We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability.

We present a canonical derivation of an influence superoperator which generates the reduced dynamics of a Fermionic quantum system linearly coupled to a Fermionic environment initially at thermal equilibrium. We use this formalism to derive a generalized Lindblad master equation (in the Markovian limit) and a generalized version of the hierarchical equations of motion valid in arbitrary parity-symmetry conditions, important for the correct evaluation of system correlation functions and spectra.

The magnetopiezoelectric effect (MPE) is a cross coupling between an electric current and strain in metals with neither inversion symmetry nor time-reversal symmetry. Unlike the conventional piezoelectric effect, the electric current allows a MPE-like response in superconductors, which we call the superconducting piezoelectric effect (SCPE). The SCPE may enable a piezoelectric response without Joule heating and may provide a probe of exotic superconducting symmetry. In this paper, we propose a formulation of the SCPE and calculate both the MPE and SCPE in a two-dimensional noncentrosymmetric $s$-wave superconductor under an in-plane magnetic field. We find that the magnitude of the SCPE is comparable to the MPE. We also clarify that the finite total momentum of Cooper pairs in the helical superconducting state plays a crucial role in the SCPE.

The technology of superconductor-semiconductor nanowire devices has matured in recent years. This makes it feasible to make more complex and sophisticated devices. We investigate multiterminal superconductor-semiconductor wires to access the feasibility of another topological phenomenon: Weyl singularities in their spectrum. We have found an abundance of Weyl singularities for devices with an intermediate size of the electrodes. We describe their properties and the ways the singularities emerge and disappear upon variation of the setup parameters.

Single crystals of ${\mathrm{La}}_2{\mathrm{Ni}}_7$ have been grown out of a binary La-Ni melt. Temperature-dependent, zero magnetic field, specific heat, electrical resistivity, and low field magnetization measurements indicate that there is a series of antiferromagnetic (AFM) phase transitions at $T_1=61.0\pm 0.2\mathrm{K}, T_2=56.5\pm 0.2\mathrm{K}$, and $T_3=42.2\pm 0.2\mathrm{K}$. The three specific heat anomalies found at these temperatures qualitatively have very small entropy changes associated with them, and the anisotropic $M$($H$) data saturate at $\sim 0.12{\mu }_{\mathrm{B}}/\mathrm{Ni}$; both observations strongly suggesting the AFM order is associated with very small, itinerant moments. Anisotropic $H_{\left|\right|c}$ and $H_{\perp c}$, ρ($H$) and $M$($H$) isotherms as well as constant field ρ($T$) and $M$($T$) sweeps manifest signatures of multiple phase lines and result in $H\text{−}T$ phase diagrams that are clearly anisotropic. Analysis of $M$($T$) and $M$($H$) data allow for the identification of the two lower temperature magnetically ordered states as AFM ordered, with the moments aligned along the crystallographic $c$ axis, and the higher temperature $T_2<T<T_1$ state as having a finite ferromagnetic component. In addition, the metamagnetic transition at low temperatures, for $H$ applied along the crystallographic $c$ axis ($H_{\left|\right|c}$), appears to be a near classic example of a spin-flop transition, resulting in a field stabilized AFM state with the moments ordered perpendicular to the $c$ axis. Although the small moment ordering and existence of multiple phase transitions in field and temperature, suggesting an energetic proximity of these states, could foretell a degree of pressure sensitivity, our measurements of $R$($T$) for applied pressures up to 2.0 GPa indicate that there is very little pressure dependence of $T_1, T_2$, and $T_3$.

