The decades-long search for a shape that tiles the plane only aperiodically under translations and rotations recently ended with the discovery of the “spectre” aperiodic monotile. In this setting we study the dimer model, in which dimers are placed along tile edges such that each vertex meets precisely one dimer. The complexity of the tiling combines with the dimer constraint to allow an exact solution to the model. The partition function is $\mathcal{Z}=2^{N_{\text{mystic}}+1}$ where $N_{\text{mystic}}$ is the number of “mystic” tiles. We exactly solve the quantum dimer (Rokhsar-Kivelson) model in the same setting by identifying an eigenbasis at all interaction strengths $V/t$. We find that test monomers, once created, can be infinitely separated at zero energy cost for all $V/t$, constituting a deconfined phase in a $(2+1)$-dimensional bipartite quantum dimer model.

Chiral topological orders formed in correlated fermion systems have been widely explored. However, the mechanism of how they emerge from interacting fermions is still unclear. Here, we propose a susceptibility condition. Under this condition, we show that chiral topological orders can spontaneously take place in correlated fermion systems. The condition leads to a low-energy effective theory of bosons with strong frustration, mimicking flat-band systems. The frustration then melts the long-range orders and results in topological orders with time-reversal symmetry breaking. We apply the theory to strongly correlated semiconductors doped to the metallic phase. An excitonic topological order with semionic excitations and a chiral excitonic edge state is revealed. We also discuss the application to frustrated magnets. The theory predicts a chiral spin-liquid state, which is numerically confirmed by our tensor network calculations. These results demonstrate an indicator for chiral topological orders, which bridges the existing gap between interacting fermions and correlated topological matter.

Interlayer magnetism was tuned by many interlayer means, e.g., stacking, distance, and external fields in two-dimensional (2D) magnets. As an exception, the interlayer magnetism of CrSBr few layers was, however, experimentally changed by applied intralayer strains [Nat. Nanotechnol. 17, 256 (2022)], the mechanism of which is yet to be unveiled. Here, we uncovered its mechanism by investigating in-plane strained bilayer CrSBr using density functional theory calculations. Under in-plane tensile strain, wavefunction overlaps are strengthened for Br $p$ electrons within each CrSBr layer, which delocalizes intralayer electrons and, as a consequence, promotes interlayer electron hopping. A negative interlayer Poisson's ratio also enlarges interlayer spacing for bilayer CrSBr, which reduces the interlayer Pauli repulsion. This joint effect, further verified by examining interlayer sliding and interfacial element substitution, leads to an interlayer antiferromagnetic to ferromagnetic transition, consistent with the previous experimental observation. This mechanism enables a route to tune interlayer magnetism by modifying intralayer electron localization in 2D magnets.

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to on-site Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$, which is difficult to tune with external stimuli. One approach to address this problem is applying a dc electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$. Through density matrix renormalization group calculations, we compute the ground-state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.

In a recent publication, we showed that a monoaxial chiral magnet has a continuum of metastable helical states differing by the helix wave number. This intriguing result was obtained for the case of an infinite magnet (or a magnet with periodic boundary conditions). However, it has been pointed out that in a real magnet only one of these states is compatible with the boundary conditions, because the helix wave number is determined by the surface chiral twist. Thus, only one of the continuum of states is physically realizable. This is true for the case of a chiral magnet in contact with a nonmagnetic medium (vacuum or air, for instance), but the boundary conditions can be altered by setting the chiral magnet in contact with another magnetic medium, which may be able to absorb the surface chiral twist. We show here that this is indeed the case by studying a composite magnet system, which consists of one monoaxial chiral magnet of rectangular parallelepiped shape which has two similar slabs of a uniaxial ferromagnet attached to each of the faces that are perpendicular to the chiral axis. We show that, in the case of zero applied field, this composite system has a number of metastable helical states that are proportional to the length $L_0$ of the chiral magnet along the chiral axis, and that the results of our previous publication are recovered in the limit $L_0\to \infty$.

The search for evidence of Majorana states on the edges of topological superconductors is challenging due to the difficulty of detecting such charge-neutral electronic quasiparticles. Local microwave spectroscopy has been shown to be a possible method to detect propagating Majorana modes, where a spatially focused light beam must be used. Here, we show that helical Majorana modes in topological superconductors contribute to the optical conductivity under a spatially uniform light. The existence of such a signal requires the system to break certain symmetries so that the projection of charge current operator onto helical Majorana edge states leads to interbranch hybridization terms. The general form of this contribution under a tunable time-reversal breaking field is obtained, which is valid in the subgap low-frequency regime where the edge energy spectrum is linear. In comparison, the current operator for normal helical edge states, such as in quantum spin Hall insulators, does not cause interbranch transitions and the related optical conductivity vanishes unless the time-reversal symmetry is broken. Our results may help guide feasible experiments to provide evidence of Majorana edge modes in topological superconductors.

