We investigate the inhomogeneous Rashba chain coupled to a superconducting substrate, hosting the Majorana quasiparticles near its edges. We discuss its subgap spectrum and study how robust the zero-energy quasiparticles are against the diagonal and off-diagonal disorder. Studying the ${\mathbb{Z}}_2$ topological invariant we show that disorder-induced transition from the topologically nontrivial to trivial phases is manifested by characteristic features in the spatially resolved quasiparticle spectrum at zero energy. We provide evidence for the nonlocal nature of the zero-energy Majorana quasiparticles that are well preserved upon partitioning the chain into separate pieces. Even though the Majorana quasiparticles are not completely immune to inhomogeneity, we show that they can spread onto other (normal) nanoscopic objects via the proximity effect.

We establish some general dynamical properties of quantum many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasiconserved extensive quantity $H_{*}$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well approximated by the evolution with the Hamiltonian $H_{*}$ up to time ${\tau }_{*}$, which is exponentially large in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_{*}$ is ergodic, the driven system prethermalizes to a thermal state described by $H_{*}$ at intermediate times $t\lesssim {\tau }_{*}$, eventually heating up to an infinite-temperature state after times $t\sim {\tau }_{*}$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.

The domain structure of hexagonal manganites is simulated based on the phenomenological Ginzburg-Landau theory, and special attention is paid to the evolution of a topological vortex-antivortex pattern with the varying out-of-plane anisotropies of two stiffness parameters for the in-plane ($xy$-plane) trimerization amplitude $Q$ and out-of-plane ($z$-axis) polarization $P$. It is revealed that the topological domain structure can be remarkably modulated by the stiffness anisotropies. A larger stiffness for $Q$ along the $z$ axis causes the trajectory lines of the vortex nodes and antivortex nodes to be seriously stretched along the $z$ axis, eventually leading to the topological stripelike domain pattern. The larger stiffness for either $Q$ or $P$ along the $z$ axis makes the domain walls perpendicular to the $z$ axis wider, while the domain walls parallel to the $z$ axis remain less affected. The present work suggests that the topological domain structure may be controlled by some approaches (e.g., lattice strain) which can change the trimerization stiffness and polarization stiffness in hexagonal manganites.

We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean-field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time-reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.

We report experimental investigations of the electrical transport, magnetic, and thermodynamic properties of $\mathrm{IrT}{\mathrm{e}}_2$ single crystals. The resistivity, magnetization, and specific heat display anomalies at $T_{\mathrm{S}1}\approx 283\mathrm{K},T_{\mathrm{S}2}\approx 167\mathrm{K}$, and $T_{\mathrm{c}}\approx 2.5\mathrm{K}$, corresponding to two structural and one superconducting phase transitions, respectively, demonstrating the coexistence of all of these transitions in high-quality stoichiometric samples. While there is little magnetic anisotropy, a large $ab$-plane $\left({\rho }_{\mathrm{ab}}\right)$ and $c$-axis $\left({\rho }_{\mathrm{c}}\right)$ electrical resistivity ratio $({\rho }_{\mathrm{c}}/{\rho }_{\mathrm{ab}}\approx 730$ at $T=4\mathrm{K})$ is observed. This two-dimensional (2D) electronic character is further reflected in the disparate temperature dependences of ${\rho }_{\mathrm{ab}}$ and ${\rho }_{\mathrm{c}}$, with ${\rho }_{\mathrm{ab}}$ exhibiting a Fermi-liquid-like $T^2$ dependence below $\sim 25\mathrm{K}$, while ${\rho }_{\mathrm{c}}$ deviates significantly from this standard metallic behavior. In contrast, the magnetization is almost isotropic and negative over a wide temperature range. This can be explained by larger diamagnetism induced by electronic structure reconstruction as probed by the Hall effect and smaller positive contribution from itinerant electrons due to a low density of states (DOS) at the Fermi level. A small electronic specific heat coefficient with $\gamma \approx 1.8\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$ confirms this assertion. This implies that $\mathrm{IrT}{\mathrm{e}}_2$ is a weakly coupled superconductor. The connection between the superconductivity and the two structural transitions is discussed.

