High-$T_c$ superconductivity (SC) has been found experimentally in the bilayer material ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under high pressure recently, in which the Ni-$3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals are expected to play a key role in the electronic structure and the SC. Here we study the two-orbital electron correlations and the nature of the SC in the framework of the dynamical mean-field theory using the bilayer two-orbital Hubbard model downfolded from the band structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. We find that each of the two orbitals forms $s_{\pm }$-wave SC pairing. Because of the interorbital hoppings, the two-orbital SCs are concomitant, and furthermore they transition to Mott insulating states simultaneously when tuning the system to half filling. The Hund's coupling induced local interorbital spin coupling enhances the electron correlations pronouncedly and is crucial to the SC.

Rydberg excitons are the solid-state analogs of Rydberg atoms and can, e.g., for cuprous oxide, easily reach a large size in the region of $\mu \mathrm{m}$ for principal quantum numbers up to $n=25$. The fabrication of quantum welllike structures in the crystal leads to quantum confinement effects and opens the possibility to study a crossover from three-dimensional to two-dimensional excitons. For small widths of the quantum well (QW), there are several well-separated Rydberg series between various scattering thresholds, leading to the occurrence of electron-hole resonances with finite lifetimes above the lowest threshold. By application of the stabilization method to the parametric dependencies of the real-valued eigenvalues of the original three-dimensional Schrödinger equation, we calculate the resonance energies and linewidths for Rydberg excitons in QWs in regimes where a perturbative treatment is impossible. The positions and finite linewidths of resonances at energies above the third threshold are compared with the complex resonance energies obtained within the framework of the complex-coordinate-rotation technique. The excellent agreement between the results demonstrates the validity of both methods for intermediate sizes of the QW-like structures, and thus for arbitrary widths.

We theoretically investigate the magneto-optical (MO) properties of monolayer (ML) transition metal dichalcogenides (TMDs) in the presence of external electrical and quantizing magnetic fields and of the proximity-induced exchange interaction. The corresponding Landau Level (LL) structure is studied by solving the Schrödinger equation and the spin polarization in ML-TMDs under the action of the magnetic field is evaluated. The impact of trigonal warping on LLs and MO absorption is examined. Furthermore, the longitudinal MO conductivity is calculated through the dynamical dielectric function under the standard random-phase approximation (RPA) with the Kubo formula. We take ${\mathrm{ML-MoS}}_2$ as an example to examine the effects of proximity-induced exchange interaction, external electrical and magnetic fields on the MO conductivity induced via intra- and interband electronic transitions among the LLs. For intraband electronic transitions within the conduction or valence bands, we can observe two absorption peaks in terahertz (THz) frequency range. While the interband electronic transitions between conduction and valence LLs show a series of absorption peaks in the visible range. We find that the proximity-induced exchange interaction, the carrier density, the strengths of the external electrical and magnetic fields can effectively modulate the positions of the absorption peaks and the shapes of the MO absorption spectra. The results obtained from this study can benefit to an in-depth understanding of the MO properties of ML-TMDs which can be potentially applied for magneto-optic, spintronic, and valleytronic devices working in visible to THz frequency bandwidths.

Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated transverse-field Ising model on the square lattice for the purpose of quantitatively relating two different order parameters to each other. We consider a “primary” spin order parameter and a “secondary” dimer order parameter, which both lead to the same phase diagram but detect ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_4$ symmetry breaking, respectively. While at $T>0$ their scaling exponents are simply related to each other, as explained by a mapping to a height model, we show that at $T=0$ they correspond to different charge sectors of the O(2) model in $2+1$ dimensions with nontrivial exponents that are not simply related to each other. Our insights are transferrable to a broad class of Ising models whose low-energy physics involves dimer degrees of freedom, and also serve as a guide to treating primary and secondary order parameters more generally.

We demonstrate terahertz chiral subwavelength cavities that break time-reversal symmetry by coupling the degenerate linearly polarized modes of two orthogonal sets of nanoantenna arrays using the inter-Landau-level transition of a two-dimensional (2D) electron gas in a perpendicular magnetic field, realizing normalized light-matter coupling rates up to ${\mathrm{\Omega }}_R/{\omega }_{\mathrm{cav}}=0.78$ with a dispersion that is modified by the parasitic capacitive coupling between the orthogonal antennas. The deep subwavelength confinement of the nanoantennas means that the ultrastrong-coupling regime can be reached even with a small number of carriers compared to Fabry-Pérot cavities, making it viable to be used with a variety of 2D materials. The nondegenerate circularly polarized ground state was only obtained after carefully optimizing the optical design to minimize the parasitic coupling to linearly polarized light.

