Recent experiments on the twisted transition metal dichalcogenide (TMD) material ${\mathrm{WSe}}_2/{\mathrm{WS}}_2$ have observed insulating states at fractional occupancy of the moiré bands. Such states were conceived as generalized Wigner crystals (GWCs). In this paper, we investigate the problem of Wigner crystallization in the presence of an underlying (moiré) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_s$ indicates that ${\mathrm{MoSe}}_2$ (among the homobilayers) and ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ or ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ (among the heterobilayers) are the best candidates for realizing GWCs. We also establish that due to larger effective mass of the valence bands, in general, hole crystals are easier to realize that electron crystals as seen experimentally. For completeness, we show that satisfying the Mott criterion $n_{\mathrm{Mott}}^{1/2}{a}_{*}=1$ requires densities nearly three orders of magnitude larger than the maximal density for GWC formation. This indicates that for the typical density of operation, bilayer moiré systems are far from the Mott insulating regime. These crystals realized on a moiré lattice, unlike the conventional Wigner crystals, are incompressible due to the gap arising from pinning with the lattice. Finally, we capture this many-body gap by variationally renormalizing the dispersion of the vibration modes. We show these low-energy modes, arising from the coupling of the WC with the moiré lattice, can be effectively modeled as a Sine-Gordon theory of fluctuations.

We study a Josephson junction involving an inversion asymmetric Weyl semimetal in the presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0-\pi$ transition and a zero-bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC), and the TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry and ${\mathbb{Z}}_2$ symmetry broken by the respective tilt. We obtain the reversal of a pure VJC and pure CJC even in the zero-bias condition controllable by the junction length. Our analysis of controllability of valley- and chirality-dependent transport in an inversion asymmetric Weyl semimetal junction could allow applications in valleytronics and chiralitytronics, respectively. The tilt-induced Josephson effect provides an alternative route for supercurrent $0-\pi$ transition, different from the conventional ferromagnetism Josephson junctions where the spin polarization is essential. In the long junction and zero-temperature limit, VJC and CJC are associated with a quantum anomaly which is manifested through a discontinuous jump in the current in absence of TRS and TRS breaking tilts, respectively.

The semiclassical transport theory is especially powerful for investigating galvanomagnetic effects. Generally, the semiclassical theory is applicable only in weak fields because it does not consider Landau quantization. Herein, we extend the conventional semiclassical theory by considering Landau quantization through the field dependence of carrier density in semimetals. Using this approach, we simultaneously explain the qualitative change in the angular dependence of transverse magnetoresistance (TMR), anisotropic magnetoresistance, and planar Hall effect in bismuth with an increase in the magnetic field. We also considered the quantitative applicability of our theory. We found that the field dependence of mobility can result in a qualitative agreement in TMR far beyond the quantum limit ($\gtrsim 10$ T).

We study a cluster of quantum dots defined within silicene that hosts confined electron states with spin and valley degrees of freedom. Atomistic tight-binding and continuum Dirac approximations are applied for a few-electron system in the quest for spontaneous valley polarization driven by interdot tunneling and an electron-electron interaction, i.e., a valley counterpart of itinerant Nagaoka ferromagnetic ordering recently identified in a GaAs square cluster of quantum dots with three excess electrons [J. P. Dehollain et al., Nature (London) 579, 528 (2020)]. We find that for a Hamiltonian without intrinsic spin-orbit coupling the valley polarization in the ground state can be observed in a range of interdot spacings provided that the spin of the system is frozen by an external magnetic field. The intervalley scattering effects are negligible for a cluster geometry that supports the valley-polarized ground state. In the presence of a strong intrinsic spin-orbit coupling that is characteristic to silicene, no external magnetic field is necessary for the observation of a ground state that is polarized in both the spin and valley. The effective magnetic field due to the spin-orbit interaction produces a perfect anticorrelation of the spin and valley isospin components in the low-energy spectrum. Experimental detection of spin-valley ground-state polarization by a charge response to a potential variation is discussed.

Destructive quantum interference (DQI) and its effects on electron transport are studied in chemical molecules and finite physical lattices that can be described by a discrete Hamiltonian. Starting from a bipartite system whose conductance zeros are known to exist between any two points of a specially designated set, the interference set, we use the Dyson equation to develop a general algorithm for determining the zero conductance points in complex systems, which are not necessarily bipartite. We illustrate this procedure as it applies to the fulvene molecule. The stability of the conductance zeros is analyzed with respect to external perturbations.

We study the polaritonic band structure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having resonant atomic transitions to excited states with different angular momentum. We employ a computational method based on the recently proposed Dirichlet-to-Neumann map technique, which accurately models non-Markovian dynamics, as well as interactions involving higher-order electric and magnetic multipole transitions. We design topologically robust edge states which are used to achieve unidirectional emission and nonreciprocal transmission of single photons. We also point out the challenges in realizing bands with higher Chern numbers in such systems.