We calculate the topological part of the electromagnetic response of bosonic integer quantum Hall (BIQH) phases in odd (space-time) dimensions, and bosonic topological insulator (BTI) and bosonic chiral semimetal (BCSM) phases in even dimensions. To do this, we use the nonlinear sigma model (NLSM) description of bosonic symmetry-protected topological (SPT) phases, and the method of gauged Wess-Zumino (WZ) actions. We find the surprising result that for BIQH states in dimension $2m-1$ $\left(m=1,2,\cdots \right)$, the bulk response to an electromagnetic field $A_{\mu }$ is characterized by a Chern-Simons term for $A_{\mu }$ with a level quantized in integer multiples of $m!$ (factorial). We also show that BTI states (which have an extra ${\mathbb{Z}}_2$ symmetry) can exhibit a ${\mathbb{Z}}_2$-breaking quantum Hall effect on their boundaries, with this boundary quantum Hall effect described by a Chern-Simons term at level $\frac{m!}{2}$. We show that the factor of $m!$ can be understood by requiring gauge invariance of the exponential of the Chern-Simons term on a general Euclidean manifold, and we also use this argument to characterize the electromagnetic and gravitational responses of fermionic SPT phases with $\text{U}\left(1\right)$ symmetry in all odd dimensions. We then use our gauged boundary actions for the BIQH and BTI states to (i) construct a bosonic analog of a chiral semimetal (BCSM) in even dimensions, (ii) show that the boundary of the BTI state exhibits a bosonic analog of the parity anomaly of Dirac fermions in odd dimensions, and (iii) study anomaly inflow at domain walls on the boundary of BTI states. In a series of Appendixes we derive important formulas and additional results. In particular, in Appendix A we use the connection between equivariant cohomology and gauged WZ actions to give a mathematical interpretation of the actions for the BIQH and BTI boundaries constructed in this paper.

A relative coordinate breathing mode in the quantum Hall system is predicted to exist with different behavior under either Coulomb or dipole-dipole interactions. While Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)] predicts that any relative coordinate interaction will fail to alter the center-of-mass energy spectrum, it can affect excitations in the relative coordinates. One such collective excitation, which we call the hyperradial breathing mode, emerges naturally from a few-body, hyperspherical representation of the problem and depends on the interparticle interactions, the ground state wave function, and the number of particles participating in the excitation. Possible observations of this excitation will be discussed in the context of both conventional quantum Hall experiments and cold, rotating atomic simulations.

The (111) surface of Cu, Ag, and Au is characterized by a band of surface Shockley states with a constant density of states beginning slightly below the Fermi energy. These states as well as bulk states hybridize with magnetic impurities which can be placed above the surface. We calculate the characteristic low-temperature energy scale, the Kondo temperature $T_K$ of the impurity Anderson model, as the bottom of the conduction band $D_s$ crosses the Fermi energy ${\epsilon }_F$. We find simple power laws $T_K\simeq {|D_s-{\epsilon }_F|}^{\eta }$, where $\eta$ depends on the sign of $D_s-{\epsilon }_F$, the ratio between surface and bulk hybridizations with the impurity ${\mathrm{\Delta }}_s/{\mathrm{\Delta }}_b$, and the ratio between on-site and Coulomb energy $E_d/U$ in the model.

We describe the computational ingredients for an approach to treat interacting fermion systems with pairing fields, based on path integrals in the space of Hartree-Fock-Bogoliubov (HFB) wave functions. The path integrals can be evaluated by Monte Carlo, via random walks of HFB wave functions whose orbitals evolve stochastically. The approach combines the advantage of HFB theory in paired fermion systems and many-body quantum Monte Carlo techniques. The properties of HFB states, written in the form of either product states or Thouless states, are discussed. The states preserve forms when propagated by generalized one-body operators. They can be stabilized for numerical iteration. Overlaps and one-body Green's functions between two such states can be computed. A constrained-path or phaseless approximation can be applied to the random walks of the HFB states if a sign problem or phase problem is present. The method is illustrated with an exact numerical projection in the Kitaev model, and in the Hubbard model with attractive interaction under an external pairing field.

In a one-dimensional weakly interacting Bose-Fermi mixture, one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons is equal to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $q<k_F$, while we find $q^6$ scaling at $q>k_F$. For a high-momentum Bogoliubov quasiparticle, we find a constant decay rate for $q<k_F$, while it scales as $1/q$ for $q>k_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.

We study exchange coupling due to the interelectron Coulomb interaction between two ferromagnetic grains embedded into an insulating matrix. This contribution to the exchange interaction complements the contribution due to virtual electron hopping between the grains. We show that the Coulomb and the hopping-based exchange interactions are comparable. However, for most system parameters these contributions have opposite signs and compete with each other. In contrast to the hopping-based exchange interaction the Coulomb-based exchange is inversely proportional to the dielectric constant of the insulating matrix $\varepsilon$. The total intergrain exchange interaction has a complicated dependence on the dielectric permittivity of the insulating matrix. Increasing $\varepsilon$ one can observe the ferromagnet-antiferromagnet (FM-AFM) and AFM-FM transitions. For certain parameters no transition is possible, however even in this case the exchange interaction has large variations, changing its value three times by increasing the matrix dielectric constant.

