The recently introduced concept of synthetic dimensions allows for the realization of higher-dimensional topological phenomena in lower-dimensional systems. In this paper, we propose a setup where synthetic dimensions arise in mesoscopic hybrid devices and discuss how they provide a natural route to topological states. We demonstrate this for the current induced into a closed one-dimensional Aharonov-Bohm ring by the interaction with a dynamic mesoscopic magnet. The quantization of the magnetic moment provides a synthetic dimension that complements the charge motion around the ring. We present a direct mapping that places the combined ring-magnet system into the class of quantum Hall models and demonstrate that topological features, combined with the magnet's anisotropy, can lead to clear signatures in the persistent current of the single-particle ground state. Our synthetic-dimension model also extends to the many-electron case, where the collective electronic motion couples with the magnet.

Recent research demonstrated the electrical switching of antiferromagnets via intrinsic spin-orbit torque or the spin Hall effect of an adjacent heavy metal layer. The electrical readout is typically realized by measuring the transverse anisotropic magnetoresistance at planar cross- or star-shaped devices with four or eight arms, respectively. Depending on the material, the current density necessary to switch the magnetic state can be large, often close to the destruction threshold of the device. We demonstrate that the resulting electrical stress changes the film resistivity locally and thereby breaks the fourfold rotational symmetry of the conductor. This symmetry breaking due to film inhomogeneity produces signals, that resemble the anisotropic magnetoresistance and is experimentally seen as a “saw-tooth”-shaped transverse resistivity. This artifact can persist over many repeats of the switching experiment and is not easily separable from the magnetic contribution. We discuss the origin of the artifact, elucidate the role of the film crystallinity, and propose approaches how to separate the resistive contribution from the magnetic contribution.

We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site $\delta \le 12.5\%$ using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping $t^{\prime }$. Without $t^{\prime }$ the ground state of the system corresponds to the insulating filled stripe phase with long-range charge-density-wave (CDW) order, and short-range incommensurate spin correlations appears. However, for a small negative $t^{\prime }$ a phase characterized by coexisting algebraic $d$-wave superconducting (SC) and algebraic CDW correlations. In addition, it shows short-range spin- and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge and spin periodicities are consistent with half-filled stripes instead of the $4k_F$ and $2k_F$ wave vectors that are generic for one-dimensional chains. For a small positive $t^{\prime }$ yet another phase takes over, showing similar SC and CDW correlations. However, the fermions are now characterized by a (nearly) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE liquid formed from a weakly coupled (BCS like) $d$-wave superconductor on the ladder where the interactions have only the effect of stabilizing a cuprate style magnetic resonance.

Cadmium telluride (CdTe) has been studied using synchrotron powder x-ray diffraction in a diamond anvil cell up to 63 GPa at room temperature combined with density functional calculations. The experiment reveals two pressure-induced structural phase transitions with the following sequence: rocksalt $\to$ $Cmcm$ (12 GPa) $\to$ post-$Cmcm$ (42 GPa). The crystal structure of the long-sought post-$Cmcm$ phase is characterized. It has a monoclinic unit cell and the $P{2}_1/m$ space group. Calculation confirms this phase transition sequence and further predicts a $P{2}_1/m$ to $P4/nmm$ transition near 68 GPa. Interestingly, the enthalpy of CdTe is found to be higher than the enthalpy sum of its constituents Cd and Te at pressures higher than 34 GPa. This suggests that CdTe becomes a high-enthalpy compound at high pressure. Extraordinary dynamic stability revealed in the phonon dispersion relations prevents the decomposition of CdTe at high pressure.

We establish an analytic low-energy theory describing higher-order topological insulator (HOTI) phases in quasicrystalline systems. We apply this to a model consisting of two stacked Haldane models with oppositely propagating edge modes, analogous to the Kane-Mele model, and with a ${30}^{\circ }$ twist. We show that the resulting localized modes at corners, characteristic of a HOTI, are not associated with conventional mass inversions but are instead associated with what we dub “fractional mass kinks.” By generalizing the low-energy theory, we establish a classification for arbitrary $n$-fold rotational symmetries. We also derive a relationship between corner modes in a bilayer and disclination modes in a single layer. By using numerics to go beyond the weak-coupling limit, we show that a hierarchy of additional gaps occurs due to the quasiperiodicity, which also harbor corner-localized modes.

We study entanglement properties of free-fermion systems without Hermiticity by use of correlation matrix and overlap matrix in the biorthogonal basis. We find at a critical point in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) the entanglement entropy exhibits a logarithmic scaling with corresponding central charge $c=-2$, signaling the emergence of nonunitary conformal field theory. In addition, we demonstrate that, in the PT-symmetric SSH model and the non-Hermitian Chern insulators, the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states.