Motivated by the link between Anderson localization on high-dimensional graphs and many-body localization, we study the effect of periodic driving on Anderson localization on random trees. The time dependence is eliminated in favor of an extra dimension, resulting in an extended graph wherein the disorder is correlated along the new dimension. The extra dimension increases the number of paths between any two sites and allows for interference between their amplitudes. We study the localization problem within the forward scattering approximation (FSA), which we adapt to this extended graph. At low frequency, this favors delocalization as the availability of a large number of extra paths dominates. By contrast, at high frequency, it stabilizes localization compared to the static system. These lead to a regime of re-entrant localization in the phase diagram. Analyzing the statistics of path amplitudes within the FSA, we provide a detailed theoretical picture of the physical mechanisms governing the phase diagram.

The miscibility of Au and Li exhibits a potential application as an adhesion layer and electrode material in secondary batteries. Here, to explore alloying properties, we constructed a neural network potential (NNP) of Au-Li binary systems based on density functional theory (DFT) calculations. To accelerate construction of NNPs, we proposed an efficient and inexpensive method of structural dataset generation. The predictions by the constructed NNP on lattice parameters and phonon properties agree well with those obtained by DFT calculations. We also investigated the mixing energy of ${\mathrm{Au}}_{1-x}{\mathrm{Li}}_x$ with fine composition grids, showing excellent agreement with DFT verifications. We found the existence of various compositions with structures on and slightly above the convex hull, which can explain the lack of consensus on the Au-Li stable phases in previous studies. Moreover, we found other stable phases, namely ${\mathrm{Au}}_{0.45}{\mathrm{Li}}_{0.55}, {\mathrm{Au}}_{0.389}{\mathrm{Li}}_{0.611}$, and ${\mathrm{Au}}_{0.357}{\mathrm{Li}}_{0.643}$. Finally, we examined the alloying process starting from the phase separated structure to the complete mixing phase. We found that when multiple adjacent Au atoms dissolved into Li, the alloying of the entire Au/Li interface started from the dissolved region. This paper demonstrates the applicability of NNPs toward miscible phases, and it provides an understanding of the alloying mechanism.

Weyl materials, exhibiting topologically nontrivial touching points in band dispersion, are fascinating subjects of research, which have been extensively studied in electron-related systems. In this paper, by employing first-principles calculations of topological phonons in wurtzite-structured phases of $MX$ chalcogenides (where $M=\mathrm{Zn}$ and Cd and $X=\mathrm{O}$, S, Se, and Te), we demonstrate the existence of ideal type-II Weyl phonons in wurtzite ZnSe, a well-known II-VI semiconductor. There are in the ${\mathbf{q}}_z=0.0$ plane six pairs of Weyl points stemming from the inversion between the two optical branches. The nontrivial phonon surface states and surface arcs projected on the semifinite (0001) surfaces are investigated. Phonon surface arcs connecting each pair of Weyl points with opposite chirality, guaranteed to be $0.55{\AA }^{-1}$ and very long, are readily observable in experiment. The opposite chirality of Weyl points with quantized Berry curvature produces the Weyl phonon Hall effect. Our results propose a potential platform for future experimental study of type-II Weyl phonons in realistic materials.

One primary concern in diluted magnetic semiconductors (DMSs) is how to establish a long-range magnetic order with low magnetic doping concentration to maintain the gate tunability of the host semiconductor, as well as to increase Curie temperature. Several van der Waals semiconductors have been investigated recently to demonstrate the magnetic order in DMSs. Nonetheless, a comprehensive understanding of the operative mechanism has remained elusive. Here, we demonstrate concrete evidence of the long-range magnetic order through itinerant spin-polarized holes in a monolayer V-doped $\mathrm{W}{\mathrm{Se}}_2$ semiconductor. Hybridization between V impurity states and the host valence band has been investigated using scanning tunneling microscopy. Transport characteristics reveal the itinerant holes within the hybridized band and hysteresis in magnetoresistance; this clearly resembles the Zener-type description of the itinerant ferromagnetism as predicted by density functional theory calculations.

