Analytical expressions for the longitudinal and transverse correlation functions pertaining to inertial magnetic relaxation are obtained by expanding the deterministic magnetization trajectories into a Fourier series and averaging the result over all possible initial conditions applying the stationary Boltzmann distribution function. The longitudinal and transverse components of the magnetic susceptibility tensor are calculated for a system of noninteracting macrospins in a strong uniform external field using Bloch's phenomenological approach, which postulates the exponential evolution of the spin system towards equilibrium, and the Lorentz model of rotational diffusion of the magnetization vector. It is shown that the strength of the external field and the magnitude of the inertia parameters noticeably affect the shape of the susceptibility in the THz (nutation resonance) spectrum region. It is also demonstrated that the simple analytical Lorentz-type expression describes the main features of the complex susceptibility in the ferromagnetic resonance and nutation resonance regions.

Caroli–de Gennes–Matricon (CdGM) states are localized states with a discrete energy spectrum bound to the core of vortices in superconductors. In topological superconductors, CdGM states are predicted to coexist with zero energy, chargeless states widely known as Majorana zero modes (MZMs). Due to their energy difference, current experiments rely on scanning tunneling spectroscopy methods to distinguish between them. This work shows that electrostatic inhomogeneities can push trivial CdGM states arbitrarily close to zero energy in nontopological systems where no MZM is present. Furthermore, the BCS charge of CdGM states is suppressed under the same mechanism. Through exploration of the impurity parameter space, we establish that these two phenomena generally happen in consonance. Our results show that energy and charge shifts in CdGM may be enough to imitate the spectroscopic signatures of MZMs even in cases where the estimated CdGM level spacing (in the absence of impurities) is much larger than the typical experimental level broadening.

Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by nonperturbative interactions without generating any fermion bilinear condensation. The previous studies of SMG have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this paper, we generalize the concept of SMG to Fermi liquid (FL) with a finite Fermi volume and discuss how to gap out the Fermi surfaces (FSs) by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of FS SMG in both $(1+1)$-dimensional $\left[\right(1+1\left)\mathrm{D}\right]$ and $(2+1)$-dimensional FL systems when several FSs together cancel the FS anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the $(1+1)\mathrm{D}$ U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

The quantum geometry in the momentum space of semiconductors and insulators, described by the quantum metric of the valence-band Bloch state, has been an intriguing issue owing to its connection to various material properties. Because the Brillouin zone is periodic, the integration of quantum metric over momentum space represents an average distance between neighboring Bloch states, which we call the fidelity number. We show that this number can further be expressed in real space as a fidelity marker, which is a local quantity that can be calculated directly from diagonalizing the lattice Hamiltonian. A linear-response theory is further introduced to generalize the fidelity number and marker to finite temperature and moreover demonstrates that they can be measured from the global and local optical absorption power against linearly polarized light. In particular, the fidelity number spectral function in two-dimensional systems can be easily measured from the opacity of the material. Based on the divergence of quantum metric, a nonlocal fidelity marker is further introduced and postulated as a universal indicator of any quantum phase transitions provided the crystalline momentum remains a good quantum number, and it may be interpreted as a Wannier state correlation function. The ubiquity of these concepts is demonstrated for a variety of topological insulators and topological phase transitions in different dimensions.

Although one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the Kane-Mele model with and without Rashba spin-orbit coupling as a well-known model to describe a two-dimensional version of the ${\mathbb{Z}}_2$ topological insulator to study the properties of its edge states analytically. By considering the tight-binding model on a honeycomb lattice with zigzag boundaries and introducing a perturbative approach, we derive explicit expressions for the wave functions, energy dispersion relations, and the spin rotations of the (generic) helical edge states. To this end, we first map the edge states of the ribbon geometry into an effective two-leg ladder model with momentum-dependent energy parameters. Then, we split the Hamiltonian of the system into an unperturbed part and a perturbation. The unperturbed part has a flat-band energy spectrum and can be solved exactly, which allows us to consider the remaining part of the Hamiltonian perturbatively. The resulting energy dispersion relation within the first-order perturbation, surprisingly, is in excellent agreement with the numerical spectra over a very wide range of wave numbers. Our perturbative framework also allows deriving an explicit form for the rotation of the spins of the momentum edge states in the absence of axial spin symmetry due to the Rashba spin-orbit interaction.

