Inhomogeneous superconductivity was studied in ${\mathrm{ZrB}}_{12}$ $\left(T_{\mathrm{c}}\approx 6\mathrm{K}\right)$ using heat capacity and x-ray diffraction data. Evidence of two-band superconductivity with two branches of upper critical field ${\mathbf{H}}_{c2}\left(T_c\right)$ is obtained in a magnetic field applied along the [110] axis of the crystal. On the contrary, at H || [100], a single dependence $\mathbf{H}{c}_2\left(T_c\right)$ was observed. This finding is consistent with the checkerboard-type patterns observed on the difference Fourier maps of the electron density distribution. These patterns are compared to those for the weakly coupled superconductor ${\mathrm{LuB}}_{12}$, $T_{\mathrm{c}}$ of which is 15 times lower than that of ${\mathrm{ZrB}}_{12}$. The probable nature of the two-gap superconductivity in ${\mathrm{ZrB}}_{12}$ is discussed.

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wavelike structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interaction due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave vectors in the limit of weakly coupled ladders.

Strontium titanate ($\mathrm{SrTi}{\mathrm{O}}_3$) is regarded as an essential material for oxide electronics. One of its many remarkable features is the subtle structural phase transition, driven by the antiferrodistortive lattice mode, from a high-temperature cubic phase to a low-temperature tetragonal phase. Classical molecular dynamics (MD) simulation is an efficient technique to reveal atomistic features of phase transition, but its application is often limited by the accuracy of empirical interatomic potentials. Here, we develop an accurate deep potential (DP) model of $\mathrm{SrTi}{\mathrm{O}}_3$ based on a machine learning method using data from first-principles density functional theory (DFT) calculations. The DP model has DFT-level accuracy, capable of performing efficient MD simulations and accurate property predictions. Using the DP model, we investigate the temperature-driven cubic-to-tetragonal phase transition and construct the in-plane biaxial strain-temperature phase diagram of $\mathrm{SrTi}{\mathrm{O}}_3$. The simulations demonstrate that the strain-induced ferroelectric (FE) phase is characterized by two order parameters, FE distortion and antiferrodistortion, and the FE phase transition has both displacive and order-disorder characters. In this paper, we lay the foundation for the development of accurate DP models of other complex perovskite materials.

It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-$\frac{1}{2}$ Heisenberg diamond and octahedral chains. In addition to monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-$\frac{1}{2}$ Heisenberg diamond (octahedral) chain. The feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly degenerate manifold of low-lying excitations.

In ${\mathrm{Sr}}_2{\mathrm{NiIrO}}_6$ long-range Ir-Ir antiferromagnetic exchange interactions have been reported to overcome the ferromagnetic Ni-Ir interactions hampering the otherwise expected ferromagnetic behavior. Prompted by this, a combination of x-ray absorption spectroscopy and x-ray diffraction at high pressure is used here to investigate the interplay between the magnetic structure of the Ir sublattice and lattice degrees of freedom. The compression of ${\mathrm{Sr}}_2{\mathrm{NiIrO}}_6$ drives an unexpected nonmonotonic change of the x-ray magnetic circular dichroism (XMCD) spectra: The intensity first decreases in the 0- to 18-GPa range, then shows an increase in the 18- to 30-GPa range and again decreases for higher pressures. The XMCD intensity, a measure of the net magnetization in the Ir sublattice, however, is found to remain very low in the whole pressure range so the observed changes do not correspond with a transition from antiferromagnetic to ferromagnetic or ferrimagnetic order. The evolution of the XMCD is better explained in terms of a weakening/strengthening of the long-range antiferromagnetic (AFM) Ir-Ir interaction between ferromagnetic planes associated with the reduction of the lattice parameters. In particular, a correlation can be established between the evolution of the $b$/$a$ ratio and the weakening/strengthening of the AFM interaction.

