The utilization of semiconducting two-dimensional (2D) materials in photonics or optoelectronics depends on having a tunable optical band gap, typically influenced by the material's layer count and modified interlayer interactions. Extensive research has been conducted on semiconducting transition metal dichalcogenides to explore their potential in light-matter applications through the manipulation of electronic states' interactions. Notably, intrinsic defects in these 2D materials generate electronic states within the mid-gap regions, enhancing their versatility as promising candidates for potential optoelectronic applications. In this study, we realized the optical transitions from the mid-gap states in liquid-phase exfoliated ${\mathrm{MoS}}_2$ through varying light intensity. We note the emergence and reversible evolution of two additional photoluminescence emissions at lower energy, complementing the standard photoluminescence spectra of ${\mathrm{MoS}}_2$ at room temperature. Our density functional theory simulations indicate that these novel optical pathways stem from sulfur vacancy defect states in the mid-gap regions and the intensity of the optical excitation can be used to tune the transitions. This finding presents an exciting opportunity for further investigation and control of mid-gap states, which could have potential applications in optical communication.

The generation of nonlinear spin photocurrents by circularly polarized light in two-dimensional systems is theoretically investigated by calculating the shift spin conductivities. In time-reversal symmetric systems, shift spin photocurrent can be generated under the irradiation of circularly polarized light, while the shift charge photoccurrent is forbidden by symmetry. We show that the $k$-cubic Rashba-Dresselhaus system, the $k$-cubic wurtzite system, and Dirac surface states can support the shift spin photocurrent. By symmetry analysis, it is found that, in the Rashba type spin-orbit coupled systems, mirror symmetry requires that the spin polarization and the moving direction of the spin photocurrent be parallel, which we name longitudinal shift spin photocurrent. The Dirac surface states with warping term exhibit mirror symmetry, similar to the Rashba type system, and support longitudinal shift spin photocurrent. In contrast, in the Dresselhaus type spin-orbit coupled systems, the parity-mirror symmetry requires that the spin polarization and the moving direction of the spin photocurrent be perpendicular, which we dub transverse shift spin photocurrent. Furthermore, we find that the shift spin photocurrent always vanishes in any $k$-linear spin-orbit coupled system unless the Zeeman coupling ${\mu }_z$ is turned on. We find that the splitting of degenerate energy bands due to Zeeman coupling ${\mu }_z$ causes the van Hove singularity. The resulting shift spin conductivity has a significant peak at optical frequency $\omega =2{\mu }_z/\hslash$.

We theoretically investigate the fusion rules of Majorana Kramers pairs in time-reversal invariant topological superconductors. We find that the fusion of Majorana Kramers pairs is a process that Ising anyons fuse independently in the two distinct time-reversal sectors. Considering the full fusion including the initialization and the fusion, we explore the observation of a supersymmetry that emerges in time-reversal invariant topological superconductors, and design the schemes for the nontrivial fusion and the trivial fusion to show the non-Abelian statistics of Majorana Kramers pairs. We also show the possible influence of local adiabatic mixing on the fusion can generally be negligible and the differentiation between distinct fusion processes remains feasible even in the presence of such mixing. Our proposals are applied in $d_{x^2-y^2}$-wave topological superconductors, and the theoretical framework can be extended to the fusion of multiple Majorana zero modes protected by unitary symmetry.

We investigate the Emery model on several ladder-like lattices including two legs of copper $d$ orbitals and various numbers of oxygen $p$ orbitals. Pair binding energy, pair spatial structure, density distribution, and pairing correlation functions are calculated using the density-matrix renormalization group (DMRG). We show that a Luther-Emery phase with enhanced pairing correlations can be found for hole doping as well as for electron doping with realistic model parameters. Ladder properties depend sensitively on model parameters, the oxygen $p$ orbitals taken into account, and boundary conditions. The pair binding energy is a more reliable quantity than correlation functions for ascertaining the occurrence of pairing in ladders. Overall, our results for two-leg Emery ladders support the possibility of superconductivity in the hole-doped 2D model. The issue is rather to determine which of the various ladder structures and model parameters are appropriate to approximate the two-dimensional cuprates.