Using the recently introduced multiloop extension of the functional renormalization group, we compute the frequency- and momentum-dependent self-energy of the two-dimensional Hubbard model at half filling and weak coupling. We show that, in the truncated-unity approach for the vertex, it is essential to adopt the Schwinger-Dyson form of the self-energy flow equation in order to capture the pseudogap opening. We provide an analytic understanding of the key role played by the flow scheme in correctly accounting for the impact of the antiferromagnetic fluctuations. For the resulting pseudogap, we present a detailed numerical analysis of its evolution with temperature, interaction strength, and loop order.

The Mott insulating phase of parent compounds is frequently taken as a starting point for underdoped high-$T_c$ cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, we systematically investigate different weakly doped Mott insulators on a square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absence of a pseudogap depends sensitively on noninteracting band parameters, and we identify the crucial role played by the van Hove singularities of the system. Motivated by a SU(2) gauge theory for the pseudogap state, we propose and verify numerically a simple equation that governs the evolution of characteristic features in the electronic scattering rate.

We present a systematic classification and analysis of possible pairing instabilities in graphene-based moiré superlattices. Motivated by recent experiments on twisted double bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an ${\mathrm{SU}\left(2\right)}_{+}\times {\mathrm{SU}\left(2\right)}_{-}$ symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. The consequences of the additional microscopic or emergent approximate symmetries relevant for superconductivity in twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are described in detail. We also analyze which of the pairing states can arise in mean-field theory and study the impact of corrections coming from ferromagnetic fluctuations. For instance, we show that, close to the parameters of mean-field theory, a nematic mixed singlet-triplet state emerges. Our paper illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.

The spin relaxation time in solids is determined by several competing energy scales and processes, and distinct methods are called for to analyze the various regimes. We present a stochastic model for the spin dynamics in solids which is equivalent to solving the spin Boltzmann equation and takes the relevant processes into account on an equal footing. The calculations reveal yet unknown parts of the spin-relaxation phase diagram, where strong reversible spin dephasing occurs in addition to spin relaxation. Spin-relaxation times are obtained for this regime by introducing the numerical Loschmidt echo. This allows us to construct a generic approximate formula for the spin-relaxation time, ${\tau }_{\text{s}}$, for the entire phase diagram, involving the quasiparticle scattering rate, $\mathrm{\Gamma }$, spin-orbit coupling strength, $L$, and a magnetic term, ${\mathrm{\Delta }}_{\text{Z}}$ due to the Zeeman effect. The generic expression reads as $\hslash /{\tau }_{\text{s}}\approx \mathrm{\Gamma }{L}^2/({\mathrm{\Gamma }}^2+L^2+{\mathrm{\Delta }}_{\text{Z}}^2)$.

The gap structure of a novel uranium-based superconductor ${\mathrm{UTe}}_2$, situated in the vicinity of ferromagnetic quantum criticality, has been investigated via specific-heat $C(T,H,\mathrm{\Omega })$ measurements in various field orientations. Its angular $\mathrm{\Omega }(\varphi ,\theta )$ variation shows a characteristic shoulder anomaly with a local minimum in $H\parallel a$ at moderate fields rotated within the $ab$ and $ac$ planes. Based on theoretical calculations, these features can be attributed to the presence of point nodes in the superconducting gap along the $a$ direction. Under the field orientation along the easy-magnetization $a$ axis, an unusual temperature dependence of the upper critical field at low fields together with a convex downward curvature in $C\left(H\right)$ were observed. These anomalous behaviors can be explained on the basis of a nonunitary triplet state model with equal-spin pairing whose $T_{\mathrm{c}}$ is tuned by the magnetization along the $a$ axis. From these results, the gap symmetry of ${\mathrm{UTe}}_2$ is most likely described by a vector order parameter of $\mathit{d}\left(\mathit{k}\right)=(\mathit{b}+i\mathit{c})(k_b+i{k}_c)$.

We present an ab initio study of the structural and electronic transport properties of tetrahedrite, ${\mathrm{Cu}}_{12}{\mathrm{Sb}}_4{\mathrm{S}}_{13}$, in its high-temperature phase. We show how this complex compound can be seen as the outcome of an ordered arrangement of S-vacancies in a semiconducting fematinite-like structure (${\mathrm{Cu}}_3{\mathrm{SbS}}_4$). Our calculations confirm that the S-vacancies are the natural doping mechanism in this thermoelectric compound and reveal a similar local chemical environment around crystallographically inequivalent Cu atoms, shedding light on the debate on x-ray photoelectron spectroscopy measurements in this compound. To access the electrical transport properties as a function of temperature we use the Kubo-Greenwood formula applied to snapshots of first-principles molecular dynamics simulations. This approach is essential to effectively account for the interaction between electrons and lattice vibrations in such a complex crystal structure where a strong anharmonicity plays a key role in stabilizing the high-temperature phase. Our results show that the Seebeck coefficient is in good agreement with experiments and the phonon-limited electrical resistivity displays a temperature trend that compares well with a wide range of experimental data. The predicted lower bound for the resistivity turns out to be remarkably low for a pristine mineral in the Cu-Sb-S system but not too far from the lowest experimental data reported in literature. The Lorenz number turns out to be substantially lower than what is expected from the free-electron value in the Wiedemann-Franz law, thus providing an accurate way to estimate the electronic and lattice contributions to the thermal conductivity in experiments, of great significance in this very low thermal conductivity crystalline material.