The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk continuum can become localized on the edges, making the distinction between edge and bulk states challenging. We establish the bulk-boundary correspondence for a Chern insulator model with non-Hermitian skin effect by combining two approaches (“non-Bloch” approach and “biorthogonal” approach). Both approaches can suppress the skin effect but they are based on different mathematical tools. A biorthogonal inverse participation ratio is used as a measure to distinguish between bulk states and edge states, and a non-Bloch Chern number is used to characterize the topology and predict the number of topological edge bands. In addition to tangential degeneracies, crossing degeneracies are found to occur between the bulk and edge bands. Their presence enriches the (de)localization behavior of the edge states but does not affect the Chern number. The phase diagram of the system has interesting features that are not found in Hermitian systems. For example, one topological transition and two non-Hermitian phase transitions can be induced by tuning a single parameter. The gapless phase is topologically protected due to the stable existence of the non-Hermitian band degeneracies guaranteed by nonzero discriminant numbers.

The local magnetic moment of an interacting quantum dot occupied by a single electron can be screened by binding a Bogoliubov quasiparticle from a nearby superconductor. This gives rise to a long-lived discrete spin-singlet state inside the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state. We study the nature of the subgap states induced by a quantum dot embedded between two small superconducting islands. We show that this system has two spin-singlet subgap states with different spatial charge distributions. These states can be put in a linear superposition and coherently manipulated using electric-field pulses applied on the gate electrode. Such a YSR qubit could be implemented using present-day technology.

We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors ${\nu }_G=-2+n/3(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $\text{SU}\left(4\right)$ symmetric limit. For all the fractions we study, there are two-component states for which the competing phases are generalizations of those occurring at neutrality ${\nu }_G=0$. They are ferromagnetic, antiferromagnetic, charge-density wave, and Kékulé phases, depending on the values of Ising or $XY$ anisotropies in valley space. The varying spin-valley content of the states leads to ground-state quantum numbers that are different from the ${\nu }_G=0$ case. For filling factor ${\nu }_G=-2+5/3$, there is a parent state in the $\text{SU}\left(4\right)$ limit that has a flavor content $(1,1/3,1/3,0)$ where the two components that are one-third filled form a two-component singlet. The addition of anisotropies leads to the formation of new states that have no counterpart at ${\nu }_G=0$. While some of them are predicted by the variational approach, we find notably that negative Ising-like valley anisotropy leads to the formation of a state that is a singlet in both spin and valley space and lies beyond the reach of the variational method. Also fully spin polarized two-component states at $\nu =-2+4/3$ and $-2+5/3$ display an emergent $\text{SU}\left(2\right)$ valley symmetry because they do not feel point-contact anisotropies. We discuss implications for current experiments concerning possible spin transitions.

Excitons in a semiconductor monolayer form a collective resonance that can reflect resonant light with extraordinarily high efficiency. Here, we investigate the nonlinear optical properties of such atomistically thin mirrors and show that finite-range interactions between excitons can lead to the generation of highly nonclassical light. We describe two scenarios, in which optical nonlinearities arise either from direct photon coupling to excitons in excited Rydberg states or from resonant two-photon excitation of Rydberg excitons with finite-range interactions. The latter case yields conditions of electromagnetically induced transparency and thereby provides an efficient mechanism for single-photon switching between high transmission and reflectance of the monolayer, with a tunable dynamical timescale of the emerging photon-photon interactions. Remarkably, it turns out that the resulting high degree of photon correlations remains virtually unaffected by Rydberg-state decoherence, in excess of nonradiative decoherence observed for ground-state excitons in two-dimensional semiconductors. This robustness to imperfections suggests a promising approach to quantum photonics at the level of individual photons.

Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons in 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, we find that phonons in both graphdiyne and $\gamma$-graphyne exhibit a second-order topology, which belongs to the specific case known as real Chern insulator. We identify the nontrivial phononic band gaps, which are characterized by nontrivial real Chern numbers enabled by the spacetime inversion symmetry. The protected phonon corner modes are verified by the calculation on a finite-size nanodisk. In addition, we show that a 3D real Chern insulator state can be realized for phonons in 3D graphdiyne. Our study extends the scope of higher-order topology to phonons in real materials. The spatially localized phonon modes could be useful for novel phononic applications.