We report on the microwave, terahertz (THz), infrared, and Raman spectroscopic studies of $\mathrm{Bi}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ ceramics, shedding more light onto the nature of two structural phase transitions and their possible relation with ferroelectricity in this compound. We observed a softening of one polar phonon in the THz range on cooling towards 460 and 300 K, i.e., temperatures at which $\mathrm{Bi}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ undergoes subsequent structural phase transitions from monoclinic $I2/m$ to polar monoclinic $\mathit{Im}$ and triclinic $P1$ phases. The soft phonon causes dielectric anomalies typical for displacive ferroelectric phase transitions. Microwave measurements performed at 5.8 GHz up to 400 K qualitatively confirmed not only the dielectric anomaly at 300 K, but also revealed two other weak dielectric anomalies near the magnetic phase transitions at 60 and 28 K. This evidences the multiferroic nature of the low-temperature phases, although the relatively high conductivity in the kHz and Hz spectral range prevented us from directly measuring the permittivity and ferroelectric polarization. Some Raman modes sense the magnetic phase transitions occurring near 60 and 25 K, showing that spin-phonon coupling is relevant in this compound and in this temperature range. The deviation of the Mn-O stretching mode frequency from the anharmonic temperature behavior was successfully explained by the spin correlation function calculated from the magnetic contribution to the specific heat.

Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eightfold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, the specific structure of the ${\mathbb{Z}}_2$ topological invariant in two dimensions makes it impossible to be generalized to the three-dimensional case. Consequently, it remains unclear whether three-dimensional higher-order topological insulators without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4e^2/h$. We show that the topological phase is characterized by the winding number of the generalized quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a generalized ${\mathbb{Z}}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals.

Investigation of Pb-free relaxor ferroelectric materials and analysis of their physical properties in relation to their local structure have emerged as captivating area of research. The ${\mathrm{CuCrO}}_2$, a centrosymmetric delafossite, exhibits a diffused ferroelectric phase transition with a broad dielectric relaxation maxima at $T_m\approx 453$ K and a Burn's temperature at $T_B\approx 468$ K. It does not exhibit a clear signature of temperature-induced structural phase transition, however, anomalous changes in crystallographic parameters across $T_B$ have been observed. Raman spectroscopy results also underline anomalies in the distinct vibrational modes below $T_B$, depicting association of local structural changes with ferroelectric ordering. Here, we report the origin of high-temperature relaxor ferroelectricity in ${\mathrm{CuCrO}}_2$, through detailed structural and local structural analysis. A real-space local structural study by x-ray pair distribution function (PDF) analysis, as a function of temperature, establishes a clear picture of temperature-induced structural instabilities from local to intermediate length scales. PDF analysis through the box car fitting demonstrate the presence of local structural disorder below $T_B$ at a length scale of $\approx 20$ Å. X-ray photoelectron spectroscopy (XPS) investigations revealed mixed oxidation states for Cu, implying the existence of charge inhomogeneity in the compound. Our findings reveal that both local structural disorder and charge inhomogeneity are responsible for appearance of relaxor ferroelectric behavior in ${\mathrm{CuCrO}}_2$.

Higgs modes emerge in superconductors as collective excitations of the order-parameter amplitude when periodically driven by electromagnetic radiation. In this work, we develop a Floquet approach to study Higgs modes in superconductors under time-periodic driving, where the dynamics of the order parameter is captured by anomalous Floquet Green's functions. We show that the Floquet description is particularly powerful as it allows one to exploit the time-periodic nature of the driving, thus considerably reducing the complexity of the time-dependent problem. Interestingly, the Floquet approach is also enlightening because it naturally offers a physical explanation for the renormalized steady-state order parameter as a result of photon-assisted transitions between Floquet sidebands. We demonstrate the usefulness of Floquet engineering Higgs modes in time-periodic $s$-wave superconductors.

