${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ is a magnetic Weyl semimetal, in which ferromagnetic ordering at 177 K is predicted to stabilize Weyl points. We perform temperature and spatial dependent angle-resolved photoemission spectroscopy measurements through the Curie temperature ($T_c$), which show large band shifts and renormalization concomitant with the onset of magnetism. We argue that ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ evolves from a Mott ferromagnet below $T_c$ to a correlated metallic state above $T_c$. To understand the magnetism, we derive a tight-binding model of Co-$3d_{x^2-y^2}$ orbitals on the kagome lattice. At the filling obtained by first-principles calculations, this model reproduces the ferromagnetic ground state, and results in the reduction of Coulomb interactions due to cluster effects. Using a disordered local moment simulation, we show how this reduced Hubbard $U$ leads to a collapse of the bands across the magnetic transition, resulting in a correlated state, which carries associated characteristic photoemission signatures that are distinct from those of a simple lifting of exchange splitting. The behavior of topology across $T_c$ is discussed in the context of this description of the magnetism.

We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in a homogeneous $p+ip$ superconducting (SC) phase at high or low fermion densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain $p$-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above $T_{\mathrm{sc}}$, generating a homogeneous normal phase (far away from $n=1/2$), or a PS between normal phases with different densities (close to $n=1/2$). Further increasing temperature to $T_{\mathrm{ps}}$, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on the filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/particle doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite $V$ and extends to finite doping regime.

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with nonzero chemical potential is one such problem. Our method is based on projected entangled pair states using imaginary-time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably. In particular, it shows near to optimal, that is linear, scaling in lattice size. We also present an approach to directly simulate the subspace with an odd number of fermions. It allows to independently determine the ground state in both sectors. Without a chemical potential, this corresponds to half-filling and the lowest-energy state with one additional electron or hole. We identify several stability issues, such as degenerate ground states and large single-particle gaps, and provide possible fixes.

Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of projected entangled pair states, topological order is characterized by an entanglement symmetry of the local tensor that describes the model. This symmetry can take the form of a tensor product of group representations [for quantum double models $D\left(G\right)$ of a group $G]$, or in the more general case a correlated symmetry action in the form of a matrix product operator (MPO), which encompasses all string-net models, including those that are not quantum double models. Among other things, these entanglement symmetries allow for the succinct description of ground states and topological excitations (anyons). Recently, the idea has been put forward to use those symmetries and the anyonic objects they describe as order parameters for probing topological phase transitions, and the applicability of this idea has been demonstrated for Abelian groups. In this paper, we extend this construction to the domain of non-Abelian models with MPO symmetries, and we use it to study the breakdown of topological order in the double Fibonacci (DFib) string-net model and its Galois conjugate, namely the non-Hermitian double Yang-Lee (DYL) string-net model. We start by showing how to construct topological order parameters for condensation and deconfinement of anyons using the MPO symmetries. Subsequently, we set up interpolations from the DFib and the DYL model to the trivial phase, and we show that these can be mapped to certain restricted solid on solid (RSOS) models, which are equivalent to the $[(5\pm \sqrt{5})/2]$-state Potts model, respectively. Moreover, the order parameter for condensation maps to the RSOS order parameter. The known exact solutions of the statistical models subsequently allow us to locate the critical points of the models, and to predict the critical exponents for the order parameters from conformal field theory. We complement this by numerical study of the phase transitions, which fully confirms our theoretical predictions; remarkably, we find that both models exhibit a duality between the behavior of order parameters for condensation and deconfinement.

Gapped bilayer graphene can support the presence of intragap states due to kink gate potentials applied to the graphene layers. Electrons in these states display valley-momentum locking, which makes them attractive for topological valleytronics. Here, we show that kink-antikink local potentials enable modulated scattering of topological currents. We find that the kink-antikink coupling leads to anomalous steps in the junction conductance. Further, when the constriction detaches from the propagating modes, forming a loop, the conductance reveals the system energy spectrum. Remarkably, these kink-antikink devices can also work as valley filters with tiny magnetic fields by tuning a central gate.

