In van der Waals heterostructures consisting of stacked ${\mathrm{MoSe}}_2$ and ${\mathrm{WSe}}_2$ monolayers, optically bright interlayer excitons can be observed when the constituent layers are crystallographically aligned. The symmetry of the monolayers allows for two different types of alignment, in which the momentum-direct interlayer transitions are either valley conserving ($R$-type alignment) or change the valley index ($H$-type antialignment). Here, we study the valley polarization dynamics of interlayer excitons in magnetic fields up to 30 T by time-resolved photoluminescence. For all interlayer exciton types, we find a finite initial photoluminescence circular degree of polarization after unpolarized excitation in applied magnetic fields. For interlayer excitons in $H$-type heterostructures, we observe a systematic increase of the photoluminescence circular degree of polarization with time in applied magnetic fields, which saturates at values close to unity for the largest fields. By contrast, for interlayer excitons in $R$-type heterostructures, the photoluminescence circular degree of polarization shows a decrease and a zero crossing before saturating with opposite polarization. This unintuitive behavior can be explained by a model considering the different interlayer exciton states in $H$- and $R$-type heterostructures and their selection rules coupling photoluminescence helicity and valley polarization.

We study dynamical correlation functions in the random-field Heisenberg chain, which probes the relaxation times at different length scales. First, we show that the relaxation time associated with the dynamical imbalance (examining the relaxation at the smallest length scale) decreases with disorder much faster than the one determined by the dc conductivity (probing the global response of the system). We argue that the observed dependence of relaxation on the length scale originates from local nonresonant regions. The latter have particularly long relaxation times or remain frozen, allowing for nonzero dc transport via higher-order processes. Based on the numerical evidence, we introduce a toy model that suggests that the nonresonant regions asymptotic dynamics are essential for the proper understanding of the disordered chains with many-body interactions.

Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as (i) a tool for revealing the nature of correlated insulators and (ii) a platform for Majorana-based topological qubits. We show that the band structure of a gate-defined wire immersed in an intervalley coherent correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the wire by a superconducting TBG region on one side and an intervalley coherent correlated insulator on the other further enables the formation of Majorana zero modes—possibly even at zero magnetic field depending on the precise symmetry-breaking order present. Our proposal not only introduces a highly gate-tunable topological qubit medium relying on internally generated proximity effects but can also shed light on the Cooper-pairing mechanism in TBG.

The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrinsically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter we pose the question of whether this property allows for inducing topological bands via a linearly polarized but twisted light beam. To this end we study a graphenelike model of electrons on a honeycomb lattice interacting with a twisted light field. To identify the topological behavior of the electrons, we calculate their local markers of Chern number and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is experimentally straightforward. With this, our work establishes a mechanism for generating fermionic topological phases of matter that can harness the central phase singularity of an optical vortex beam.

We study how the electron-electron interactions influence the charge distributions in the metallic state of quasicrystals. As a simple theoretical model, we introduce an extended Hubbard model on the Penrose lattice, and numerically solve the model (up to $\sim 1.4$ million sites) within the Hartree-Fock approximation. Because each site on the quasiperiodic lattice has a different local geometry, the Coulomb interaction, in particular the intersite one, works in a site-dependent way, leading to a nontrivial redistribution of the charge. The resultant charge distribution patterns are not multifractal but characterized by hyperuniformity, which offers a measure to distinguish various inhomogeneous but ordered distributions. We clarify how the electron interactions alter the order metric of the hyperuniformity, revealing that the intersite interaction considerably affects the hyperuniformity in particular on the electron-rich side.

Recently, investigations of the quantum properties of an antiferromagnet in the spin wave approximation have identified the eigenstates as two-mode squeezed sublattice-magnon states. The uniform magnon states were shown to display a massive sublattice entanglement. Here we extend this idea and study the squeezing properties of all sublattice Fock states throughout the magnetic Brillouin zone. We derive the full statistics of the sublattice magnon number with wave number $\vec{k}$ in the ground state and show that sublattice magnons occur in pairs with opposite wave vectors, hence, resulting in entanglement of both modes. To quantify the degree of entanglement we apply the Duan-Giedke-Cirac-Zoller inequality and show that it can be violated for all modes. The degree of entanglement decreases towards the corners of the Brillouin zone. We relate the entanglement to measurable correlations of components of the Néel and the magnetization vectors, thus allowing one to experimentally test the quantum nature of the squeezed vacuum. The distinct $k$-space structure of the entanglement shows that the squeezed vacuum has a nonuniform shape that is revealed through the $\vec{k}$-dependent correlators for the magnetization and the Néel vectors.