We derive the bosonization of the interacting fermionic Su-Schrieffer-Heeger (SSH) model with open boundaries. We use the classical Euler-Lagrange equations of motion of the bosonized theory to compute the density profile of the zero-energy edge mode and observe excellent agreement with numerical results, notably the localization of the mode near the boundaries. Remarkably, we find that repulsive or attractive interactions do not systematically localize or delocalize the edge mode but their effects depend on the value of the staggering parameter. We provide quantitative predictions of these effects on the localization length of the edge mode. Our study shows that bosonization is able to quantitatively describe edge modes of interacting topological one-dimensional systems and pave the way to generalization to other models.

We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at the oxide interface to form a quasi-one-dimensional conductor. We reveal an anomalous critical current behavior with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with the appearance of orbital-flavored Majorana bound states (OMBSs) pinned at the edges of the superconducting leads. Signatures of OMBSs also include a sawtooth profile in the current-phase relation. Our findings allow us to recognize fingerprints of topological superconductivity in noncentrosymmetric materials and confined systems with a spin-orbit interaction. They also explain recent experimental observations for which a microscopic description is still lacking.

A quasi-two-dimensional quantum magnet with competing ferro- and antiferromagnetic exchange interactions, $\mathrm{BaCdVO}{\left({\mathrm{PO}}_4\right)}_2$, is studied using the magnetic resonance technique in a wide frequency range. The magnetic resonance spectra of the ordered phase confirm the collinear antiferromagnetic spin structure oriented along the $a$ axis. The frequency-field diagram of antiferromagnetic resonance demonstrates two low-frequency excitation branches with different energy gaps, indicating a biaxial nature of anisotropy. We observe a critical softening of the longitudinal resonance mode in a field of 3.8 T, which is the lower boundary of a previously proposed presaturation phase positioned below the saturation field of 6.5 T. An interpretation of the presaturation phase as a state with variable magnetization of spin-vacancy defects is proposed. It may be considered an alternative to the spin-nematic phase initially supposed.

Efficient and fast manipulation of antiferromagnets has to date remained a challenging task, hindering their application in spintronic devices. For ultrafast operation of such devices, it is highly desirable to be able to control the antiferromagnetic order within picoseconds—a timescale that is difficult to achieve with electrical circuits. Here, we demonstrate that bursts of spin-polarized hot-electron currents emerging due to laser-induced ultrafast demagnetization are able to efficiently excite spin dynamics in antiferromagnetic ${\mathrm{Mn}}_2\mathrm{Au}$ by exerting a spin-transfer torque on femtosecond timescales. We combine quantitative superdiffusive transport and atomistic spin-model calculations to describe a spin-valve-type trilayer consisting of $\mathrm{Fe}\left|\mathrm{Cu}\right|{\mathrm{Mn}}_2\mathrm{Au}$. Our results demonstrate that femtosecond spin-transfer torques can switch the ${\mathrm{Mn}}_2\mathrm{Au}$ layer within a few picoseconds. In addition, we find that spin waves with high frequencies up to several THz can be excited in ${\mathrm{Mn}}_2\mathrm{Au}$.

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with nontrivial strong topological invariants (protected by internal symmetries) with additional “weak” topological indices. In this paper, we study the edge physics of systems with a nontrivial shift invariant, which is protected by either a continuous $\text{U}{\left(1\right)}_r$ or discrete ${\text{C}}_n$ rotation symmetry, along with internal $\text{U}{\left(1\right)}_c$ charge conservation. Specifically, we construct an interface between two systems that have the same Chern number but are distinguished by their Wen-Zee shift, and, through analytic arguments supported by numerics, we show that the interface hosts counterpropagating gapless edge modes that cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian subalgebra framework for gapped boundaries, while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and we compute them in the case in which the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Our work paves the way for studying the edge physics associated with spatial symmetries in strongly interacting symmetry enriched topological phases.

