The study of the charge excitations in cuprates is presently an interesting topic because of the development of new and precise x-ray experiments. Based on a large-$N$ formulation of the two-dimensional $t\text{−}J$ model, which allows us to consider all possible charge excitations on an equal footing, we investigate the charge spectrum for both electron- and hole-doped cases. In both cases, the instability toward phase separation, which has momentum modulation $\mathbf{q}=(0,0)$, is found to be robust in a large region of the doping-temperature phase diagram. If a short-range Coulomb repulsion is included the phase separation region shrinks, but the instability remains at $\mathbf{q}=(0,0)$. If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at $\mathbf{q}$ momenta forming a ring around $\mathbf{q}=(0,0)$. The computed charge spectrum in the translation-invariant phase shows well-formed rings. We discuss our results in the light of recent x-ray experiments in electron- and hole-doped cuprates, where ring-like shaped charge modulations have been reported.

We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory, and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on interlayer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of thermal critical points. From a perturbative approach in terms of an effective Ising model description, we identify a quadratic suppression of the critical temperature scale in the strongly plaquettized region. Based on free-energy arguments we furthermore obtain the full phase boundary of the low-temperature dimer-singlet regime, which agrees well with the quantum Monte Carlo data.

We explore superconductivity in strongly interacting electrons on a decorated honeycomb lattice (DHL). An easy-plane ferromagnetic interaction arises from spin-orbit coupling in the Mott insulating phase, which favors a triplet resonance valence bond spin liquid state. Hole doping leads to partial occupation of a flat band and to triplet superconductivity. The order parameter is highly sensitive to the doping level and the interaction parameters, with $p+ip$, $f$, and $p+f$ superconductivity found, as the flat band leads to instabilities in multiple channels. Typically, first-order transitions separate different superconducting phases, but a second-order transition separates two time-reversal symmetry breaking $p+ip$ phases with different Chern numbers ($\nu =0$ and 1). The Majorana edge modes in the topological ($\nu =1$) superconductor are almost localized due to the strong electronic correlations in a system with a flat band at the Fermi level. This suggests that these modes could be useful for topological quantum computing. The “hybrid” $p+f$ state does not require two phase transitions as temperature is lowered. This is because the symmetry of the model is lowered in the $p$-wave phase, allowing arbitrary admixtures of $f$-wave basis functions as overtones. We show that the multiple sites per unit cell of the DHL, and hence multiple bands near the Fermi energy, lead to very different nodal structures in real and reciprocal space. We emphasize that this should be a generic feature of multisite/multiband superconductors.

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. Here we demonstrate that the existence of a two-dimensional topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $Lln\left(L\right)$. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\omega =k_x{k}_y.$

We introduce and analyze an extended Hubbard model, in which intersite Coulomb interaction as well as a staggered local potential (SLP) are considered, on the square lattice at half band filling, in the thermodynamic limit. Using both Hartree-Fock approximation and Kotliar and Ruckenstein slave boson formalism, we show that the model harbors charge order (CO) as well as joint spin and charge modulations (SCO) at finite values of the SLP, while the spin-density wave (SDW) is stabilized for vanishing SLP only. We determine their phase boundaries and the variations of the order parameters in dependence on the SLP, as well as on the on-site and nearest-neighbor interactions. Domains of coexistence of CO and SCO phases, suitable for resistive switching experiments, are unraveled. We show that the novel SCO systematically turns into the more conventional SDW phase when the zero-SLP limit is taken. We also discuss the nature of the different phase transitions, both at zero and finite temperature. In the former case, no continuous CO to SDW (or SCO) phase transition occurs. In contrast, a paramagnetic phase (PM), which is accompanied with continuous phase transitions towards both spin or charge ordered phases, sets in at finite temperature. A good quantitative agreement with numerical simulations is demonstrated, and a comparison between the two used approaches is performed.

We study the effects of disorder in a one-dimensional model of ${\mathbb{Z}}_3$ Fock parafermions which can be viewed as a generalization of the prototypical Kitaev chain. Exact diagonalization is employed to determine level statistics, participation ratios, and the dynamics of domain walls. This allows us to identify ergodic as well as finite-size localized phases. In order to distinguish Anderson from many-body localization, we calculate the time evolution of the entanglement entropy in random initial states using tensor networks. We demonstrate that a purely quadratic parafermion model does not feature Anderson but many-body localization due to the nontrivial statistics of the particles.