Using the nonequilibrium Green's function technique, we calculate spin-orbit torques in a ${\mathrm{Mn}}_2\mathrm{Au}$/heavy-metal bilayer, where the heavy metal (HM) is W or Pt. Spin-orbit coupling (SOC) in the bulk of ${\mathrm{Mn}}_2\mathrm{Au}$ generates a strong fieldlike torquance, which is parallel on the two sublattices and scales linearly with the conductivity, and a weaker dampinglike torquance that is antiparallel on the two sublattices. Interfaces with W or Pt generate parallel dampinglike torques of opposite signs that are similar in magnitude to those in ferromagnetic bilayers and similarly insensitive to disorder. The dampinglike torque efficiency depends strongly on the termination of the interface and on the presence of spin-orbit coupling in ${\mathrm{Mn}}_2\mathrm{Au}$, suggesting that the dampinglike torque is not due solely to the spin-Hall effect in the HM layer. Interfaces also induce antiparallel fieldlike and dampinglike torques that can penetrate deep into ${\mathrm{Mn}}_2\mathrm{Au}$.

The recent detailed study of quasi-one-dimensional iron-based ladders, with the $3d$ iron electronic density $n=6$, has unveiled surprises, such as orbital-selective phases. However, similar studies for $n=6$ iron chains are still rare. Here a three-orbital electronic Hubbard model was constructed to study the magnetic and electronic properties of the quasi-one-dimensional $n=6$ iron chain ${\mathrm{Ce}}_2{\mathrm{O}}_2\mathrm{Fe}{\mathrm{Se}}_2$, with focus on the effect of doping. Specifically, introducing the Hubbard $U$ and Hund $J_H$ couplings and studying the model via the density matrix renormalization group, we report the ground-state phase diagram varying the electronic density away from $n=6$. For the realistic Hund coupling $J_H/U=1/4$, several electronic phases were obtained, including a metal, orbital-selective Mott, and Mott insulating phases. Doping away from the parent phase, the competition of many tendencies leads to a variety of magnetic states, such as ferromagnetism, as well as several antiferromagnetic and magnetic “block” phases. In the hole-doping region, two different interesting orbital-selective Mott phases were found: OSMP1 (with one localized orbital and two itinerant orbitals) and OSMP2 (with two localized orbitals and one itinerant orbital). Moreover, charge disproportionation phenomena were found in special doping regions. We argue that our predictions can be tested by simple modifications in the original chemical formula of ${\mathrm{Ce}}_2{\mathrm{O}}_2\mathrm{Fe}{\mathrm{Se}}_2$.

This work considers a two-dimensional artificial triangular anti-dot lattice (TAL): a semiconductor-based artificial crystal hosting Dirac cones, flat bands, and Fermi surface nesting. All such single-particle features have dramatic implications for the emergent correlated phases. This work predominantly focuses on the existence of a robust flat band and enumerates the possible correlated phases that follow. We find that the flat band is generated, in the single-particle theory, when charges align themselves along a kagome lattice with the same period as the TAL. The correlated phases are studied using complementary techniques of expansion in strong and weak Coulomb interactions. Our microscopic modeling shows that for the purpose of generating strongly correlated phases, hole-doped TALs have significant advantages over electron-doped ones.

Chiral Majorana modes (CMMs) have attracted considerable interest due to non-Abelian statistics and potential applications in topological quantum computations, but still lack conclusive experimental evidence. Here, we propose that the nonlocal nature of CMMs leads to another transport signature, an anomalous Josephson effect with a tunable ground-state phase difference modulated by a transverse electric field. The CMMs can mediate nonlocal Andreev reflections from the top edge state to the bottom edge state in the quantum anomalous Hall insulator and vice versa. This nonlocal Andreev reflection leads to the spatial separation of electrons and holes. We refer to such Andreev bound states (ABSs) as nonlocal ABSs. It is shown that such nonlocal ABSs and the corresponding Josephson current can be shifted in the dependence on the superconducting phase difference by a transverse electric field. As a result, an electrically modulated anomalous Josephson effect should be observable in experiments. Moreover, when the Josephson junction is sandwiched between two quantum anomalous Hall insulator leads, the electrically tunable phase shift in ABSs results in a conductance oscillation which is applicable in transistors. These findings provide different proposals to experimentally verify the existence of CMMs, and as well as promise potential applications in phase-controllable Josephson devices and topological transistors.