We study charge pumping in generic non-Hermitian settings and show that quantized charge pumping is only guaranteed under a biorthogonal formalism therein, where the charge transport is evaluated using the left and right eigenvectors of the non-Hermitian Hamiltonian. Specifically, for biorthogonal charge pumping in generic one-dimensional non-Hermitian models, we demonstrate how quantized transport is related to the Chern number in the parameter space. When the non-Hermitian model possesses the non-Hermitian skin effect, under which Bloch states in the bulk are deformed and localize toward boundaries, we propose a scenario where the pumped charge is related to the non-Bloch Chern number defined in the parameter space involving the generalized Brillouin zone. We illustrate the validity of our analytic results using concrete examples and, in the context of the biorthogonal charge pumping, discuss in detail a recent experiment where quantized charge pumping was observed in a lossy environment.

The entanglement entropy of black holes is expected to follow the Page curve. After an initial linear increase with time the entanglement entropy should reach a maximum at the Page time and then decrease. This paper introduces an exactly solvable model of free fermions that explicitly shows such a Page curve: The entanglement entropy vanishes asymptotically for late times instead of saturating at a volume law. The bending down of the Page curve is accompanied by a breakdown of the semiclassical connection between particle current and entanglement generation, a quantum phase transition in the entanglement Hamiltonian and nonanalytic behavior of the $q\to \infty$ Rényi entropy. These observations are expected to hold for a larger class of systems beyond the exactly solvable model analyzed here.

We conduct an exploration of the energy landscape of two coupled ferromagnetic layers with perpendicular-to-plane uniaxial anisotropy using finite-element micromagnetic simulations. These multilayers can be used to produce noncollinearity in spin-transfer torque magnetic random-access memory cells, which has been shown to increase the performance of this class of computer memory. We show that there exists a range of values of the interlayer exchange coupling constants for which the magnetic state of these multilayers can relax into two energy minima. The size of this region is determined by the difference in the magnitude of the layer anisotropies and is minimized when this difference is large. In this case, there is a wide range of experimentally achievable coupling constants that can produce desirable and stable noncollinear alignment. We investigate the energy barriers separating the local and global minima using string method simulations, showing that the stabilities of the minima increase with increasing difference in the anisotropy of the ferromagnetic layers. We provide an analytical solution to the location of the minima in the energy landscape of coupled macrospins, which has good agreement with our micromagnetic results for a case involving ferromagnetic layers with the same thickness and anisotropy, no demagnetization field, and large exchange stiffness. These results are important to understand how best to employ noncollinear coupling in the next generation of thin-film magnetic devices.

Quantum Griffiths singularity (QGS) has been experimentally observed in a range of two-dimensional (2D) superconducting systems. Although it is theoretically suggested that the QGS also exists in three-dimensional (3D) superconductors, there is almost no experimental support to the theoretical prediction. In the present paper, we observe the occurrence of QGS in a series of $\sim 80$-nm-thick ${\mathrm{Mo}}_{0.8}{\mathrm{Ti}}_{0.2}{\mathrm{N}}_x$ $(0.84\lesssim x\lesssim 1.12)$ superconducting films (with a NaCl structure) near the field-driven superconductor-metal transition (SMT). For each film, the low-temperature magnetoresistance isotherms, measured at magnetic fields being perpendicular or parallel to the film plane, do not cross at a single point but in a wide region. The dynamical critical exponents $z{\nu }_{\perp }$ (for perpendicular field) and $z{\nu }_{\parallel }$ (for parallel field) obtained by analyzing the related magnetoresistance isotherms increase with decreasing temperature and tend to diverge as $T\to 0\mathrm{K}$. In addition, the corrected resistivities for the perpendicular and parallel field in the vicinity of the SMTs both obey an activated scaling based on the random transverse-field Ising model. Although these films are 3D with respect to the superconductivity, the activated scaling near the SMT for these films is as same as that for 2D superconductors with QGS. The QGS in the 3D ${\mathrm{Mo}}_{0.8}{\mathrm{Ti}}_{0.2}{\mathrm{N}}_x$ superconducting films originates from the slow dynamics of the rare regions in these systems. We also fabricate a $\sim 80$-nm-thick ${\left({\mathrm{Mo}}_{0.8}{\mathrm{Ti}}_{0.2}\right)}_2{\mathrm{N}}_{1.06}$ superconducting film with face-centered cubic structure at low nitrogen partial pressure. It is found that the low-temperature magnetoresistance isotherms for the perpendicular (parallel) field cross at a single point and the resistivity data for the perpendicular (parallel) field in the vicinity of the field-induced SMT obey the power-law scaling deduced from the dirty-boson model. Our results provide unambiguous experimental evidence for the existence of QGS in 3D superconductors.