Using first-principles calculations we examine the crystal structures and phase transitions of nitride perovskite ${\mathrm{LaWN}}_3$. Lattice dynamics calculations indicate that the ground-state structure belongs to space group $R3c$. Two competitive phase transition pathways are identified which are characterized by symmetry-adapted distortion modes. The results suggest that $R3c{\mathrm{LaWN}}_3$ should be an excellent ferroelectric semiconductor, as its large spontaneous polarization of around 61 $\mu \mathrm{C}/{\mathrm{cm}}^2$ is comparable to that of ${\mathrm{PbTiO}}_3$, and its band gap is about 1.72 eV. Ferroelectricity is found to result from the $B$-site instability driven by hybridization between $\mathrm{W}-5d$ and $\mathrm{N}-2p$ orbitals. These properties make ${\mathrm{LaWN}}_3$ an attractive candidate material for use in ferroelectric memory devices and photovoltaic cells.

Whereas a great deal of work is being devoted to magnetic singularities in two-dimensional (2D) systems (surfaces, interfaces, films) due to their possible applications, much less is known about their properties along the perpendicular direction. Here, we report on a pronounced asymmetry of the in-depth distribution of meronlike magnetic textures, which are magnetic singularities similar to ½ skyrmions, in magnetic layers. Meron textures are observed to be distributed in two groups defined by their topology. One of them resides almost exclusively at the top surface of the film and the other at the bottom one. This observation has been brought to light with element-specific magnetic transmission soft x-ray microscopy. Micromagnetic simulations reveal that closure domains are at the origin of this asymmetry. The result might be of general interest for controlling magnetic three-dimensional (3D) architectures.

Using an atomistic model that simultaneously treats the dynamics of translational and spin degrees of freedom, we perform combined molecular and spin dynamics simulations to investigate the mutual influence of the phonons and magnons on their respective frequency spectra and lifetimes in ferromagnetic bcc iron. By calculating the Fourier transforms of the space- and time-displaced correlation functions, the characteristic frequencies and the linewidths of the vibrational and magnetic excitation modes were determined. Comparison of the results with that of the stand-alone molecular dynamics and spin dynamics simulations reveals that the dynamic interplay between the phonons and magnons leads to a shift in the respective frequency spectra and a decrease in the lifetimes. Moreover, in the presence of lattice vibrations, additional longitudinal magnetic excitations were observed with the same frequencies as the longitudinal phonons.

Electronic spin current is convertible to magnonic spin current via the creation or annihilation of thermal magnons at the interface of a magnetic insulator and a metal with a strong spin-orbital coupling. So far this phenomenon was evidenced in the linear regime. Based on analytical and full-fledged numerical results for the nonlinear regime we demonstrate that the generated thermal magnons or magnonic spin current in the insulator is asymmetric with respect to the charge current direction in the metal and exhibits a nonlinear dependence on the charge current density, which is explained by the tuning effect of the spin Hall torque and the magnetization damping. The results are also discussed in light of, and are in line with, recent experiments pointing to a new way of nonlinear manipulation of spin with electrical means.

The nickel-carbon system has received increased attention over the past years due to the relevance of nickel as a catalyst for carbon nanotube and graphene growth, where nickel carbide intermediates may be involved or carbide interface layers form in the end. Nickel-carbon composite thin films comprising ${\mathrm{Ni}}_3\mathrm{C}$ are especially interesting in mechanical sensing applications. Due to the metastability of nickel carbides, formation conditions and the coupling between mechanical and electrical properties are not yet well understood. Using first-principles electronic structure methods, we calculated the elastic properties of ${\mathrm{Ni}}_3\mathrm{C},{\mathrm{Ni}}_2\mathrm{C}$, and $\mathrm{NiC}$, as well as changes in electronic properties under mechanical strain. We observe that the electronic density of states around the Fermi level does not change under the considered strains of up to 1%, which correspond to stresses up to $3\mathrm{GPa}$. Relative changes in conductivity of ${\mathrm{Ni}}_3\mathrm{C}$ range up to maximum values of about 10%.

Here we present inelastic neutron scattering measurements from the frustrated, quantum spin-1/2 chain material linarite, ${\mathrm{PbCuSO}}_4{\left(\mathrm{OH}\right)}_2$. Time of flight data, taken at 0.5 K and zero applied magnetic field reveals low-energy dispersive spin wave excitations below 1.5 meV both parallel and perpendicular to the Cu-chain direction. From this we confirm that the interchain couplings within linarite are around 10% of the nearest neighbor intrachain interactions. We analyze the data within both linear spin-wave theory and density matrix renormalization group theories and establish the main magnetic exchange interactions and the simplest realistic Hamiltonian for this material.