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with nonlocal interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling limit and ignoring the retardation effect, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or spin-triplet superconducting phases.

The Aubry-André-Harper (AAH) model with a self-dual symmetry plays an important role in studying the Anderson localization. Here we find a self-dual symmetry determining the quantum phase transition between extended and localized states in a non-Hermitian AAH model and show that the eigenenergies of these states are characterized by two types of winding numbers. By constructing and studying a non-Hermitian generalized AAH model, we further generalize the notion of the mobility edge, which separates the localized and extended states in the energy spectrum of disordered systems, to the non-Hermitian case and find that the generalized mobility edge is of a topological nature even in the open boundary geometry in the sense that the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. Finally, we propose an experimental scheme to realize these models with electric circuits.

Quantum fluctuating loops in $2+1$ dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that reconnection of a pair of strands is forbidden. This happens at previously studied multicritical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators at these fixed points are classified by topology and not only by symmetry. We introduce the concept of the topological operator classification, provide universal scaling forms for correlation functions, and analytical and numerical results for critical exponents. We use an exact correspondence between the imaginary-time dynamics of the $2+1\mathrm{D}$ quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight (for which we also provide scaling results). We comment on open questions and generalizations of the models discussed for both quantum criticality and classical Markov processes.

Competing density waves play an important role in the mystery of high-temperature cuprate superconductors. In spite of the large amount of experimental evidence, the fundamental question of whether these modulations represent charge or pairing density waves (CDWs or PDWs) is still debated. Here we present a method to answer this question using both momentum and energy-resolved resonant x-ray-scattering maps. Starting from a minimal model of density waves in superconductors, we identify distinctive signatures of incipient CDWs and PDWs. The generality of our approach is confirmed by a self-consistent solution of an extended Hubbard model with attractive interaction. By considering the available experimental data, we claim that the spatial modulations in cuprates have a predominant PDW character. Our work paves the way for using x ray to identify competing and intertwined orders in superconducting materials.

We investigate a Bose-Einstein condensate in strong interaction with a single impurity particle. While this situation has received considerable interest in recent years, the regime of strong coupling remained inaccessible to most approaches due to an instability in the Bogoliubov theory arising near the resonance. We present a nonlocal extension of the Gross-Pitaevskii theory that is free of such divergences and does not require the use of the Born approximation in any of the interaction potentials. We find a new dynamical transition regime between attractive and repulsive polarons, where an interaction quench results in a finite number of coherent oscillations in the density profiles of the medium and in the contact parameter before equilibrium is reached.

The periodic driving of a quantum system can enable new topological phases without analogs in static systems. This provides a route towards preparing nonequilibrium quantum phases rooted in the nonequilibrium nature by periodic driving engineering. Motivated by the ongoing considerable interest in topological semimetals, we are interested in the novel topological phases in the periodically driven topological semimetals without a static counterpart. We propose to design nonequilibrium topological semimetals in the regime of a weakly driving field where the spectrum width has the same magnitude as the driving frequency. We identify two types of nonequilibrium Weyl semimetals (i.e., Floquet and anomalous Floquet Weyl semimetals) that do not exhibit analogs in equilibrium. The proposed setup is shown to be experimentally feasible using the state-of-the-art techniques used to control ultracold atoms in optical lattices.

Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower bounds the thermalization time for any scar state as $t^{*}\sim O\left({\lambda }^{-1/(1+d)}\right)$, where $d$ is the spatial dimension of the system and $\lambda$ is the perturbation strength.

The finite coupling between Weyl nodes due to residual disorder is investigated by magnetotransport studies in ${\mathrm{WTe}}_2$. The anisotropic scattering of quasiparticles is evidenced from classical and quantum transport measurements. A theoretical approach using the real band structure is developed in order to calculate the dependence of the scattering anisotropy with the correlation length of the disorder. A comparison between theory and experiments reveals a short correlation length in ${\mathrm{WTe}}_2$ ($\xi \sim 5$ nm). This result implies a significant coupling between Weyl nodes and other bands. Our study thus shows that a finite intercone scattering rate always exists in weakly disordered type-II Weyl semimetals, such as ${\mathrm{WTe}}_2$, which strongly suppresses topologically nontrivial properties.