According to Faraday's law in classical physics, a varying magnetic field stimulates an electric eddy field. Intuitively, when a classical field is constant and imposed on a lattice, the Wannier-Stark ladders can be established, resulting in Bloch oscillations. In this work, we investigate the dynamics of an interacting system on a (generalized) ring lattice threaded by a varying magnetic flux. Based on the rigorious results, we demonstrate that there exist many invariant subspaces in which the dynamics is periodic when the flux varies linearly over time. Nevertheless, for a given initial state, the evolved state differs from that driven by a linear field. However, the probability distributions of the two states are identical, referred to as the quantum analog of Faraday's law. Our results are ubiquitous for a wide variety of interacting systems. We demonstrate these results through numerical simulations in an extended Fermi-Hubbard model.

Superconducting systems based on attractive electron-phonon interactions are the ones which are best understood at a fundamental level. They are well described using Eliashberg theory, which, unlike BCS theory, explicitly takes into account phonon dynamics. It is most often assumed that only linear electron-phonon interactions are relevant. However, for some superconductors like ${\mathrm{MgB}}_2$ or hydride based superconductors, nonlinear electron-phonon interactions are known to contribute significantly, which is not taken into account in conventional Eliashberg theory. We provide a modification to Eliashberg theory by introducing nonlinear electron-phonon interactions. We show that the Eliashberg equations remain unchanged apart from a nonlinear extension of the Eliashberg spectral function. This extended spectral function can be used as a baseline for future ab initio calculations. We use it to construct an analytical toy model and show that the nonlinear electron-phonon coupling affects the superconducting gap function on the imaginary and real axis and causes an increase in the superconducting critical temperature.

The non-Hermitian Aharonov-Bohm (AB) cage is a unique localization phenomenon that confines all possible excitations. This confinement leads to fully flat spectra in momentum space, which are typically accompanied with the degeneracy with various types. Classifying the degeneracy type is crucial for studying the dynamical properties of the non-Hermitian AB cage, but the methods for such classification and their physical connections are not very clear. Here, we construct a non-Hermitian AB cage in a bosonic Bogoliubov-de Gennes system with various types of degenerate flat bands (DFBs). Using the transfer matrix, we demonstrate the localization mechanism for the formation of an AB cage and derive the minimal polynomial in mathematics for classifying the degeneracy types of DFBs, thus providing comprehensive understanding of the correspondence among the degeneracy type of DFBs, the minimal polynomial, and the transfer matrix. With such correspondence, we propose a scheme to realize highly degenerate flat bands.

Edges are essential for the mechanical, chemical, electronic, and magnetic properties of two-dimensional (2D) materials. Research has shown that features assigned to edges are not strictly localized but often penetrate the bulk to some degree. However, mechanical edge properties, such as edge energies and stresses, are typically assigned at the system level, with spatial bulk penetrations that remain unknown. Here, we use density-functional tight-binding simulations to study how deep various edge properties spatially penetrate the 2D bulk. We study nine different edges made of four materials: graphene, goldene, boron nitride, and molybdenum disulfide. By investigating edge energies, edge stresses, and edge elastic moduli, we find that although the edge properties typically originate near the edges, they still penetrate the bulk to some degree. An utmost example is goldene with a staggered edge, whose edge properties penetrate the bulk nanometer deep. Our results caution against associating system-level edge properties too strictly with the edge, especially if those properties are further used in continuum models.

We investigated quantum spin pumping in a non-Hermitian triple-quantum-dot (TQD) system governed by a parity-time ($\mathcal{PT}$)-symmetric Hamiltonian. Using the nonequilibrium Green's function (NEGF) formalism, we derived spin current expressions for both adiabatic and nonadiabatic regimes, and performed numerical simulations to study the impact of the non-Hermitian component on the spin current. Our results show that $\mathcal{PT}$-symmetric complex potentials significantly affect spin current behavior. Notably, even weak non-Hermitian strength generates a substantial pure spin current at the Fermi level in the adiabatic regime, where none would occur in a Hermitian system. This arises from the breakdown of wavefunction antisymmetry in the $\mathcal{PT}$-symmetric non-Hermitian system. We also found that the distribution and magnitude of the spin current depend on the parity of $(L+1)/2$, where $L$ is the number of TQD units. Odd values of $(L+1)/2$ show a pronounced spin current peak at the Fermi level, while even values display a dip, revealing an even-odd oscillation. This effect is linked to the wavefunction symmetry in the $\mathcal{PT}$-symmetric Hamiltonian. In the nonadiabatic regime, the spin current shows nonlinear dependence on the magnetic field oscillation frequency, with its magnitude influenced by the non-Hermitian strength. These findings offer valuable insights into spin transport in non-Hermitian systems, with potential applications in nanoelectronics and spintronics.