Monolayer $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ $(M=\mathrm{Cr},\mathrm{V};X=\mathrm{S},\mathrm{Se})$ has been attracting increasing attention due to the ferromagnetism derived from the indirect exchange interaction between Cr (V) atoms and the ferroelectricity originating from the spontaneous displacement of Cu atoms. Using first-principles calculations, we predicted the intrinsic valley splittings and anomalous valley Hall effect in $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ monolayers. In addition, the valley splittings and Berry curvature are independent of the orientation of out of plane (OOP) ferroelectric polarization, which makes it a promising storage device with dual degrees of freedom in ferroelectric polarization and ferrovalleys. Due to the variations in the energy of the spin-dependent valence-band maximum (VBM) and orbital compositions of the valleys, the magnitude of valley splitting at VBM can be effectively tuned by the biaxial strain and external electric field. Large OOP magnetic anisotropy can be obtained by changing the energy and occupation (unoccupation) states of $d$ orbital compositions through strain and charge doping, respectively, and the magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ increases with increasing tensile biaxial strain from −5% to 5%. Our research results are expected to tune the valley splittings and magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ and to help understand the physical mechanism.

Optical second-harmonic generation (SHG) can only occur in noncentrosymmetric crystals in the leading electric-dipole approximation. Transition metal dichalco genides with the $1T$ octahedral coordination is centrosymmetric, hence precluding SHG. Here we report the surprising observation of SHG in atomically thin $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$, a prototypical charge density wave (CDW) material. Its intensity peaks in the trilayer, reaching 2% of that in monolayer $\mathrm{Mo}{\mathrm{S}}_2$, a two-dimensional crystal featuring pronounced nonlinear optical effect. The SHG signal exhibits a sixfold polarization dependence characteristic of a lattice with threefold rotational symmetry. It monotonically decreases with increasing temperature and persists at room temperature. Raman spectroscopy demonstrates that the CDW order is robust in atomically thin samples, with the transition temperature slightly lower than in the bulk. The SHG can be explained by the lattice distortion associated with the CDW as well as its fluctuation above the transition temperature. These results challenge the exciton insulator scenario and the chiral nature of the CDW, but support the band Jahn-Teller mechanism. Our work demonstrates SHG as a sensitive probe of the stacking order of the CDW in $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ and enriches the material base for nonlinear optical effects.

We consider the process of flux insertion for ground states of almost local commuting projector Hamiltonians in two spatial dimensions. In the case of finite-dimensional local Hilbert spaces, we prove that this process cannot pump any charge, and we conclude that the Hall conductance must vanish.

Quantum confinement has remarkable effects on the band structures and optoelectronic performance of semiconducting materials. The confinement of electronic states developed along van der Waals (vdW) gaps in transition metal dichalcogenides (TMDs) has unique advantages compared with those of artificial quantum wells. Here, we detected the quantized electronic states of few-layered ${\mathrm{MoS}}_2$ in real space using scanning tunneling microscope/spectroscopy. Combined with density-functional theory calculations, the quantized states were attributed to quantum-well states (QWSs), and the number of the states was strictly determined by the ${\mathrm{MoS}}_2$ layer thickness. We further regulated the QWSs of few-layered ${\mathrm{MoS}}_2$ by tuning the strength of interlayer hybridization through directly adjusting the interlayer distance. More importantly, substitutional defects in few-layered ${\mathrm{MoS}}_2$ were introduced to control the energy eigenvalues of the QWSs. Our work proves the existence of the interlayer electronic hybridization in conventional weakly coupled vdW interfaces, and provides a way to manipulate the electronic states of few-layered TMD through controlling interlayer hybridization. It also suggests potential applications of quantum-well materials in subband transitions, spin splitting, photoexcitation, and electronic devices.

$1T\text{−}{\mathrm{TiSe}}_2$ has been found to host a chiral charge density wave (CDW). Some studies suggest the microscopic origin of this phase is due to electron-phonon coupling while other studies suggest it is due to an excitonic insulator phase transition based on nonthermal melting of the charge density wave. First, we propose these interpretations can be reconciled if one analyzes the available experimental and theoretical data within a formal definition of what constitutes an excitonic insulator as initially proposed by Keldysh and Kopaev. Next, we present pump-probe measurements of circularly polarized optical transitions and first-principles calculations to highlight the role of elevated electronic temperatures on structural distortions to understand the nonthermal melting of the CDW phase. We also uncover a noncentrosymmetric CDW structure that explains the finite chirality of the optical transitions observed in the CDW phase of ${\mathrm{TiSe}}_2$.

We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. First, we strictly demonstrate that there exists an interesting dual mapping relation between $\left|a\right|<1$ and $\left|a\right|>1$ with regard to the potential tuning parameter $a$. The localization property of $\left|a\right|<1$ can be directly mapped to that of $\left|a\right|>1$, the analytical expression of the mobility edge of $\left|a\right|>1$ is therefore obtained through the spectral properties of $\left|a\right|<1$. More impressive, we prove rigorously that, even if the phase $\theta \ne 0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symmetric, however, there still exists a type of real-complex transition driven by non-Hermitian disorder, which is a class beyond the $\mathcal{PT}$-symmetric class.