Auger-like exciton-exciton annihilation (EEA) is considered the key fundamental limitation to quantum yield in devices based on excitons in two-dimensional (2D) materials. Since it is challenging to experimentally disentangle EEA from competing processes, guidance of a quantitative theory is highly desirable. The very nature of EEA requires a material-realistic description that is not available to date. We present a many-body theory of EEA based on first-principle band structures and Coulomb interaction matrix elements that goes beyond an effective bosonic picture. Applying our theory to monolayer ${\mathrm{MoS}}_2$ encapsulated in hexagonal BN, we obtain an EEA coefficient on the order of ${10}^{-3}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$ at room temperature, suggesting that carrier losses are often dominated by other processes, such as defect-assisted scattering. Our studies open a perspective to quantify the efficiency of intrinsic EEA processes in various 2D materials in the focus of modern materials research.

Heavy-fermion metals typically exhibit an unconventional quantum critical point or quantum critical phase at zero temperature due to the competition of the Kondo effect and magnetism. Previous theories were often based on certain local types of assumptions, and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice, and we introduce the concept of a nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations but a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy-fermion quantum criticality.

We study quantum phase transitions out of the fracton ordered phase of the ${\mathbb{Z}}_N$ X-cube model. These phase transitions occur when various types of subdimensional excitations and their composites are condensed. The condensed phases are either trivial paramagnets, or are built from stacks of $D=2$ or 3 deconfined gauge theories, where $D$ is the spatial dimension. The nature of the phase transitions depends on the excitations being condensed. Upon condensing dipolar bound states of fractons or lineons, for $N\ge 4$ we find stable critical points described by decoupled stacks of $D=2$ conformal field theories. Upon condensing lineon excitations, when $N>4$ we find a gapless phase intermediate between the X-cube and condensed phases, described as an array of $D=1$ conformal field theories. In all these cases, effective subsystem symmetries arise from the mobility constraints on the excitations of the X-cube phase and play an important role in the analysis of the phase transitions.

We study the thermal conductivity in an excitonic insulator using a simple quasi-one-dimensional two-band model consisting of electron and hole bands with the Coulomb interactions between these bands. Based on the linear response theory within a mean-field scheme, we develop a method to identify the contributions to thermal conductivity driven by the excitonic insulator. It is found that there is an additional heat current operator owing to the excitonic phase transition, and that it gives contributions to the thermal conductivity which are not expressed in the form of Sommerfeld-Bethe relations written in the form of an imaginary-time derivative of the electric current operator. Finally, we discuss the relationship between the additional contribution and the heat current carried by excitons.

Effective gauge theories based on slave particle construction are widely used to describe quantum number fractionalization in strongly correlated electron systems. However, even setting aside the debates on the confinement issue of the slave particles, there are still significant conflicts between theory and experiment. In particular, a $T^{2/3}$ specific heat anomaly has been predicted to be the smoking-gun signature of low-lying gauge fluctuation in a $U\left(1\right)$ spin liquid with a large spinon Fermi surface, which has, however, never been observed. Here we show that such an anomaly is actually an artifact of a Gaussian approximation and is absent when the no-double-occupancy constraint on the slave particles is strictly enforced. We also show that projective construction based on slave particle representation provides a unified understanding of the mechanism of spin fractionalization in one- and two-dimensional spin liquids.

An $\mathit{ab}\mathit{initio}$-based fully microscopic approach is applied to study the nonlinear optical response of bulk tellurium. The structural and electronic properties are calculated from first principles using the shLDA-1/2 method within density functional theory. The resulting band structure and dipole matrix elements serve as input for the quantum mechanical evaluation of the anisotropic linear optical absorption spectra, yielding results in excellent agreement with published experimental data. Assuming quasiequilibrium carrier distributions in the conduction and valence bands, absorption/gain and spontaneous emission spectra are computed from the semiconductor Bloch and luminescence equations. For ultrafast intense off-resonant excitation, the generation of high harmonics is evaluated and the emission spectra are calculated for samples of different thicknesses.