From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac insulators, featuring a Fermi surface. Otherwise a simply connected Fermi surface becomes annular deep inside the topological regime. In the absence of chemical doping, such systems describe quantum anomalous or spin Hall and normal insulators. By considering all symmetry allowed repulsive local four-fermion interactions, we show that the nature of the resulting superconducting states at low temperature follows certain Clifford algebraic selection rules, irrespective of the underlying Fermi surface topology. Within the framework of a microscopic Hubbard model, on-site repulsion among fermions with opposite orbitals (spin projections) typically favors odd-parity topological $p$-wave (conventional even-parity $s$-wave) pairing. Theoretically predicted superconductivity can in principle be observed in experiments once the promising candidate materials for quantum anomalous and spin Hall insulators are doped to foster Fermi surfaces, realizable in quantum materials and on optical lattices of cold atoms.

We study creation of quasiparticles in fractional Chern insulators (FCIs) under magnetic fields. We consider two representative models, the Kapit-Mueller model and the checkerboard model, which have distinct band properties in terms of the quantum geometry. The former satisfies the so-called ideal condition and well mimics the lowest Landau level, while the latter is not ideal for realization of FCI states. It is found within exact diagonalization that both quasiholes and quasielectrons are stably created by the magnetic fields in the Kapit-Mueller model. On the other hand, stability of the quasiparticle creation depends on directions of the magnetic field in the checkerboard model. Although the quasielectron creation is stable under a magnetic field, the quasihole creation and the underlying FCI state are unstable for the opposite field direction, leading to a field-induced non-FCI state. We point out that this difference can be understood based on the multiband quantum geometry in the presence of the magnetic fields.

CrSBr is a layered van der Waals insulator with a quasi-one-dimensional electronic structure and in-plane ferromagnetic order. Recent experimental work on Li-doped CrSBr reveals quasi-1D charge-modulated states. In this study, we develop ab initio effective models for CrSBr to investigate these states and solve them using mean-field theory and density matrix embedding theory. The models are parametrized using density functional theory, the constrained random-phase approximation, and the Rytova-Keldysh form of the long-range Coulomb interaction. Our simulations indicate the emergence of a charge-density-wave state characterized by cosinelike intrachain density modulations and interchain phase shifts that minimize the Coulomb repulsion. Notably, at a doping level corresponding to $1/n$ electron per CrSBr unit, the most stable pattern exhibits a periodicity of $n$ cells, in agreement with experimental observations and Peierls' instability arguments. Moreover, we demonstrate that the interchain order is sensitive to the range of Coulomb interactions. If the interaction is hard truncated to a short-ranged form, some localized stripelike states are computationally favored. This work provides an ab initio framework for understanding the interplay of competing electronic and magnetic phases in CrSBr and related materials.

Bloch's theorem provides a conventional starting point for describing wave propagation in periodic media, but in ordered materials where competing spatial periods coexist it is rendered ineffective, often with dramatic consequences. Here we develop an alternate approach that uses coherent free-particle vortex states to study quantum states in supertwisted crystals: three-dimensional stacks of atomically thin two-dimensional layers. This formalism leads naturally to the representation of the spectrum using squeezed coherent states, and it reveals the crucial role of a Coriolis coupling in the equations of motion. This identifies an underlying noncommutative geometry and novel edge state structure in a family of complex ordered structures.