Two-dimensional semi-Dirac materials, with quadratic dispersion in one direction and linear dispersion in the orthogonal direction, provide a route to formation of the Chern-insulating states in solids. Within the framework of the Floquet theory, we investigate the photon-modulated linear and nonlinear anomalous Hall effect (AHE) in type-II semi-Dirac semimetals and find that rich topological phases, as well as interesting phenomena related to the topological transitions, can be realized and manipulated by circularly polarized light (CPL). By tuning the CPL parameters, we can control the local inverted gaps independently and switch the system between different topological phases optionally. We also demonstrate that, when the Fermi level locates outside the gap, the Drude component of the conductivity can contribute to the AHE as well, because of the anisotropy of the electronic structure. Besides, the nonlinear Hall effect due to the Berry curvature dipole can be observable when the inversion symmetry between opposite valleys is broken. Our findings are helpful to understand the topological properties of the emergent type-II semi-Dirac semimetals.

We study the spin of the localized quasiparticle excitations of lowest-Landau-level quantum Hall states defined on a disk. The spin that we propose satisfies the spin-statistics relation and can be used to reconstruct the topological geometric phase associated to the exchange of two arbitrarily chosen quasiparticles. Since it is related to the quadrupole moment of the quasiparticle charge distribution, it can be measured in an experiment and could reveal anyonic properties in a way that is complementary to the interferometric schemes employed so far. We first discuss our definition for the quasiholes of the Laughlin state, for which we present a numerical and analytical study of our spin, and we proceed with a discussion of several kinds of quasiholes of the Halperin 221 state. Finally, we discuss the link between our spin and the adiabatic rotation of the quasiparticles around their axis and demonstrate that our spin obeys the spin-statistics relation.

In this work, we report the coexistence of type-II Weyl points and triply degenerate points while taking the nonlocal effect into account in a chiral photonic metamaterial system. The chiral effect introduces a break in the spatial inversion symmetry, which is necessary for the generation of nodal points. These nodal points are symmetrically distributed on the $k_z$ axis and possess the time-reversal symmetry-protection mechanism. Remarkably, the projections of all nodal points are connected by a Fermi arc surface state, and it agrees well with the single monopole charges of these nodal points, which demonstrates the topological characteristics of the band degenerate points. We theoretically show that the localized Fermi arc can be formed at the interface between the metamaterial and vacuum, which may improve the compactness of photonic devices. Especially, the nonreciprocal surface waves can propagate forward around the sharp corner without experiencing backscattering, which can be used for the robust transmission of information.

We study the spin-one Kitaev model on the honeycomb lattice in the presence of single-ion anisotropies. We consider two types of single ion anisotropies: A $D_{111}$ anisotropy which preserves the symmetry between $X, Y$, and $Z$ bonds but violates flux conservation and a $D_{100}$ anisotropy that breaks the symmetry between $X, Y$, and $Z$ bonds but preserves flux conservation. We use series expansion methods, degenerate perturbation theory, and exact diagonalization to study these systems. Large positive $D_{111}$ anisotropy leads to a simple product ground state with conventional magnonlike excitations, while large negative $D_{111}$ leads to a broken symmetry and degenerate ground states. For both signs there is a phase transition at a small $|D_{111}|\approx 0.12$ separating the more conventional phases from the Kitaev spin liquid phase. With large $D_{100}$ anisotropy, the ground state is a simple product state, but the model lacks conventional dispersive excitations due to the large number of conservation laws. Large negative $D_{100}$ leads to decoupled one-dimensional systems and many degenerate ground states. No evidence of a phase transition is seen in our numerical studies at any finite $D_{100}$. Convergence of the series expansion extrapolations all the way to $D_{100}=0$ suggests that the nontrivial Kitaev spin liquid is a singular limit of this type of single-ion anisotropy going to zero, which also restores symmetry between the $X, Y$, and $Z$ bonds.