We study the electronic transport through uniformly bent carbon nanotubes. For this purpose, we describe the nanotube with the tight-binding model and calculate the local current flow by employing nonequilibrium Green's functions (NEGF) in the Keldysh formalism. In addition, we describe the low-energy excitations using an effective Dirac equation in curved space with a strain-induced pseudomagnetic field, which can be solved analytically for the torus geometry in terms of the Mathieu functions. We obtain a perfect quantitative agreement with the NEGF results. For nanotubes with an armchair edge, already a weak bending of $1\%$ substantially changes the electronic properties. Depending on the valley, the current of the zero mode flows either on the outer or the inner side of the torus and, therefore, can be used as a valley splitter. In contrast, the zigzag nanotubes are largely unaffected by the bending. Our findings are of importance for nanoelectronic applications of carbon nanotubes and open new possibilities for valleytronics.

Recently there has been intense interest in kagome metals, which are expected to host flat bands (FBs). However, the observed “FBs” are not flat over the whole two-dimensional Brillouin zone and overlap strongly with other bands. In fact, the FB does not truly exist in a default $d$-orbital kagome lattice, and the conditions for its existence in kagome metals are unknown. Here, based on tight-binding model analyses of the interplay between orbital and lattice symmetry, we establish such conditions. We show that for a single $d$-orbital kagome lattice assuming large crystal field splitting (CFS), only the $d_{z^2}$ orbital gives rise to a FB, while $d_{xy}, d_{x^2-y^2}, d_{xz}$, and $d_{yz}$ orbitals can only produce a FB with a rotated $d$-orbital basis so that they conform with the underlying kagome lattice symmetry. Most importantly, we demonstrate that both conditions of $d$-orbital rotation and large CFS can be ideally satisfied by intercalating the kagome lattice with a hexagonal sublattice without disrupting the destructive interference of FB wave function. Furthermore, we propose layered metalorganic frameworks as promising candidate kagome metals to realize FBs.

Elucidating the microscopic mechanisms responsible for the charge density wave (CDW) instability of the $A{\text{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{Cs},\mathrm{K},\mathrm{Rb})$ family of kagome metals is critical for understanding their unique properties, including superconductivity. In these compounds, distinct CDW phases with wave vectors at the $M$ and $L$ points are energetically favorable, opening the possibility of tuning the type of CDW order by appropriate external parameters. Here, we shed light on the CDW landscape of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ via a combination of first-principles calculations and phenomenology, which consists of extracting the coefficients of the CDW Landau free-energy expansion from density functional theory. We find that while the main structural distortions of the kagome lattice in the staggered tri-hexagonal CDW phase are along the nearest-neighbor V–V bonds, distortions associated with the Sb ions play a defining role in the energy gain in this and all other CDW states. Moreover, the coupling between ionic displacements from different unit cells is small, thus explaining the existence of multiple CDW instabilities with different modulations along the $c$ axis. We also investigate how pressure and temperature impact the CDW phase of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. Increasing pressure does not change the staggered tri-hexagonal CDW ground state, even though the $M$-point CDW instability disappears before the $L$-point one, a behavior that we attribute to the large nonlinear coupling between the order parameters. Upon changing the temperature, we find a narrow regime in which another transition can take place, toward a tri-hexagonal star-of-David CDW phase. We discuss the implications of our results by comparing them with experiments on this compound.

Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called $t\text{−}{t}^{\prime }\text{−}{t}^{\prime \prime }\text{−}J$ model, where the determination of the parameter $t^{\prime }$ in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the $t\text{−}{t}^{\prime }\text{−}{t}^{\prime \prime }\text{−}J$ model using two machine-learning techniques: $K$-nearest neighbor regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about $1.3\times {10}^5$ spectral functions. We show that, for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing, e.g., rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density of states. Our results suggest that it may be possible to use deep-learning methods to predict materials parameters from experimentally measured spectral functions.