The discovery of many strongly correlated metallic phases has inspired different routes to generalize or go beyond the celebrated Landau Fermi liquid theory. To this end, from universal consideration of symmetries and anomalies, Else, Thorngren, and Senthil (ETS) have introduced a class of theories called ersatz Fermi liquids which possess a Fermi surface and satisfy a generalized Luttinger's theorem. In this work, we view all such fermion liquids obeying the Luttinger theorem as incompressible quantum Hall liquids in higher-dimensional phase space and use it as the starting point to derive their effective low-energy field theory. The noncommutativity of phase space motivates us to use the Seiberg-Witten map to derive the field theory in an ordinary (commutative) space and naturally leads to terms that correspond to the correct topological Chern-Simons action postulated by ETS in one, two, and three dimensions. Additionally, our approach also reproduces all the nontopological terms that characterize important contributions to the response, including the semiclassical equations of motion. Finally, our derivations of Chern-Simons terms from the Seiberg-Witten map also verify a longstanding conjecture in noncommutative field theory.

Analytic continuation is a critical step in quantum many-body computations, connecting imaginary-time or Matsubara Green's functions with real-frequency spectral functions, which can be directly compared to experimental results. However, because of the ill-posed nature of the analytic continuation problems, they have not been completely solved so far. In this paper, we suggest a simple, yet highly efficient method for analytic continuations of Matsubara Green's functions. This method takes advantage of barycentric rational functions to directly interpolate Matsubara Green's functions. At first, the nodes and weights of the barycentric rational functions are determined by the adaptive Antoulas-Anderson algorithm, avoiding reliance on nonconvex optimization. Next, the retarded Green's functions and the related spectral functions are evaluated by the resulting interpolants. We systematically explore the performance of this method through a series of toy models and realistic examples, comparing its accuracy and efficiency with other popular methods, such as the maximum entropy method. The benchmark results demonstrate that the new method can accurately reproduce not only continuous but also discrete spectral functions, irrespective of their positive definiteness. It works well even in the presence of intermediate noise, and outperforms traditional analytic continuation methods in computational speed. We believe that this method should stand out for its robustness against noise, broad applicability, high precision, and ultra-efficiency, offering a promising alternative to the maximum entropy method.

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multiband system with nearly flat bands, while offering unprecedented control over the filling fraction of electron and hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent tradeoff between accurately describing the band structure and incorporating the interactions within the Hamiltonian, particularly given the topological obstruction—so-called fragile topology—to the description of the model in terms of localized symmetric Wannier functions within the flat band manifold. Here, we circumvent this obstruction by using an extended eight-orbital model, for which localized Wannier orbitals have been formulated by [Carr et al., Phys. Rev. Res. 1, 033072 (2019)]. We constructed an extended multiorbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings from $-3$ to 3. We found several nearly degenerate insulating states at charge neutrality, all of which exhibit orbital orders. Crucially, TBG near magic angle is known to be particle-hole asymmetric, which is naturally captured by the single-particle band structure of our model and is reflected in the distinction between the symmetry broken states obtained at electron and hole dopings away from the charge neutral point. At filling $-1$ and $+2$, quantum anomalous hall state and inter-orbital inter-valley coherent states are obtained, while for the rest of the integer fillings away from charge neutrality, we found the system to realize metallic states with various orbital, valley and spin orderings. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund's-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intravalley and intervalley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

Materials with strong electronic correlations often exhibit a superconducting phase in close competition with other insulating phases, which is outstandingly difficult to resolve, e.g., for a group of quasi-two-dimensional (Q2D) materials such as the cuprates, even for the simplified minimal model of these materials, the doped 2D Hubbard model. The present work shows how quasi-one-dimensional (Q1D) systems, 2D and three-dimensional (3D) arrays of weakly coupled 1D correlated electrons, are much more amenable to resolving such competition, treating both instabilities on equal footing. Using the recently established matrix product state plus mean field $(\mathrm{MPS}+\mathrm{MF})$ approach for fermions [Bollmark et al., Phys. Rev. X 13, 011039 (2023)], we demonstrate that large systems can be reached readily in these systems, which opens up the thermodynamic regime via extrapolation. Focusing on basic model systems, 3D arrays of negative-$U$ Hubbard chains with additional nearest-neighbor interaction $V$, we show that despite the MF component of the $\mathrm{MPS}+\mathrm{MF}$ technique, we can reproduce the expected coexistence of the superconductivity and charge density wave at $V=0$ for density $n=1$. We then show how we can tune away from coexistence by both tuning $V$ and doping the system. This work thus paves the way to deploy two-channel $\mathrm{MPS}+\mathrm{MF}$ theory on some highly demanding high-$T_c$ superconducting systems, such as 3D arrays of repulsive-$U$ doped Hubbard ladders; we recently characterized the properties of such arrays in single-channel $\mathrm{MPS}+\mathrm{MF}$ calculations [Bollmark et al., Phys. Rev. X 13, 011039 (2023)].