We provide numerical evidence of the Nagaoka's theorem in the $\mathrm{SU}\left(N\right)$ Fermi-Hubbard model on various cluster geometries, such as the square, the honeycomb, and the triangular lattices. In particular, by diagonalizing several finite-size clusters, we show that for one hole away from filling $1/N$, the itinerant ferromagnetism arises for $U$ (the positive on-site interaction) larger than $U_c$ (the value at the transition), which depends strongly on the coordination number $z$ and on $N$, the number of degenerate orbitals, that we vary from $N=2$ to 6 in our simulations. We prove that $U_c$ is a nondecreasing function of $N$. In addition, we find that the lattice dependency is rooted in the kinetic energy of the hole. We find that large coordination numbers $z$ lower the value of $U_c$. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism, and we demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small $U$. Finally, the effects of both the presence of some additional holes and the finite size of the clusters are briefly discussed.

By constructing germanene (silicene, stanene)/$M{\mathrm{Bi}}_2{\mathrm{Te}}_4$ ($M=3d$-transition elements) heterostructures, we discovered and designed multimechanism quantum-anomalous-Hall (QAH) systems, including $\mathrm{\Gamma }$-based QAH, $K-K^{\prime }$-connected QAH, and valley-polarized $K$- or $K^{\prime }$-based QAH states via first-principle computations. The unique systems possess a global gap and tunable Chern number. The coexisting conventional $\mathrm{\Gamma }$-based QAH state of $M{\mathrm{Bi}}_2{\mathrm{Te}}_4$ and valley-polarized $K$($K^{\prime }$)-based QAH state of germanene (silicene, stanene), with opposite chirality, can interact with each other. Adjusting magnetic configurations of $M{\mathrm{Bi}}_2{\mathrm{Te}}_4$-layers not only switch on (off) the QAH conductance, but also modulate Chern numbers exactly. For example, the germanene/bilayer-${\mathrm{NiBi}}_2{\mathrm{Te}}_4$ possesses the Chern number $\mathit{C}=+1$ in ferromagnetic couplings and $\mathit{C}=+2$ in antiferromagnetic couplings. The novel multimechanism QAH insulators, which are achievable in experiments, provide a new approach to spintronics and valleytronics based on topological states of matter.

The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its computational cost is notably high, particularly in calculating physical observables like correlation functions. To surmount the computational challenge and enhance efficiency, we propose integrating the Green's function Monte Carlo (GFMC) method with the projected entangled pair state (PEPS) ansatz. This approach combines the high-efficiency characteristics of Monte Carlo with the sign-free nature of tensor network states and proves effective in addressing the computational bottleneck. To showcase its prowess, we apply this hybrid approach to investigate the antiferromagnetic $J_1\text{−}{J}_2$ Heisenberg model on the square lattice, a model notorious for its sign problem in quantum Monte Carlo simulations. Our results reveal a substantial improvement in the accuracy of ground-state energy when utilizing a preliminary PEPS as the guiding wave function for GFMC. By calculating the structure factor and spin-spin correlation functions, we further characterize the phase diagram, identifying a possible columnar valence-bond state phase within the intermediate parameter range of $0.52<J_2/J_1<0.58$. This comprehensive study underscores the efficacy of our combined approach, demonstrating its ability to accurately simulate frustrated quantum spin systems while ensuring computational efficiency.

We study the influence of impurities in graphene described by a scattering rate $\mathrm{\Gamma }$ on the Casimir interaction between graphene and an ideal conductor or between two identical sheets of graphene at zero temperature and chemical potential. To this end, we compute the polarization tensor of quasiparticles in graphene and corresponding conductivities for TE and TM channels. The Casimir energy density is evaluated with the help of the Lifshitz formula. We find that depending on the value of the mass gap parameter, the presence of $\mathrm{\Gamma }$ may lead to a slight damping or to a considerable enhancement of the Casimir interaction.

We develop the Floquet-Bloch theory of noninteracting fermions on a periodic lattice in the presence of a constant electric field. As long as the field lies along a reciprocal-lattice vector, time periodicity of the Bloch Hamiltonian is inherited from the evolution of momentum in the Brillouin zone. The corresponding Floquet quasienergies yield the Wannier-Stark ladder with interband couplings included to all orders. These results are compared to perturbative results where the lowest-order interband correction gives the field-induced polarization shift in terms of the electric susceptibility. Additionally, we investigate electronic transport by coupling the system to a bath within the Floquet-Keldysh formalism. We then study the breakdown of the band-projected theory from the onset of interband contributions and Landau-Zener resonances in the band-resolved currents. In particular, we consider the transverse quantum-geometric response in two spatial dimensions due to the Berry curvature. In the strong-field regime, the semiclassical theory predicts a plateau of the geometric response as a function of field strength. Here, we scrutinize the conditions under which the semiclassical results continue to hold in the quantum theory.