A first-principle-based effective Hamiltonian model is developed to investigate electrocaloric effects (ECE) of ferroelectric $\mathrm{Pb}\left({\mathrm{Sc}}_{0.5}{\mathrm{Ta}}_{0.5}\right)\mathrm{O}3$ (PST) possessing different degrees of chemical ordering between Sc and Ta cations. It is found that PST exhibits large electrocaloric effects when the electric field drives a paraelectric-to-ferroelectric phase transition isothermally above the Curie temperature. More precisely, for any specific temperature above the Curie temperature, the electrocaloric coefficient exhibits its maximum at a critical electric field that is precisely the threshold of percolation for which the polar nanoregions begin to propagate inside the whole sample, with dipoles being parallel to the field's direction. This percolation-induced maximal ECE occurs for all the possible degrees of chemical ordering, therefore making it a general and novel mechanism, based on which a strategy is further proposed to improve the ECE.

The Heisenberg antiferromagnet with discrete disorder on an infinite square lattice is evolved in time from an initial Néel state. The simulation is performed with the neighborhood tensor update algorithm for an infinite projected entangled pair state [Dziarmaga, Phys. Rev. B 104, 094411 (2021)]. Ancillary spins are used to average over two or five discrete values of disorder. With a bond dimension up to 20, evolution times are long enough to identify a many-body localized regime for a strong enough disorder. Furthermore, the same Hamiltonian is subject to periodic spin flips. Simulations of the Floquet dynamics show that it can sustain a time crystalline stage for a strong enough disorder.

In this paper, we provide a complete description of the life cycle of entanglement during the real-time motion of open quantum systems. The quantum environment can have arbitrary (e.g., structured) spectral density. The entanglement can be seen constructively as a Lego: its bricks are the modes of the environment. These bricks are connected to each other via operator transforms. The central result is that during each infinitesimal time interval one new (incoming) mode of the environment gets coupled (entangled) to the open system, and one new (outgoing) mode gets irreversibly decoupled (disentangled from the future). Moreover, each moment of time, only a few relevant modes (three to four in the considered cases) are non-negligibly coupled to the future quantum motion. These relevant modes change (flow or renormalize) with time. As a result, the temporal entanglement has the structure of a matrix-product operator. This allows us to pose a number of questions and to answer them in this paper: What is the intrinsic quantum complexity of a real time motion? Does this complexity saturate with time or grow without bounds? How does one do the real-time renormalization group in a justified way? How do the classical Brownian stochastic trajectories emerge from the quantum evolution? How does one construct the few-mode representations of non-Markovian environments? We provide illustrative simulations of the spin-boson model for various spectral densities of the environment: semicircle, subohmic, ohmic, and superohmic.