Nontrivial topology in type-II Dirac semimetal ${\mathrm{NiTe}}_2$ leading to topologically protected surface states gives rise to fascinating phenomena holding great promise for next-generation electronic and spintronic devices. Key parameters such as lattice parameter, disorder, vacancies, and electron correlation, significantly influence the electronic structure and, subsequently, the physical properties. To resolve the discrepancy between the theoretical description and experimentally observed topological surface states, we comprehensively investigate the electronic structure of ${\mathrm{NiTe}}_2$ using angle-resolved photoemission spectroscopy and density functional theory. Although the bulk electronic structure is found to be well described within mean-field approaches, an accurate description of topological surface states is obtained only by incorporating surface electronic correlation. We reveal that the strongly correlated surface states forming Dirac-like conical crossing much below Fermi level have hybridized $\mathrm{Ni}3d$ and $\mathrm{Te}5p$ character. These findings underscore the intricate interplay between electron correlation and band topology, broadening our understanding of many-body correlation effects on the topological surface states in quantum materials.

The nonmagnetic doublet systems $\mathrm{Pr}T{r}_2{\mathrm{Zn}}_{20}$ ($Tr=\mathrm{Rh},\mathrm{Ir}$) exhibit antiferroquadrupolar (AFQ) ordering in zero magnetic field. Under applied fields, the AFQ ordering is destroyed, and a field-induced phase (FIP) transition appears, although the mechanism remains elusive. A vibronic state below 2 K, characterized by the degeneracy of clockwise and anticlockwise “rotation,” and its breakdown at the FIP transition were proposed. We performed ultrasonic measurements of ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$ in magnetic fields up to 28 T at temperatures down to 0.03 K. The field ($\mathit{H}\parallel \left[110\right]$) dependence of the elastic modulus $(C_{11}-C_{12})/2$ was measured for two configurations in which the field was applied along the direction of ultrasound propagation or displacement. At 4.2 K, the difference between the two datasets is weakly dependent on the field and is reproduced by a model considering the ordinary rotational invariance effect. However, at 0.18 K, the data exhibit spontaneous separation above the FIP boundary, and this difference is not reproduced by the above model. Our experimental and theoretical results reveal an unconventional rotational effect on the elastic modulus, demonstrating that the FIP transition arises from the breakdown of the vibronic state. Above the FIP boundary, the electronic state adopts a chirality of clockwise or anticlockwise “rotation.”

Weyl semimetals have attracted significant attention due to their special topological properties, especially the Fermi arcs connecting the projection of two oppositely charged Weyl points. However, these boundary arcs are typically confined to local regions in momentum space, which is influenced by the boundary formation and restricts their universality and stability. Here, we report our realization of a triply degenerate point hosting self-connecting boundary arcs that are stable to the boundary formation in a two-dimensional acoustic crystal. By symmetry enhancement, we merge two Weyl points into a quadratic Weyl point that supports a global boundary arc. Further adjustment of geometric parameters leads to the formation of a triply degenerate point, serving as a phase transition between distinct quadratic Weyl states. Despite exhibiting a zero Berry phase, the triply degenerate point supports experimentally observed boundary arcs that are stable and immune to boundary formation. Our findings reveal the variation in topological properties during the evolution of different degenerate points and present a different approach for engineering boundary arcs, with potential applications in topological acoustics and beyond.

Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems with Ising or continuous symmetries, while the Potts symmetry, albeit being of fundamental importance also for the description of realistic physical systems, has received very little attention. In the present study, we use a recently developed quasiexact method for determining ground states in the random-field Potts model to study the problem with four states. Extending the protocol applied for the three-state model, we use extensive finite-size scaling analyses of the magnetization, Binder parameter, energy cumulant, specific heat, and the connected as well as disconnected susceptibilities to study the magnetic ordering transition of the model. In contrast to the system in the absence of disorder, we find compelling evidence for a continuous transition, and we precisely determine the critical point as well as the critical exponents, which are found to differ from the exponents of the three-state system as well as from those of the random-field Ising model.

An unexpectedly large transient magnetization induced by circularly polarized ferroelectric phonons was recently observed in a nonmagnetic insulator ${\mathrm{SrTiO}}_3$ [Basini et al., Nature (London) 628, 534 (2024)]. We use a minimal molecular orbital model to demonstrate two electronic contributions to this effect. An atomic orbital contribution arises from the pumping of orbital angular momentum of Ti by the circulating motion of coordinating oxygen atoms. An additional inter-atomic contribution is associated with the transient circulating current around the oxygen atoms, resulting in efficient dressing of phonons by electron dynamics. The insights provided by our model may facilitate the development of ultrafast magnetization control and orbitronic sources.