Theoretical calculations of thermally activated decay of skyrmions in systems comprising several magnetic monolayers are presented, with a special focus on bilayer systems. Mechanisms of skyrmion collapse are identified and corresponding energy barriers and thermal collapse rates are evaluated as functions of the interlayer exchange coupling and mutual stacking of the monolayers using transition state theory and an atomistic spin Hamiltonian. In order to contrast the results to monolayer systems, the magnetic interactions within each layer are chosen so as to mimic the well-established Pd/Fe/Ir(111) system. Even bilayer systems demonstrate a rich diversity of skyrmion collapse mechanisms that sometimes coexist. For very weakly coupled layers, the skyrmions in each layer decay successively via radially symmetric shrinking. Slightly larger coupling leads to an asymmetric chimera collapse stabilized by the interlayer exchange. When the interlayer exchange coupling reaches a certain critical value, the skyrmions collapse simultaneously. Interestingly, the overall energy barrier for the skyrmion collapse does not always converge to a multiple of that for a monolayer system in the strongly coupled regime. For a certain stacking of the magnetic layers, the energy barrier as a function of the interlayer exchange coupling features a maximum and then decreases with the coupling strength in the strong coupling regime. Calculated mechanisms of skyrmion collapse are used to ultimately predict the skyrmion lifetime. Our results reveal a comprehensive picture of the thermal stability of skyrmions in magnetic multilayers and provide a perspective for realizing skyrmions with controlled properties.

We show analytically using a macrospin approximation that easy-plane spin Hall nano-oscillators excited by a spin current polarized perpendicularly to the easy plane have phase dynamics analogous to that of Josephson junctions. Similarly to Josephson junctions, they can reproduce the spiking behavior of biological neurons that is appropriate for neuromorphic computing. To take advantage of typical spin-orbit torques, we use a nanoconstriction geometry, in which the magnetostatic interaction and magnetocrystalline anisotropy are tuned to create an easy plane that includes the interface normal direction. We perform micromagnetic simulations of such oscillators realized in this geometry and show that the easy-plane spiking dynamics is preserved in this experimentally feasible architecture. Finally we simulate two elementary neural network blocks that implement operations essential for neuromorphic computing. First, we show that output spikes energies from two neurons can be summed and injected into a following layer neuron and second, we demonstrate that outputs can be multiplied by synaptic weights implemented by locally modifying the anisotropy.

We propose nanoscale magnetometry via isolated single-spin qubits as a probe of superconductivity in two-dimensional materials. We characterize the magnetic field noise at the qubit location, arising from current and spin fluctuations in the sample and leading to measurable polarization decay of the qubit. We show that the noise due to transverse current fluctuations studied as a function of temperature and sample-probe distance can be used to extract useful information about the transition to a superconducting phase and the pairing symmetry of the superconductor. Surprisingly, at low temperatures, the dominant contribution to the magnetic noise arises from longitudinal current fluctuations and can be used to probe collective modes such as monolayer plasmons and bilayer Josephson plasmons. We also characterize the noise due to spin fluctuations, which allows probing the spin structure of the pairing wave function. Our results provide a noninvasive route to probe the rich physics of two-dimensional superconductors.

We report on the observation of the ratchet effect—generation of direct electric current in response to external terahertz radiation—in bilayer graphene, where inversion symmetry is broken by an asymmetric dual-grating gate potential. As a central result, we demonstrate that at high temperature, $T=150$ K, the ratchet current decreases at high frequencies as $\propto 1/{\omega }^2$, while at low temperature, $T=4.2$ K, the frequency dependence becomes much stronger $\propto 1/{\omega }^6$. The developed theory shows that the frequency dependence of the ratchet current is very sensitive to the ratio of the electron-impurity and electron-electron scattering rates. The theory predicts that the dependence $1/{\omega }^6$ is realized in the hydrodynamic regime, when electron-electron scattering dominates, while $1/{\omega }^2$ is specific for the drift-diffusion approximation. Therefore, our experimental observation of a very strong frequency dependence reveals the emergence of the hydrodynamic regime.

We introduce a two-dimensional electronic insulator that possesses a toric-code topological order enriched by translation symmetry. This state can be realized from disordering a weak topological superconductor by double-vortex condensation. It is termed the toric-code insulator, whose anyonic excitations consist of a charge-$e$ chargon, a neutral fermion, and two types of visons. There are two types of visons because they have constrained motion as a consequence of the fractional Josephson effect of one-dimensional topological superconductor. Importantly, these two types of visons are related by a discrete translation symmetry and have a mutual semionic braiding statistics, leading to a symmetry enrichment akin to the type in Wen's plaquette model and Kitaev's honeycomb model. We construct this state using a three-fluid coupled-wire model, and analyze the anyon spectrum and braiding statistics in detail to unveil the nature of symmetry enrichment due to translation. We also discuss potential material realizations and present a band-theoretic understanding of the state, fitting it into a general framework for studying fractionalizaton in strongly interacting weak topological phases.