This year, researchers have been on the lookout for real materials with one-nodal, two-nodal (two-NS), and three-nodal surface phonons. However, materials with two-NS phonons have been scarce until recently. This paper contributes to the understanding of the symmetry conditions of two-NS phonons. Two-NS phonons have NS states that are localized on two of three $k_i=\pm \pi$ $(i=x,y,z)$ planes in the three-dimensional Brillouin zone). They are dominated by twofold screw symmetry and time-reversal symmetry. This paper also contributes the prediction of a series of materials with two-NS states in their phonon dispersions. First, by screening all 230 space groups (SGs), we discovered 19 SG candidates (with Nos. 18, 55–60, 90, 94, 113, 114, 127–130, and 135–138) that have two-NS phonons. Second, based on first-principles calculations, we proposed 19 realistic material candidates hosting two-NS phonons: $P{2}_1{2}_{1}2$-type ${\mathrm{ZnTeMoO}}_6$ (with SG No. 18), $Pbma$-type ${\mathrm{Cs}}_2{\mathrm{Te}}_2$ (with SG No. 55), $Pccn$-type ${\mathrm{Sr}}_2{\mathrm{SnO}}_4$ (with SG No. 56), $Pbcm$-type CaAlPd (with SG No. 57), $Pnnm$-type ${\mathrm{PtO}}_2$ (with SG No. 58), $Pmmn$-type ${\mathrm{KLi}}_2\mathrm{As}$ (with SG No. 59), $Pbcn$-type ${\mathrm{CV}}_2$ (with SG No. 60), $P{42}_{1}2$-type ${\mathrm{BaVCu}}_4{\mathrm{P}}_4{\mathrm{O}}_{17}$ (with SG No. 90), $P{4}_2{2}_{1}2$-type ${\mathrm{Na}}_5{\mathrm{Fe}}_3{\mathrm{F}}_{14}$ (with SG No. 94), $P\overline{4}{2}_{1}m$-type ${\mathrm{BaS}}_3$ (with SG No. 113), $P\overline{4}{2}_{1}c$-type ${\mathrm{Na}}_4{\mathrm{SnS}}_4$ (with SG No. 114), $P4/mbm$-type ${\mathrm{ReO}}_3$ (with SG No. 127), $P4/mnc$-type ${\mathrm{Sr}}_4{\mathrm{Li}}_2{\mathrm{Si}}_4{\mathrm{N}}_8\mathrm{O}$ (with SG No. 128), $P4/nmm$-type ${\mathrm{BaHfN}}_2$ (with SG No. 129), $P4/ncc$-type ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ (with SG No. 130), $P{4}_2/mbc$-type ${\mathrm{YB}}_2\mathrm{C}$ (with SG No. 135), $P{4}_2/mnm$-type ${\mathrm{MgF}}_2$ (with SG No. 136), $P{4}_2/nmc$-type ${\mathrm{YB}}_4{\mathrm{Rh}}_4$ (with SG No. 137), and $P{4}_2/ncm$-type ${\mathrm{LiClO}}_2$ (with SG No. 138). Third, we discovered 622 (out of 10 037) materials with two-NS phonons by checking the phonon database at Kyoto University. Our present paper provides a better understanding of the two-NS states in phonon systems (or even other bosonic systems) and suggests a huge number of material candidates with two-NS phonons.

We present magnetization measurements carried out on polycrystalline and single-crystalline samples of $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under hydrostatic pressures up to 2 GPa and establish the temperature-pressure phase diagram of this material. The Néel temperature ($T_{\mathrm{N}}$) of $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ is slightly enhanced upon compression with $d{T}_{\mathrm{N}}/dp$ = 1.5 K/GPa. Above 1.2 GPa, $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ undergoes a first-order phase transition toward a nonmagnetic dimerized phase, with no traces of the magnetic phase observed above 1.8 GPa at low temperatures. The critical pressure of the structural dimerization is strongly temperature dependent. This temperature dependence is well reproduced on the ab initio level by taking into account lower phonon entropy in the nonmagnetic phase. We further show that the initial increase in $T_{\mathrm{N}}$ of the magnetic phase is due to a weakening of the Kitaev interaction $K$ along with the enhancement of the Heisenberg term $J$ and off-diagonal anisotropy $\mathrm{\Gamma }$. Our study reveals a common thread in the interplay of magnetism and dimerization in pressured Kitaev materials.

In this work we study thermodynamic manifestations of the quantum criticality in multiband unconventional superconductors. As a guiding example we consider the scenario of magnetic quantum critical point in the model that captures superconductivity coexistence with the spin-density wave. We show that in situations when the superconducting order parameter has incidental nodes at isolated points, quantum magnetic fluctuations lead to the renormalization of the relative $T$-linear slope of the London penetration depth. This leads to the nonmonotonic dependence of the penetration depth as a function of doping and the concomitant peak structure across the quantum critical point. In addition, we determine contribution of magnetic fluctuations to the specific heat at the onset of the coexistence phase. Our theoretical analysis is corroborated by making a comparison of our results with the recent experimental data from the low-temperature thermodynamic measurements at optimal composition in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$.