The term altermagnetism has recently been introduced to describe the Néel order of a class of materials whose magnetic sublattices are neither related by translation nor inversion. While these materials arguably have large technological potential, little effort has been devoted to studying the universal distinction of this phase of matter compared to collinear antiferromagnetism. Employing a recently proposed minimal microscopic model, we explicitly derive a nonlinear sigma model describing long-wavelength fluctuations of the staggered magnetization in this system, including quantum effects to leading order. The term that distinguishes the altermagnetic nonlinear sigma model from its antiferromagnetic counterpart is an interaction term that derives directly from the Berry phase of the microscopic spin degrees of freedom. Its effects on the one-loop renormalization group flow in $d=2+1$ dimensions are examined. Extending the theory to describe the fermionic excitations of the metallic altermagnet, we find an effective low-energy model of $d$-wave spin-split Dirac fermions interacting with the magnetic fluctuations. Using a Dyson-Schwinger approach, we derive the many-body effects on the dynamical critical scaling due to the competition between the long-range Coulomb interaction and the fluctuations of the staggered magnetization.

We present the low-temperature magnetic properties of two ${\mathrm{Yb}}^{3+}$-based triangular lattice compounds, $\mathrm{NaSrYb}{\left({\mathrm{BO}}_3\right)}_2$ and ${\mathrm{K}}_3{\mathrm{YbSi}}_2{\mathrm{O}}_7$, studied via thermodynamic measurements followed by crystal electric field (CEF) calculations. Magnetization and specific heat data as well as the CEF energy levels confirm that the ground state is characterized by the low-lying Kramers doublet of the ${\mathrm{Yb}}^{3+}$ ion with an effective spin-$\frac{1}{2}$ ($J_{\mathrm{eff}}=\frac{1}{2}$). A small Curie-Weiss temperature and scaling of magnetic isotherms corroborate very weak magnetic correlations among $J_{\mathrm{eff}}=\frac{1}{2}$ spins. The crystal field parameters are calculated using the point charge model, and the CEF Hamiltonian is determined for both the compounds. The simulation using the eigenvalues of the CEF Hamiltonian reproduces the experimental magnetic susceptibility, magnetic isotherms, and magnetic specific heat data very well. The large separation between the ground state and first excited state doublets implies that the ground state is a Kramers doublet with $J_{\mathrm{eff}}=\frac{1}{2}$ at low temperatures, endorsing the experimental findings.

We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional classification of 1D band topology protected by inversion symmetry and characterized by ${\mathbb{Z}}_2$-quantized polarization (Berry-Zak phase). Such kind of enriched topological phases relies on imposing restriction on tunneling forms. By considering the nontrivial relative polarization among sublattices (orbitals), we introduce the inversion winding number as a topological invariant for characterizing and categorizing band topology. The bulk-edge correspondence with regard to the inversion winding number is discussed. Leveraging real-space analysis, we discover disorder-induced topological Anderson insulators and propose to experimentally distinguish band topology through relative polarization of edge states or bulk states. Our comprehensive findings present a paradigmatic illustration for the ongoing investigation and classification of band topology in TCIs.

This paper introduces a method to identify traps in molecular charge transport networks as obtained by multiscale modeling of organic semiconductors. Depending on the materials, traps can be defect-like single molecules or clusters of several neighboring ones, and can have a significant impact on the dynamics of charge carriers. Our proposed method builds on the random walk model of charge dynamics on a directed, weighted graph, the molecular transport network. It comprises an effective heuristic to determine the number of traps or trap clusters based on the eigenvalues and eigenvectors of the random walk Laplacian matrix and uses subsequent spectral clustering techniques to identify these traps. In contrast to currently available methods, ours enables identification of trap molecules in organic semiconductors without having to explicitly simulate the charge dynamics and is applicable to a variety of energy- or topology-based traps in homomolecular or mixed systems with or without detailed-balance. As a prototypical system, we simulate an amorphous morphology of bathocuproine, a material with known high-energetic disorder and charge trapping. Based on a first-principle multiscale model, we first obtain a reference charge transport network and then purposefully modify its properties to represent different trap characteristics. In contrast to currently available methods, our approach successfully identifies both single trap, multiple distributed traps, and a combination of a single-molecule trap and trap regions on an equal footing.