The recently discovered magnetic topological insulator of $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$, has been successfully used to explore emerging physical phenomena, such as the quantum anomalous Hall effect (QAHE) and axion insulator state. Based on first-principles calculations, we have systematically investigated the electronic, magnetic, and topological properties of layered $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Te}}_4, \mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Se}}_4$, and $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Se}}_4$, where those materials host similar crystal structure as the $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. Our calculations first show that each bulk system with antiferromagnetic order can be converted into a three-dimensional topologically nontrivial insulator by applying appropriate pressure. Then, we find that ferromagnetic (FM) $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Te}}_4$ is a type II Weyl semimetal with a single pair of Weyl points near Fermi level. Specifically, FM $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Se}}_4$ and $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Se}}_4$ can be readily converted into Weyl semimetals under pressure. Furthermore, we notice that QAHE can also be achieved in layered FM $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Te}}_4$ and $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Se}}_4$. All those findings demonstrate that the $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$-like materials of $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Te}}_4, \mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Se}}_4$, and $\mathrm{Mn}{\mathrm{Sb}}_2{\mathrm{Se}}_4$ are promising candidates to explore intriguing topological quantum states.

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-$1/2$ ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a ${\mathbb{Z}}_2$ quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.

The pseudofermion functional renormalization group (PFFRG) method has proven to be a powerful numerical approach to treat frustrated quantum spin systems. In its usual implementation, however, the complex fermionic representation of spin operators introduces unphysical Hilbert-space sectors which render an application at finite temperatures inaccurate. In this work we formulate a general functional renormalization group approach based on Majorana fermions to overcome these difficulties. We, particularly, implement spin operators via an $\text{SO}\left(3\right)$ symmetric Majorana representation which does not introduce any unphysical states and, hence, remains applicable to quantum spin models at finite temperatures. We apply this scheme, dubbed pseudo-Majorana functional renormalization group (PMFRG) method, to frustrated Heisenberg models on small spin clusters as well as square and triangular lattices. Computing the finite-temperature behavior of spin correlations and thermodynamic quantities such as free energy and heat capacity, we find good agreement with exact diagonalization and the high-temperature series expansion down to moderate temperatures. We observe a significantly enhanced accuracy of the PMFRG compared to the PFFRG at finite temperatures. More generally, we conclude that the development of functional renormalization group approaches with Majorana fermions considerably extends the scope of applicability of such methods.

We show that layered superconductors, due to their peculiar nonlinear response to a weak dc magnetic field, behave as tunable hyperbolic media within a wide terahertz range. Thereby, various attractive phenomena intrinsic in hyperbolic materials can be controlled by dc magnetic field. In particular, in this work a resonant transparency of a layered superconductor induced by the excitation of localized waves with nonmonotonic dispersion, is studied. We reveal the dc magnetic field is able to adjust the electromagnetic properties of a layered superconductor in order to observe specific twin peaks in the transmittance-vs-angle dependence. In addition, solving the problem by the transfer-matrix method, we succeed in deriving the matrix responsible for the effect of dc magnetic field. It is notable that this specific matrix depends neither on the size of the layered superconductor, nor on the parameters of surroundings.

Superconductivity found in doped $\mathrm{Nd}\mathrm{Ni}{\mathrm{O}}_2$ is puzzling as two local symmetries of doped $\mathrm{Ni}{\mathrm{O}}_2$ layers compete, with presumably far-reaching implications for the involved mechanism: A cupratelike regime with Zhang-Rice singlets is replaced by local triplet states at realistic values of charge-transfer energy, which would suggest a rather different superconductivity scenario from high-$T_c$ cuprates. We address this competition by investigating ${\mathrm{Ni}}_4{\mathrm{O}}_8$ clusters with periodic boundary conditions in the parameter range relevant for the superconducting nickelates. With increasing value of charge-transfer energy we observe upon hole doping the expected crossover from the cuprate regime dominated by Zhang-Rice singlets to the local triplet states. We find that smaller charge-transfer energy $\mathrm{\Delta }$ is able to drive this change in the ground-state character when realistic values for nickel-oxygen repulsion $U_{dp}$ are taken into account. For large values of the charge-transfer energy, oxygen orbitals are less important than in superconducting cuprates as their spectral weight is found only at rather high excitation energies. However, a second $\mathrm{Ni}(3d$) orbital can easily become relevant, with either the $xy$ or the $3z^2-r^2$ orbitals contributing in addition to the $x^2-y^2$ orbital to the formation of triplet states. In addition, our result that $U_{dp}$ (acting between Ni and O) favors on-site triplets implies that correlation effects beyond purely on-site interactions should be taken into account when obtaining effective two-band models.