Accessing two-photon statistics via Hanbury, Brown, and Twiss (HBT)-type measurements is essential for investigations of excitonic Bose-Einstein condensates. In this paper, we make use of quantum hydrodynamics in order to investigate the influence of finite system size on the two-photon emission intensity of a 2D condensate of excitons. We use the developed approach to calculate the two-photon decay time of exciton condensate in GaAs quantum wells and ${\mathrm{MoS}}_2$ bilayers. We demonstrate that the registered signal scales on the sample size in a qualitatively different manner than the Bogoliubov theory predicts.

The quantum spin Hall effect has been predicted in twisted homobilayer transition metal dichalcogenides (TMDs) owing to the layer-pseudospin magnetic field. Recently, experimental observations have also confirmed such topological states of matter. However, the topological electronic properties in multilayer moiré superlattices remain to be further explored. In twisted TMDs heterotrilayers, the realization of a moiré potential with various symmetries becomes feasible. Here, we demonstrate that twisted trilayer TMDs can enter a topological insulator phase under the influence of a moiré potential with $C_6$ symmetry. Specifically, we built two types of trilayer heterostructures, where the low-energy valence band electrons are contributed by the middle layer. In the AA-stacked moiré ${\mathrm{WS}}_2/{\mathrm{WSe}}_2/{\mathrm{MoS}}_2$ heterotrilayers where only the middle layer is twisted, the maxima of the moiré potential exhibit an approximate $C_6$ symmetry. The $C_6$ symmetry effectively compensates for the spatial inversion symmetry breaking in the ${\mathrm{WSe}}_2$ layer, leading to a twist-angle-dependent topological phase transition. Leveraging a Green's function approach, we calculate the local state density of edge states at topological minigaps, confirming their nature as moiré edge states. In the helical twisted AA-stacked moiré ${\mathrm{MoS}}_2/{\mathrm{WSe}}_2/{\mathrm{MoS}}_2$ heterotrilayers, we observed a mosaic pattern of topological and trivial insulators. The emergence of a topological mosaic is attributed to the maxima of the local moiré potential possessing $C_6$ symmetry. The results provide a way for the experimental realization of topological phases in TMDs heterojunctions.

We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid ${}^4\mathrm{He}$. We uncover the complete spatiotemporal evolution of such wire-based vortex detection via direct numerical simulations of the GP-W system. Furthermore, by computing the spatiotemporal spectrum, we obtain the vortex-capture-induced change in the oscillation frequency of the wire. We quantify this frequency shift by plotting the wire's oscillation frequency versus time and obtain results that closely match experimental observations. In addition, we provide analytical support for our numerical results by deriving the dispersion relation for the oscillating wire, with and without a trapped vortex. We show that the Magnus force opens a gap in the wire dispersion relation. The size of the gap becomes the characteristic frequency of the wire when a vortex is trapped.

To explore the potential of atomic clusters in device applications, we illustrate the thermal rectification (TR) effect and underlying mechanisms in the cluster-assembled Sierpiński tetrahedron (ST) fractals. Using the synthesized supertetrahedral $T_2$-type ${\mathrm{Sn}}_4{\mathrm{Se}}_{10}$ clusters as building blocks and nonequilibrium molecular dynamics with a machine-learning neuroevolution potential trained on a multidimensional ab initio dataset, we show that the TR coefficient of the assembled ${\mathrm{ST}}_4$ fractal reaches 17.4% at an average temperature of 300 K with a temperature bias of 20 K. This further increases to 39.4% under the same temperature condition for the higher-level fractal ${\mathrm{ST}}_5$ as the void ratio and surface roughness increase significantly with the fractal level. Moreover, unlike in conventional atom-based nanosystems, the dependence of the TR coefficient on temperature bias in the ST fractals is nonmonotonic, where a high TR efficiency can be achieved just with a small temperature bias. Our work demonstrates the merits of cluster-assembled fractals for high-performance thermal rectifiers and the advantages of cluster-assembled materials for thermal energy management.

Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, $\mathrm{\Delta }T$. However, experimental studies have exhibited a finite value of $\mathrm{\Delta }T$ for a transition to TC. This paper explores the onset of TC with much higher resolution than before and over a larger temperature range. We find that TC is always present, though small at the smallest $\mathrm{\Delta }T$ that we can reliably measure. However, it grows rapidly as $\mathrm{\Delta }T$ increases, the region of rapid growth coinciding with the $\mathrm{\Delta }T$ predicted from renormalization group arguments and observed experimentally. We are able to transcend the full range of TC, from the completely reversible state to one that is maximally decorrelated from the initially prepared state.