The accurate determination of magnetic phase transitions in electronic systems is an important task of solid-state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the complexity of real materials requires additional approximations, such as the restriction to certain classes of diagrams in perturbation theory, that reduce the precision with which magnetic properties are described. In this paper, we examine the description of magnetic properties in second order perturbation theory, GW, fluctuation exchange, and two T-matrix approximations to numerically exact CT-QMC reference data. We assess finite-size effects and compare periodic lattice simulations to cluster embedding. We find that embedding substantially improves finite-size convergence. However, by analyzing different partial summation methods, we find no systematic improvement in the description of magnetic properties, with most methods considered in this paper predicting first-order instead of continuous transitions, leading us to the conclusion that nonperturbative methods are necessary for the accurate determination of magnetic properties and phase transitions.

Electronic flat bands serve as a unique platform to achieve strongly correlated phases. The emergence of a flat band around the Fermi level in $1T\text{−}{\mathrm{TaS}}_2$ accompanied by the development of a $\sqrt{13}\times \sqrt{13}$ charge density wave (CDW) superlattice has long been noticed experimentally, but a transparent theoretical understanding remains elusive. We show that without the CDW order, the primary feature of the $1\times 1$ bands can be fitted by a simple trigonometric function, and physically understood by choosing a rotated $t_{2g}$ basis with the principal axes aligning to the tilted ${\mathrm{TaS}}_6$ octahedron. Using this basis, we trace the band evolution in the $\sqrt{13}\times \sqrt{13}$ superlattice by progressively including different CDW effects. We point out that the CDW order strongly rehybridizes the three ${\tilde{t}}_{2g}$ orbitals, which leads to the formation of a well-localized molecular orbital and the flat band.

The family of metallic kagome compounds $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs})$ was recently discovered to exhibit both superconductivity and charge order. The nature of the charge density wave (CDW) phase is presently unsettled, which complicates the interpretation of the superconducting ground state. In this paper, we use group theory and density functional theory (DFT) to derive and solve a phenomenological Landau model for this CDW state. The DFT results reveal three unstable phonon modes with the same in-plane momentum but different out-of-plane momenta, whose frequencies depend strongly on the electronic temperature. This is indicative of an electronically driven CDW, stabilized by features of the in-plane electronic dispersion. Motivated by the DFT analysis, we construct a Landau free-energy expansion for coupled CDW order parameters with wave vectors at the $M$ and $L$ points of the hexagonal Brillouin zone. We find an unusual trilinear term coupling these different order parameters, which can promote the simultaneous condensation of both CDWs even if the two modes are not nearly degenerate. We classify the different types of coupled multi-$\mathbf{Q}$ CDW orders, focusing on those that break the sixfold rotational symmetry and lead to a unit-cell doubling along all three crystallographic directions, as suggested by experiments. We determine a region in parameter space, characterized by large nonlinear Landau coefficients, where these phases—dubbed staggered trihexagonal and staggered Star of David—are the leading instabilities of the system. Finally, we discuss the implications of our results for the kagome metals.

A large set of recent experiments has been exploring topological transport in bosonic systems, e.g., of photons or phonons. In the vast majority, time-reversal symmetry is preserved, and band structures are engineered by a suitable choice of geometry to produce topologically nontrivial band gaps in the vicinity of high-symmetry points. However, this leaves open the possibility of large-quasimomentum backscattering, destroying the topological protection. Up to now, it has been unclear what precisely the conditions are where this effect can be sufficiently suppressed. In the present paper, we introduce a comprehensive semiclassical theory of tunneling transitions in momentum space, describing backscattering for one of the most important system classes, based on the valley Hall effect. We predict that even for a smooth domain wall, effective scattering centers develop at locations determined by both the local slope of the wall and the energy. Moreover, our theory provides a quantitative analysis of the exponential suppression of the overall reflection amplitude with increasing domain-wall smoothness.