Understanding and tuning the factors influencing the lifetime of confined electronic states is a basic concept of quantum mechanics, whereas achieving large lifetimes in artificial nanostructures holds great potential for advancing quantum technologies. An example of such artificial structures are CO-based quantum corrals. In this study, tunneling spectroscopy measurements reveal a strong correlation between the size of the quantum corral and spectral width, characterized by a predominant Gaussian line shape. We attribute this dominant Gaussian-shaped lifetime broadening to the interaction of surface state electrons with the corral boundary. To further investigate this phenomenon, we constructed corrals of varying wall densities. Our findings indicate that elastic processes, such as tunneling, are more sensitive to the wall density than coupling to the bulk.

The quest for intrinsically low lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) has gained widespread attention in thermoelectrics and refractories. The reduction of ${\kappa }_{\mathrm{L}}$ in low-dimensional systems typically arises from anharmonicity and anisotropic chemical bonding. Due to the structural instability and the technical complexity, the thermal functional application of practical low-dimensional materials confronts great challenges. In this context, the investigations of quasi-low-dimensional bulk materials, rather than the real low-dimensional materials, hold paramount importance from both fundamental and practical perspectives. Here, we employ the ab initio self-consistent phonon (SCPH) theory in combination with the compressive sensing lattice dynamics method to explore the lattice dynamics and microscopic mechanisms of thermal transport in emerging pentanary thiophosphates $A_2\mathrm{PdP}{\mathrm{S}}_4\mathrm{I}$ ($A=\mathrm{K}$, Rb, Cs). These compounds feature covalent one-dimensional (1D) chains, providing bonding heterogeneity and resulting in flat phonon bands and low phonon group velocities ($V_{\mathrm{ph}}$). The strengthened anharmonicity stems from the cooperative rattlinglike vibrations of the interchain alkali metal atoms and I atoms. In K- and Rb-containing systems, the cooperative vibrations of the rattling unit (K/Rb-I) result in strong anharmonicity, while in Cs-containing system, the abnormally enhanced particlelike ${\kappa }_{\mathrm{L}}$ (${\kappa }_{\mathrm{p}}$) is due to the antibonding interaction breaking the cooperative vibration of the rattling unit (Cs-I), thereby weakening the anharmonicity. Upon heating, the ${\kappa }_{\mathrm{p}}$ show decreasing behavior. However, the wavelike ${\kappa }_{\mathrm{L}}$ (${\kappa }_{\mathrm{c}}$) exhibits a positive temperature dependence, highlighting the nonnegligible coherent phonon contributions to the ${\kappa }_{\mathrm{L}}$ and triggering anomalous temperature-dependent behavior of ${\kappa }_{\mathrm{L}}$. Our study uncovers the multifaceted microscopic mechanisms behind the low ${\kappa }_{\mathrm{L}}$ in three quasi-one-dimensional (Q-1D) systems of $A_2\mathrm{PdP}{\mathrm{S}}_4\mathrm{I}$ and provides fresh insights for the discovery and design of Q-1D low ${\kappa }_{\mathrm{L}}$ materials.

Topological semimetals possess nodal or nodal-line phases where conduction and valence bands touch at points or lines in momentum space, respectively. Such band touching is symmetry protected and gives rise to exotic and interesting electronic properties. Coupling topological order with magnetism provides a platform for exploring time-reversal (TR) symmetry breaking topological physics, such as axion electrodynamics, inverse spin-galvanic effect, and the quantized anomalous Hall effect. The Weyl semimetal (WSM) requires breaking either TR symmetry or lattice inversion symmetry (I). By doping inversion-symmetry-broken WSM with magnetic dopants, one can expect to create a WSM with both symmetries breaking simultaneously. Here, structural, electrical, and magnetic properties of ${\mathrm{Fe}}_x{\mathrm{W}}_{1-x}{\mathrm{Te}}_2$ ($x=0$ and 0.011) are reported. It is revealed that, with a small Fe doping concentration ($x=0.011$), a ferromagnetism is induced at low temperature (<10 K). Scanning tunneling microscopy and spectroscopy measurements in ${\mathrm{Fe}}_{0.011}{\mathrm{W}}_{0.989}{\mathrm{Te}}_2$ further reveal only substitution and no intercalated dopants being observed. The probabilities of the Fe substitutions at the two nonequivalent W sites are quantified with equal probability. The $\mathit{dI}/\mathit{dV}$ point spectra indicates that the Fe substitution in ${\mathrm{WTe}}_2$ manifests itself as electron doping regardless of doping sites. The results clearly reveal the possible coexistence of magnetism and Weyl points in the lightly Fe doped ${\mathrm{WTe}}_2$ at low temperature. This provides an ideal system for further study on the interplay between the topological Weyl points and the TR symmetry breaking.