Topological superconductors support Majorana modes, which are quasiparticles that are their own antiparticles and obey non-Abelian statistics in which successive exchanges of particles do not always commute. Here we investigate whether a two-dimensional superconductor with ordinary $s$-wave pairing can be rendered topological by the application of a strong magnetic field. To address this, we obtain the self-consistent solutions to the mean-field Bogoliubov–de Gennes equations, which are a large set of nonlinearly coupled equations, for electrons moving on a lattice. We find that the topological “quantum Hall superconductivity” is facilitated by a combination of spin-orbit coupling, which locks an electron's spin to its momentum as it moves through a material, and a coupling to an external periodic potential which gives a dispersion to the Landau levels and also distorts the Abrikosov lattice. We find that, for a range of parameters, the Landau levels broadened by the external periodic potential support topological superconductivity, which is typically accompanied by a lattice of “giant” $h/e$ vortices as opposed to the familiar lattice of $h/2e$ Abrikosov vortices. In the presence of a periodic potential, we find it necessary to use an ansatz for the pairing potential of the form $\mathrm{\Delta }\left(\mathit{r}\right)e^{i2\mathit{Q}·\mathit{r}}$ where $\mathrm{\Delta }\left(\mathit{r}\right)$ has a periodicity commensurate with the periodic potential. However, despite this form of the pairing potential, the current in the ground state is zero. In the region of ordinary superconductivity, we typically find a lattice of dimers of $h/2e$ vortices. Our work suggests a realistic proposal for achieving topological superconductivity, as well as a helical order parameter and unusual Abrikosov lattices.

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced permutation matrix representation quantum Monte Carlo [Gupta, Albash, and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the model is defined, a procedure that can be carried out efficiently and in an automated manner. To showcase the versatility of our approach, we provide simulation results for Bose-Hubbard models defined on two-dimensional lattices as well as on a number of random graphs.

Cavity materials are a frontier to investigate the role of light-matter interactions on the properties of electronic phases of matter. In this work, we raise a fundamental question: can nonlocal interactions mediated by cavity photons destabilize a topological electronic phase? We investigate this question by characterizing entanglement, energy spectrum, and correlation functions of the topological Su-Schrieffer-Heeger chain interacting with an optical cavity mode. Employing density-matrix renormalization group and exact diagonalization, we demonstrate the stability of the edge state and establish an area law scaling for the ground state entanglement entropy, despite long-range correlations induced by light-matter interactions. These features are linked to gauge invariance and the scaling of virtual photon excitations entangled with matter, effectively computed in a low-dimensional Krylov subspace of the full Hilbert space. This work provides a framework for characterizing novel equilibrium phenomena in topological cavity materials.

We study a ${\mathbb{Z}}_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible $\mathrm{U}{\left(1\right)}_{12}$ chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped two-dimensional bulk. The topological entanglement entropy is extracted and found to be in agreement with the $\mathrm{U}{\left(1\right)}_{12}$ topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the $\mathrm{U}{\left(1\right)}_{12}$ topological phase. We conclude by discussing several open questions.

We study the effect of disorder on $Z_2$ quantum spin liquids with a Majorana Fermi line (respectively a surface in three dimensions), and we show that depending on the symmetries that are preserved on average, qualitatively different scenarios will occur. In particular, we identify the relevant non-Hermitian symmetries for which disorder will effectively split the Fermi line into two exceptional lines, with $\mathrm{Re}\left(E\right)=0$ states filling the area in between. We demonstrate the different scenarios using both toy models as well as large-scale numerical simulations.

A comprehensive understanding of phonon transport is essential to develop effective solutions for heat dissipation. Gallium nitride (GaN), a representative of third-generation power semiconductors, has been extensively studied regarding its thermodynamics and lattice dynamics. However, the temperature-dependent phonon properties, especially the anharmonicity at high temperatures, are poorly understood. Here, by combining inelastic neutron scattering (INS) experiments and calculations including the temperature effect based on machine learning potentials, we report the high-order phonon anharmonicity in GaN over a wide temperature range. Our calculations agree well with the experimental phonon dispersion, density of states and entropy, underlining the significance of anharmonicity of GaN at elevated temperatures. Moreover, considering the four-phonon processes, the calculated thermal conductivity is suppressed by 20%, and the anisotropy is also reduced gradually with increasing temperature. Such behavior arises mainly from the large four-phonon scattering channels between 20 and 30 meV, where the critical scattering rule for the three-phonon process is largely restricted at high temperatures. Our study highlights the importance of high-order phonon anharmonicity for thermal transport in GaN and provides a theoretical reference for thermal management in other related semiconductors.