In this work, we present a first-principles density functional theory (DFT) computational investigation of the luminescence and absorption lineshapes associated with the neutral carbon-oxygen interstitial pair (${\mathrm{C}}_{\mathit{i}}{\mathrm{O}}_{\mathit{i}}$) defect in silicon. We obtain the lineshapes of the defect in the dilute limit using a computational methodology that constructs dynamical matrices of supercells containing tens of thousands of atoms, utilizing systems directly accessible through DFT. Both perturbed bulk phonons and localized vibrations contribute to the phonon sideband. We achieve excellent agreement with experimental luminescence data. Our findings further reinforce the attribution of the well-known C-line in silicon to the neutral ${\mathrm{C}}_{\mathit{i}}{\mathrm{O}}_{\mathit{i}}$ complex.

For an open quantum system described by the Lindblad equation, full characterization of its dynamics typically needs the knowledge of the Liouvillian spectrum and correlation functions. Solving the Liouvillian spectrum and correlation functions are usually formidable tasks, and most previous studies are constrained to simple models and lower-order correlations. In this work, we derive a closed form of dynamical recursion equations for all even-order correlation functions associated with the quadratic Liouvillian superoperator, thus extending Wick's theorem and enabling the reconstruction of the corresponding Liouvillian spectrum. Furthermore, we study the quartic Liouvillian superoperator, establishing the necessary and sufficient conditions for the closure of second-order correlation functions. Building on this, the dynamical expressions for even-order correlation functions under quadratic dissipation are derived, culminating in a method for constructing the Liouvillian spectrum in this extended framework.

Phase crystals are a class of nonuniform superconducting ground states characterized by spontaneous phase gradients of the superconducting order parameter. These phase gradients nonlocally drive periodic currents and magnetic fields, thus breaking both time-reversal symmetry and continuous translational symmetry. The phase crystal instability is generally triggered by negative and inhomogeneous superfluid stiffness. Several scenarios have been identified that can realize phase crystals, especially flat bands at specific edges of unconventional nodal superconductors. Motivated by omnipresent disorder in all materials, we employ the $t$-matrix approach within the quasiclassical theory of superconductivity to study the emergence of phase crystals at edges of a nodal $d$-wave superconductor. We quantify the full phase diagram as a function of the impurity scattering energy and the temperature, with full self-consistency in the impurity self energies, the superconducting order parameter, and the vector potential. We find that the phase crystal survives even up to $\sim 40–50\%$ of the superconducting critical impurity strength in both the Born and unitary scattering limits. Finally, we show how mesoscopic finite-size effects induce a competition with a state still breaking time-reversal symmetry but with translationally invariant edge currents.

We report on neutron scattering measurements on the vortex lattice of the noncentrosymmetric superconductor BiPd. We observe the existence of the intermediate mixed state, a region where Meissner and vortex lattice phases coexist, which is a feature of low $\kappa$ type-II superconductors. Following this, we obtain an estimate of the value of $\kappa$ using the extended London model. Finally, we find that the temperature dependence of the vortex lattice form factor fits well to a model designed to describe singlet-triplet mixing in noncentrosymmetric superconductors, which may shed light on the question of the gap structure in BiPd.

Phase diagrams and electronic transport properties of the helical states in purely two-dimensional (2D) Rashba superconductors coupled with in-plane Zeeman fields are studied. The continuum XY action is derived microscopically by integrating out the Gaussian amplitude fluctuation from the effective action. We show that the superfluid stiffness obtained from this procedure is exactly equivalent to the second-order derivative of the mean-field free-energy density with respect to Cooper pair momentum, indicating an essential role of the amplitude fluctuation. The vortex core energy is also included in this work, and its effects on the Berezinskii-Kosterlitz-Thouless (BKT) transition line are discussed. The theory of nonlinear $V\text{−}I$ characteristics in purely 2D superconductors is also revised to incorporate recent developments in the theory of the superconducting diode effect. The main results are as follows. We find that the nonlinear $V\text{−}I$ characteristics of the system become nonreciprocal in finite in-plane Zeeman fields. This is reminiscent of the superconducting diode effect in 2D systems, although the critical current is zero in purely 2D superconductors. Furthermore, we find that the bare effective superfluid stiffness along the BKT transition line has a local minimum at a certain temperature, and the nonreciprocity of the $V\text{−}I$ characteristics is strongly enhanced around this temperature.