Exploring the properties of a highly quantum-degenerate electron-hole (e-h) state as a many-body system is an interesting problem in solid-state physics. Electron-hole droplets (EHDs) offer a potential platform for investigating such a state of Fermi-degenerate carriers at an extremely high density. Herein we present dielectric response measurements of carriers in the mid-infrared (MIR) region for a definitive evaluation of the dynamic properties of the e-h state of EHDs in diamond. With photoexcitation across the band-gap energy by using the two-photon absorption process, we performed time-resolved differential transmission spectroscopy by using MIR probe light and time-resolved photoluminescence spectroscopy in the deep-ultraviolet region. By linking the two temporal profiles, we overcame the problem of previous ambiguous PL analyses and elucidated the MIR dielectric response that reveals the surface plasmon resonance (SPR) of EHDs and the effect of the e-h Coulomb interaction on the dynamic dielectric response. Thus, we found that the carrier density inside EHDs remained constant at $8\times {10}^{19}{\mathrm{cm}}^{-3}$ up to 2 ns, whereas a decay time of 1 ns of the condensed volume was found and the AC conductivity relaxation rate of $2\times {10}^{14}{\mathrm{s}}^{-1}$ maintained during this nanosecond timescale was the highest among group-IV semiconductors. We predicted a strong dependence of the e-h scattering rate on the probe frequency in the high-frequency region in which SPR appeared, suggesting that—when probed in the low-frequency region—dynamical relaxation does not interfere with the order formation expected in quantum-degenerate e-h systems at ultralow temperatures.

We consider the propagation of electrons in a lattice with an anisotropic dispersion in the $x-y$ plane (lattice constant $a$), such that it supports open orbits along the $x$ axis in an out-of-plane magnetic field $B$. We show that a point source excites a “breathing mode,” a state that periodically spreads out and refocuses after having propagated over a distance $\ell ={(eaB/h)}^{-1}$ in the $x$ direction. Unlike known magnetic focusing effects, governed by the classical cyclotron radius, this is an intrinsically quantum mechanical effect with a focal length $\propto \hslash$.

We systematically investigate possible helix states in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction. Exact solutions show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, the quench dynamics shows that a steady helix state emerges from some easily prepared initial states, including saturated and maximally mixed ferromagnetic states, according to the analysis of the perturbation method. The corresponding dynamics for near resonant cases is also investigated numerically, indicating the robustness of the scheme. Our findings highlight the cooperation of non-Hermiticity and the DM interaction in a quantum spin system, suggesting a way for preparing a steady helix state in a non-Hermitian quantum spin system.

We study the electronic thermal conductivity ${\kappa }_{\text{el}}$ and the thermal diffusion constant $D_{\text{Q,el}}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We make use of the Nernst-Einstein relation for thermal transport and connect the strong nonmonotonous temperature dependence of ${\kappa }_{\text{el}}$ to that of $D_{\text{Q,el}}$ and the electronic specific heat $c_{\text{el}}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that ${\kappa }_{\text{el}}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasiparticle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.

The interplay of light and matter gives rise to intriguing cooperative effects in quantum many-body systems. This is even true in thermal equilibrium, where the electromagnetic field can hybridize with collective modes of matter, and virtual photons can induce interactions in the solid. Here, we show how these light-mediated interactions can be treated using the dynamical mean-field theory formalism. We consider a minimal model of a two-dimensional material that couples to a surface plasmon polariton mode of a metal-dielectric interface. Within the mean-field approximation, the system exhibits a ferroelectric phase transition that is unaffected by the light-matter coupling. Bosonic dynamical mean-field theory provides a more accurate description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase.

We present a promising route to realize spontaneous magnetic order on the surface of a 3D topological insulator by applying a superlattice potential. The superlattice potential lowers the symmetry of the surface states and creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion, give rise to a topological meron lattice spin texture. The periodicity of this designer meron lattice can be tuned by varying the periodicity of the superlattice potential. We employ Ginzburg-Landau theory to classify the different magnetic orders and show that the magnetic transition temperature reaches experimentally accessible values. Our work introduces another direction to realize exotic quantum order by engineering interacting Dirac electrons in a superlattice potential, with promising applications to spintronics.

For two- and three-dimensional topological insulators whose unit cells consist of multiple sublattices, the boundary terminating at which type of sublattice can affect the time-reversal invariant momentum at which the Dirac points of helical boundary states are located. By incorporating a generic theory and a representative model, we reveal that this interesting property allows the realization of Majorana modes at sublattice domain walls forming on the boundary when the boundary Dirac points of the topological insulator are gapped by appropriate superconductivity in proximity. Remarkably, we find that the sensitive sublattice dependence of the Majorana modes allows their positions to be precisely manipulated by locally controlling the terminating sublattices or boundary potential. Our work reveals that the sublattice degrees of freedom commonly found in materials open a different route to realize and manipulate Majorana modes.