In inhomogeneous dielectric media the divergence of the electromagnetic stress is related to the gradients of $\varepsilon$ and $\mu$, which is a consequence of Maxwell's equations. Investigating spherically symmetric media we show that this seemingly universal relationship is violated for electromagnetic vacuum forces such as the generalized van der Waals and Casimir forces. The stress needs to acquire an additional anomalous pressure. The anomaly is a result of renormalization, the need to subtract infinities in the stress for getting a finite, physical force. The anomalous pressure appears in the stress in media like dark energy appears in the energy-momentum tensor in general relativity. We propose and analyze an experiment to probe the van der Waals anomaly with ultracold atoms. The experiment may not only test an unusual phenomenon of quantum forces but also an analog of dark energy, shedding light where nothing is known empirically.

Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.

We investigate single, ultrathin, pure-wurtzite-phase GaAs-AlGaAs core-shell nanowires by resonant inelastic light scattering (RILS). We observe electronic Raman excitations, which can be attributed to intersubband excitations of photoexcited electrons or holes within the quasi-one-dimensional (1D) subband structure. Our analysis reveals that the electronic systems in the narrowest investigated nanowires, with GaAs core diameters down to 25 nm, are in the 1D quantum limit. Excitation-density-dependent measurements indicate that the observed 1D intersubband excitations are mainly of single-particle origin, since no plasmonic shift can be deduced. Our experimental findings are consistent with a three-step scattering mechanism, based on the Coulomb interaction of photoexcited electron-hole pairs with free carriers, electrons, or holes. The quantized subband energies, as extracted from photoluminescence, photoluminescence-excitation, and RILS experiments, can be nicely reproduced by realistic multiband $\mathbf{k}·\mathbf{p}$ band structure calculations, taking into account the hexagonal geometry of the nanowires.

We investigate the nature of the ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the shuriken lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo (mVMC), and pseudofermion/pseudo-Majorana functional renormalization group (PFFRG/PMFRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

We present a fully relativistic first-principles-based theoretical approach for the calculation of the spectral properties of magnetic impurities on the surface of a superconducting substrate, providing a material specific framework for the investigation of the Yu-Shiba-Rusinov (YSR) states. By using a suitable orbital decomposition of the local densities of states we discuss in great detail the formation of the YSR states for an Mn adatom and for two kinds of Mn dimers placed on the Nb(110) surface and compare our results to recent experimental findings. In the case of the adatom we find that the spin-orbit coupling slightly shifts some of the YSR peaks and also the local spin polarization on the Nb atoms has marginal effects on their positions. Moreover, by scaling the exchange field on the Mn site we could explain the lack of the $d_{x^2-y^2}$-like YSR state in the spectrum. While our results for a close packed ferromagnetic dimer are in satisfactory agreement with the experimentally observed splitting of the YSR states, in the case of an antiferromagnetic dimer we find that the spin-orbit coupling is not sufficiently large to explain the splitting of the YSR states seen in the experiment. Changing the relative orientation of the magnetic moments in this dimer induces splitting of the YSR states and also shifts their energy, leading even to the formation of a zero bias peak in the case of the deepest YSR state.

Controlling amplitude, phase, and polarization of electromagnetic (EM) waves is key for a full manipulation of wave-matter interactions. The Brewster angle is one of the important features in this context. Here, we exploit metamaterial concepts with a time-modulated permittivity to propose the temporal equivalent of the spatial Brewster angle, a concept we call temporal analogue/equivalent of the Brewster angle. We consider temporal boundaries (as the temporal equivalent of the spatial boundaries between two media) by rapidly changing the permittivity of the medium where a wave travels from isotropic to an anisotropic permittivity tensor. It is theoretically shown that, when the incidence angle coincides with that of the temporal analogue of the Brewster angle, a forward (temporal transmission) wave is produced, while the backward (temporal reflection) is eliminated. We provide a closed-form analytical expression of the temporal analogue of the Brewster angle and demonstrate its performance both theoretically and numerically. Our findings may provide a fresh view on how to control EM wave propagation and wave-matter interactions in real time using temporal metamaterials.