We study the Hall conductivity of a two-dimensional electron gas under an inhomogeneous magnetic field $B\left(x\right)$. First, we prove using the quantum kinetic theory that an odd magnetic field can lead to a purely nonlinear Hall response. Second, considering a real-space magnetic dipole consisting of a sign-changing magnetic field and based on numerical semiclassical dynamics, we unveil a parametric resonance involving the cyclotron ratio and a characteristic width of $B\left(x\right)$, which can greatly enhance the Hall response. Different from previous mechanisms that rely on the bulk Berry curvature dipole, the effect largely stems from boundary states associated with the real-space magnetic dipole. Our findings pave a way to engineer current rectification and higher harmonic generation in two-dimensional materials having or not having crystal inversion symmetry.

We study coherent charge oscillations in double quantum dots tunnel coupled to metallic leads. If two such systems are coupled by Coulomb interaction, there are, in total, six (instead of only two) oscillation modes of the entangled system with interaction-dependent oscillation frequencies. By tuning the bias voltage, one can engineer decoherence such that only one of the six modes, in which the charge oscillations in both double quantum dots become synchronized in antiphase, is singled out. We suggest using waiting-time distributions and the $g^{\left(2\right)}$-correlation function to detect the common frequency and the phase locking.

Newly synthesized nanostructures of graphene appear as a promising breeding ground for new technology. Therefore it is important to identify the role played by the boundary conditions in their electronic features. In this contribution, we use the nonequilibrium Green's function method coupled to tight-binding theory to calculate and compare the current patterns of hexagonal graphene quantum dots, with contacts placed at different edge locations. Our results reveal the formation of current vortices when the geometry of the contact position is not centrosymmetric. That is when they are placed on nonfrontal armchairlike vertices of the quantum dot. The introduction of defects, leading to disorder, significantly alters the current behavior, distorting bulk vortices and annihilating the edge currents. Nevertheless, periodically distributed defects on the edge allow for the appearance of current loops that dodge the defects. The presence of current vortices suggests the use of graphene quantum dots as nanomagnets or magnetic nanosensors.

The coupling between electrical, thermal, and spin transport results in a plethora of novel transport phenomena. However, disentangling different effects is experimentally very challenging. We demonstrate that bilayers consisting of the antiferromagnetic insulator hematite ($\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$) and Pt allow one to precisely measure the transverse spin Nernst magnetothermopower (TSNM) and observe the low-temperature suppression of the platinum (Pt) spin Nernst angle. We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the Néel vector of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing one to unambiguously distinguish the TSNM from thermally excited magnon transport, which usually dominates in ferri/ferromagnets due to their nonzero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below $\sim 100\mathrm{K}$. We compare these results with theoretical calculations of the temperature-dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect.

We have recently shown that injection of magnons into a magnetic dielectric via the spin-orbit torque (SOT) effect in the adjacent layer of a heavy metal subjected to the action of short $\left(0.1\mu \mathrm{s}\right)$ current pulses allows for control of a magnon Bose-Einstein condensate (BEC). Here, the BEC was formed in the process of rapid cooling (RC), when the electric current heating the sample is abruptly terminated. In the present Letter, we show that the application of a longer $\left(1.0\mu \mathrm{s}\right)$ electric current pulse triggers the formation of a nonlinear localized magnonic bullet below the linear magnon spectrum. After pulse termination, the magnon BEC, as before, is formed at the bottom of the linear spectrum, but the nonlinear bullet continues to exist, stabilized for an additional 30 ns by the same process of RC-induced magnon condensation. Our results suggest that a stimulated condensation of excess magnons to all highly populated magnonic states occurs.

We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSCs), which are dynamical Majorana-carrying phases of matter with no static counterpart. Despite the triviality of its bulk Floquet bands, an AFHOTSC generically features the simultaneous presence of corner-localized Majorana modes at both zero and $\pi /T$ quasienergies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSCs is their unavoidable singular behavior in the phase spectrum of the bulk time-evolution operator. By mapping such evolution-phase singularities to the stroboscopic boundary signatures, we classify 2D AFHOTSCs that are protected by a rotation group symmetry in symmetry class $D$. We further extract a higher-order topological index for unambiguously predicting the presence of Floquet corner Majorana modes, which we confirm numerically. Our theory serves as a milestone towards a dynamical topological theory for Floquet superconducting systems.