The Dzyaloshinskii-Moriya interaction (DMI) in magnetic materials plays an important role in spintronics, giving rise to chiral spin textures such as the nucleation and propagation of domain walls and skyrmions. The necessary ingredient for the emergence of the DMI is the lack of inversion symmetry combined with elements with strong spin-orbit coupling. We report on a first-principles investigation of generalized DMIs in bulk centrosymmetric crystals with noncentrosymmetric local sublattices, where we consider a prototype family of $\mathcal{PT}$-symmetric antiferromagnets, including, ${\mathrm{Mn}}_2\mathrm{Au}$, ${\mathrm{MnPd}}_2$ and MnCuAs in the tetragonal and orthorhombic phases. We employ a Green's function approach to calculate the interatomic relativistic exchange coupling which can, in turn, determine the sublattice elements of the generalized fifth-order DMI tensor $D_{\alpha \beta ,\gamma }^{s{s}^{\prime }}$. We demonstrate that the breaking of the local mirror symmetry and the resulting local Rashba-type spin-momentum locking yield local DMIs with opposite signs on the two antiparallel sublattices. We present numerical results and provide analytical expressions for the magnon dispersion in the presence of the sublattice DMI and show that the intra- (inter-) sublattice DMIs result in identical (opposite) contributions to the nonreciprocal components of the two low-frequency antiferromagnetic magnon modes.

The spin-dependent transport properties of paramagnetic metals are roughly invariant under rotation. By contrast, in ferromagnetic materials, the magnetization breaks the rotational symmetry, and, thus, the spin Hall effect is expected to become anisotropic. Here, using a specific design of lateral spin valves, we measure electrically the spin Hall effect anisotropy in ferromagnetic NiCu and NiPd. We show that the magnetization vector does not lead to a sizable anisotropy of the spin charge interconversion and spin transport parameters in materials with a spin-orbit coupling comparable to the exchange interaction.

We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s\le 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach and the discrete Lehmann representation we reveal that even in the small-$r_s$ limit, the dominant mechanism behind Cooper instability is based on dynamic screening of the Coulomb interaction—accurately captured by the random phase approximation, whereas the Kohn-Luttinger contribution is negligibly small and, thus, not relevant.

Strontium titanate is an incipient ferroelectric in which superconductivity emerges at exceptionally low doping levels. Remarkably, stabilizing the polar phase through strain or chemical substitution has been shown to significantly enhance the superconducting critical temperature, and the polar instability plays a pivotal role in most proposed superconducting pairing mechanisms. A rigorous understanding of ferroelectricity is therefore essential to elucidate the electron pairing mechanism in this material. To investigate the nature of the polar order in strontium titanate, we develop a simplified free energy model that only includes the degrees of freedom necessary to capture the relevant physics in a biaxially compressively strained system. Our model can calculate the energies of large, disordered systems with near density functional theory-level accuracy. We simulate the ferroelectric and antiferrodistortive phase transitions using the Monte Carlo method and discuss the coupling between various order parameters. Finally, we assess the character of the polar transition, which we find to be neither strictly displacive nor order-disorder.

Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the “forward” type in that the objective was to solve various confinement, transport, and scattering problems with given structures that can be generated by, e.g., applying an external electrical field. There are applications such as cloaking or superscattering where the challenging problem of inverse design needs to be solved: Finding a quantum-dot structure according to certain desired functional characteristics. A brute-force search of the system configuration based directly on the solutions of the Dirac equation is computationally infeasible. We articulate a machine-learning approach to addressing the inverse-design problem where artificial neural networks subject to physical constraints are exploited to replace the rigorous Dirac equation solver. In particular, we focus on the problem of designing a quantum-dot structure to generate both cloaking and superscattering in terms of the scattering efficiency as a function of the energy. We construct a physical loss function that enables accurate prediction of the scattering characteristics. We demonstrate that, in the regime of Klein tunneling, the scattering efficiency can be designed to vary over two orders of magnitude, allowing any scattering curve to be generated from a proper combination of the gate potentials. Our physics-based machine-learning approach can be a powerful design tool for 2D Dirac material-based electronics.

Niobium is one of the most studied superconductors, both theoretically and experimentally. It is tremendously important for applications, and it has the highest superconducting transition temperature, $T_c=9.32$ K, of all pure metals. In addition to power applications in alloys, pure niobium is used for sensitive magnetosensing, radio-frequency cavities, and, more recently, as circuit metallization layers in superconducting qubits. A detailed understanding of its electronic and superconducting structure, especially its normal and superconducting state anisotropies, is crucial for mitigating the loss of quantum coherence in such devices. Recently, a microscopic theory of the anisotropic properties of niobium with the disorder was put forward. To verify theoretical predictions, we studied the effect of disorder produced by 3.5 MeV proton irradiation of thin Nb films grown by the same team and using the same protocols as those used in transmon qubits. By measuring the superconducting transition temperature and upper critical fields, we show a clear suppression of $T_c$ by potential (nonmagnetic) scattering, which is directly related to the anisotropic order parameter. We obtain a very close quantitative agreement between the theory and the experiment.

We study quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model, whose amount of entanglement is limited by the size of the matrices used in the representation of the states. By measuring entanglement entropy and other physical properties, we observe that the Mott-insulator-to-superfluid transitions occur sharp and continuous, accompanied by shifting transition points that are not blurred by finite entanglement effects. This strongly suggests that the transition always occurs between the Mott insulator and a mean-field-like compressible state, followed by the more entangled superfluid state. Both $O\left(2\right)$ and the commensurate-incommensurate transitions are studied, whose properties can be characterized by entanglement spectra and critical exponents.