed Hamiltonians. The capacity, that is, a bound on the stored or extractable energy, is derived with the help of the energy-entropy diagram, and this bound is respected as long as the charging and discharging processes are entropy preserving. While studying power, we consider a geometric approach for the evolution of the battery state in the energy eigenspace of the battery Hamiltonian. Then, an upper bound for power is derived for arbitrary charging process, in terms of the Fisher information and the energy variance of the battery. The former quantifies the speed of evolution, and the latter encodes the nonlocal character of the battery state. Indeed, due to the fact that the energy variance is bounded by the multipartite entanglement properties of batteries composed of qubits, we establish a fundamental bound on power imposed by quantum entanglement. We also discuss paradigmatic models for batteries that saturate the bounds both for the stored energy and power. Several experimentally realizable quantum batteries, based on integrable spin chains, the Lipkin-Meshkov-Glick and the Dicke models, are also studied in the light of these newly introduced bounds.

We present ultrafast resonant inelastic x-ray scattering (RIXS) experiments performed at the vanadium $L$ edge to track changes in the electronic structure of ${\mathrm{V}}_2{\mathrm{O}}_3$, a classical Mott-Hubbard material. The probed orbital excitations within the $d$ shell of the V ion show a sub-ps time response, which evolves at later times to a state that appears electronically indistinguishable from the high-temperature metallic state. For low excitation fluences, a transient recovery or delay is observed, which could be related to a transient dimerization of the V-V bonds. Our results demonstrate the great potential for RIXS spectroscopy to study the ultrafast orbital dynamics in strongly correlated materials.

An accurate description of the two-electron density, crucial for magnetic coupling in spin systems, provides in general a major challenge for density functional theory calculations. It affects, e.g., the calculated zero-field splitting (ZFS) energies of spin qubits in semiconductors that frequently deviate significantly from experiment. In the present work, (i) we propose an efficient and robust strategy to correct for spin contamination in both extended periodic and finite-size systems, (ii) verify its accuracy using model high-spin molecules, and finally, (iii) apply the methodology to calculate accurate ZFS of spin qubits (${\mathrm{NV}}^{-}$ centers, divacancies) in diamond and silicon carbide. The approach is shown to reduce the dependence on the used exchange-correlation functional to a minimum.