We investigate the energy spectrum of a single- and two-electron quantum dot (QD) embedded in two-dimensional electron gas at the interface between ${\mathrm{SrTiO}}_3$ and ${\mathrm{LaAlO}}_3$, in the presence of the external magnetic field. For this purpose, the three-band model of $3d$ electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low-energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one $d_{xy}$ orbital with the spin-orbit interaction originating from the coupling to the $d_{xz}$ and $d_{yz}$ bands. This is not the case for stronger confinement where contribution of the states related to the $d_{xz/yz}$ orbital is relevant. Based on the time-dependent calculations, we discuss in detail the manipulation of the electron spin in a QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in detail with respect to the parity selection rule. Our calculations show that, for a single-electron QD, the spin flip in the ground state has the character of a Rabi resonance, while for two electrons, the singlet-triplet transition is forbidden by the parity symmetry. For the two-electron QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.

Quasiclassical Anderson transition (QAT) represents the crossover from metallic to activated conduction in heavily doped highly compensated semiconductors (HDHCSs) due to large-scale potential fluctuations. The spatial inhomogeneity of the charged dopants in HDHCSs localizes carriers, forming metallic droplets surrounded by potential barriers. Nitride semiconductors are seldom explored for HDHCS studies due to the difficulty in synthesizing stoichiometric high-quality films and self-compensation effects. Here we show conclusive experimental evidence of the QAT in compensated scandium nitride (ScN) single-crystalline films. Mg (hole) doping in $n$-type ScN increases the resistivity by nine orders and leads to semi-insulating films exhibiting a distinct crossover from the hopping conduction at low temperatures to thermally activated percolative transport at high temperature. The sign reversal of the Seebeck coefficient, anomalously low Hall mobility that increases with raising temperature, and persistent photoconductivity support the QAT and carrier transport mechanisms. QAT in single-crystalline nitrides could lead to lattice-matched devices with lasers, modulators, and dynamic holographic applications.

Distinct from the flat band in two dimensions, the three-dimensional (3D) flat band and the corresponding physics have been relatively unexplored. Here, based on tight-binding models, we present a theoretical study of the evolution of the 3D flat band between pyrochlore and perovskite lattices, which are structurally interconvertible through diagonal strain and host double-degenerate flat bands. We discovered the presence of a persistent 3D flat band during the transition, which is stabilized by a robust compact localized state within the preserved kagome plane perpendicular to the diagonal direction. Furthermore, under the influence of spin-orbit coupling and Zeeman field, we can consistently achieve a magnetic Weyl semimetal state during this transition process due to the unique 3D flat band nature. Pairs of Weyl points form near the conserved flat band, leading to a large anomalous Hall conductivity (AHC) peak right at the energy of the flat band. Interestingly, we also observe an enhanced AHC during the transition from pyrochlore to perovskite lattice due to the enlarged momentum separation between Weyl points and the superimposition with another AHC peak from the dispersive Dirac bands.

We investigated the electronic structure of ${\mathrm{BaEu}}_2{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ and ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ by means of hard x-ray photoelectron spectroscopy. The Eu $3d$ core level spectra are primarily dominated by ${\mathrm{Eu}}^{2+}$ signals. The well-screened feature in the Nb $3d$ core level spectra of ${\mathrm{BaEu}}_2{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ is suppressed in ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$, consistent with the insulating behavior of ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ due to the atomic disorder and/or the rattling effect of the small Eu ions in the spacious $A2$ site. In the valence band spectra, the Nb $4d$ states at the Fermi level are close to the Eu $4f$ states located around 2 eV below it. This suggests that the degree of localization of the Nb $4d$ electrons can be enhanced through the Eu $4f$–Nb $4d$ hybridization with the atomically and magnetically disordered Eu ions at the $A2$ site.