We have investigated the bulk and microscopic properties of the rhombohedral intermediate valence superconductor ${\mathrm{CeIr}}_3$ by employing magnetization, heat capacity, and muon spin rotation and relaxation ($\mu \mathrm{SR}$) measurements. The magnetic susceptibility indicates bulk superconductivity below $T_{\mathrm{C}}=3.1\mathrm{K}$. Heat capacity data also reveal a bulk superconducting transition at 3.1 K with a second weak anomaly near 1.6 K. Zero-field $\mu \mathrm{SR}$ data show no strong evidence of broken time-reversal symmetry but support the presence of spin fluctuations below $T_{\mathrm{C}}$. Transverse-field $\mu \mathrm{SR}$ measurements suggest a fully gapped, isotropic, $s$-wave superconductivity with $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{C}}=3.76\left(3\right)$, very close to 3.53, the Bardeen-Cooper-Schrieffer gap value for weak-coupling superconductors. From the temperature variation of the magnetic penetration depth, we have also determined the London penetration depth ${\lambda }_{\mathrm{L}}\left(0\right)=435\left(2\right)\mathrm{nm}$, the carrier effective-mass enhancement $m^{*}=1.69\left(1\right)m_{\mathrm{e}}$, and the superconducting carrier density $n_{\mathrm{s}}=2.5\left(1\right)\times {10}^{27}$ carriers ${\mathrm{m}}^{-3}$. The fact that ${\mathrm{LaIr}}_3$, with no $4f$ electrons, and ${\mathrm{CeIr}}_3$ with $4f^n$ electrons where $n\le 1$ (Ce ion in a valence fluctuating state), both exhibit the same $s$-wave gap symmetry indicates that the $\mathrm{Ir}\text{−}d$ band governs the physics of these two compounds near the Fermi level, which is in agreement with previous band structure calculations.

We present extensive large-scale dynamical simulations of phase-separated states in the double exchange model. These inhomogeneous electronic states that play a crucial role in the colossal magnetoresistance phenomenon are composed of ferromagnetic metallic clusters embedded in an antiferromagnetic insulating matrix. We compute the dynamical structure factor of these nanoscale textures using an efficient real-space formulation of coupled spin and electron dynamics. Dynamical signatures of the various underlying magnetic structures are identified. At small hole doping, the structure factor exhibits a dominating signal of magnons from the background Néel order and localized modes from magnetic polarons. A low-energy continuum due to large-size ferromagnetic clusters emerges at higher doping levels. Implications for experiments on magnetoresistive manganites are discussed.

Fractional Chern insulator (FCI) states have been proposed in singular lattices with arbitrary $n$-fold rotational symmetry. Particles occupy non-defect-core orbitals in previously reported FCIs. However, the role of defect-core orbitals in the singular-lattice FCI states has seldom been discussed. In this paper, we report a series of singular-lattice FCI states with one particle occupying the defect-core orbital. This singular-lattice FCI state can be identified with the aid of the edge excitations, the angular momentum of the ground state (GS), and the optimal trial wave functions. Edge excitations and GS angular momentum are obtained using exact diagonalization. Optimal trial wave functions are constructed on the basis of the generalized Pauli principle, the Jack polynomials, and single-particle states. The present FCI state is identified as a $\nu =1/2$ FCI with high values of wave function overlap, where one particle occupies the low-energy defect-core orbital. Our studies reveal the intriguing interplay between the singular-lattice FCI and the defect-core orbital and provide an effective approach for future researches on FCIs with various defects or disorders.

Using the Lindblad equation approach, we derive the range of the parameters of an interacting one-dimensional electronic chain connected to two reservoirs in the large bias limit in which an optimal working point (corresponding to a change in the monotonicity of the stationary current as a function of the applied bias) emerges in the nonequilibrium stationary state. In the specific case of the one-dimensional spinless fermionic Hubbard chain, we prove that an optimal working point emerges in the dependence of the stationary current on the coupling between the chain and the reservoirs, both in the interacting and in the noninteracting case. We show that the optimal working point is robust against localized defects of the chain, as well as against a limited amount of quenched disorder. Eventually, we discuss the importance of our results for optimizing the performance of a quantum circuit by tuning its components as close as possible to their optimal working point.

The Lorenz ratio serves as a measure to compare thermal and electric conductivities of metals. Recent experiments observed small Lorenz ratios in the compensated metal $\mathrm{W}{\mathrm{P}}_2$, indicating that charge flow is strongly favored over heat conduction. Motivated by these findings, we study transport properties of compensated metals in the presence of electron-electron collisions and electron-impurity scattering. We focus on intermediate temperatures, where the phonon contributions to transport are weak and elastic and inelastic scattering rates are comparable. Our exact solution for the kinetic equation in the presence of general Fermi-liquid interactions is used to extract the Lorenz ratio for short- and long-range interactions. We find that the Lorenz ratio develops a temperature dependence and gets enhanced as a consequence of disorder scattering. For collisions mediated by the Coulomb interaction, impurities give rise to a nonmonotonic dependence of the Lorenz ratio on the screening wave number with a minimum for intermediate screening strength. To help future experimental efforts, we establish a scheme to connect the exact results with the solution of the Boltzmann equation under the relaxation time approximation for all collision integrals. Our recipe provides simple phenomenological expressions for the transport coefficients and it allows for a physically transparent interpretation of the results.