In this paper, we employ electronic structure theory to investigate the nature of the exchange coupling in transition metal doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. We focus on V, Cr, Mn, and Fe, which have been under scrutiny for the realization of the quantum anomalous Hall effect. For simplicity, we model the doping process as happening inside a single layer of Bi within a single quintuple layer inside a three-formula-unit conventional hexagonal cell and consider situations of full coverage or half coverage. Due to the covalent nature of the chemical bond between transition metal atoms and selenium, this simple model is capable of describing the fundamental features of the intraplane exchange coupling, while offering a clearer analysis of the response to structural, magnetic, and electronic perturbations. In agreement with recent literature, our results confirm that the van Vleck mechanism has a very marginal contribution to the exchange coupling. Depending on the filling of the $3d$ shell and on the details of the electronic structure, several other mechanisms compete and cooperate to induce the magnetic order. For V, double exchange and superexchange cooperate to have the strongest ferromagnetic coupling among the investigated elements, followed by Cr where only superexchange is active. For Mn, superexchange and double exchange compete to create an extremely weak ferromagnetic order. For Fe, a strong antiferromagnetic coupling caused by the double exchange is observed to dominate over the ferromagnetic Ruderman-Kittel-Kasuya-Yosida interaction, but the high sensitivity of this competition to the doping concentration suggests that our conclusion may not hold in the dilute limit. Overall, Fe doping seems to offer the most intriguing competition of exchange mechanisms that can be tuned by adjusting the doping concentration and the details of the host, as, e.g., by replacing Se with Te or Bi with Sb.

Using a known distribution of the Meissner currents over the surface of an infinitely long superconducting slab with a rectangular cross section, we find an applied magnetic field at which vortices begin to penetrate into the superconductor. This vortex-penetration field is determined by an interplay of the geometrical and Bean-Livingston barriers. The obtained results enable one to find the lower critical field and the London penetration depth from measurements of the magnetic induction on the surface of the superconducting slab, using, e.g., the micro-Hall probes.

Correlated electron systems often show strong bosonic fluctuations, e.g., of antiferromagnetic nature, around a large wave vector such as $\mathbf{q}=(\pi ,\pi ...)$. These fluctuations can give rise to vertex corrections to the optical conductivity through the (transversal) particle-hole channel, coined $\pi$-ton contributions. Previous numerical results differed qualitatively on how such vertex corrections alter the optical conductivity. Here we clarify that $\pi$-ton vertex corrections lead to a displaced Drude peak, by studying the weakly correlated regime of a one-dimensional single-orbital Hubbard model. The proximity and enhancement of the effect when approaching a phase transition of, e.g., antiferromagnetic nature can be utilized for discriminating $\pi$-tons in experiments from other physics leading to a displaced Drude peak.

We investigate the metallic van der Waals itinerant ferromagnet ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ with atomic scale, spatially resolved low-temperature scanning tunneling microscopy (STM), and spectroscopy (STS). STM images unveil a new structural order $2a\times 1a$ along with the known order $\sqrt{3}a\times \sqrt{3}a$ manifesting as nonuniform domains. STS shows spatial and energy resolved local density of states that reveal the crucial influence of Fe(1) site occupancy on the system's electronic interactions. Our magnetization measurements show magnetic anomalies at lower temperatures and identify a Curie temperature (${\mathrm{T}}_c$) surpassing room temperature. Collectively, our results elucidate the intricate nature of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ and underscore its potential for tunability of spintronics and high-temperature magnetic applications.

Confining Dirac fermions in graphene using electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope tip can trap zero-energy quasiparticles. The Lorentzian quantum well provides a faithful, exactly solvable approximation for such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free-particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy.

Two-band Chern insulators are topologically classified by the Chern number, $c$, which is given by the integral of the Berry curvature of the occupied band over the Brillouin torus. The curvature itself comes from the imaginary part of a more basic object, the quantum geometric tensor, $Q$. On the other hand, the integral over the Brillouin torus of the real part of $Q$ gives rise to another magnitude, the quantum volume, $v_g$, that like $c$, jumps when the system undergoes a topological phase transition and satisfies the inequality $v_g\ge 2\left|c\right|$. The information contained in $v_g$ about the topology of the system has been investigated recently. In this paper we present new results regarding the underlying geometric structure of two-dimensional two-band topological insulators. Since a generic model describing the system can be characterized by a map, the classifying map, from the Brillouin torus to the two-sphere, we study its properties at the geometric level. We present a procedure for splitting the Brillouin torus into different sectors in such a way that the classifying map when restricted to each of them is a local diffeomorphism. By doing so, in the topological phases we are able to isolate a region contained in the Brillouin torus whose volume is the minimal one, $v_{\min }=2\left|c\right|$, and the integral of the Berry curvature on it is $c$. For cases in which $v_g>2\left|c\right|$, the regions contributing to the excess of volume, $v_{\mathrm{ex}}=v_g-2\left|c\right|$, are found and characterized. In addition, the present work makes contact with, and clarifies, some interpretations of the quantum volume in terms of the Euler characteristic number that were done in the recent literature. We illustrate our findings with a careful analysis of some selected models for Chern insulators corresponding to tight-binding Hamiltonians.

Noncentrosymmetric quantum materials can convert ac input current into dc transverse current through the nonlinear Hall effect at zero magnetic field. We analyze the ac-dc power conversion efficiency of such “Hall rectifier” and suggest its application in wireless charging and energy harvesting. Our key observation is that the development of Hall voltage results in a change of longitudinal resistance, resulting in a violation of Ohm's law due to the nonlinear Hall effect. This feedback mechanism balances the input power and the output power and hence is crucial for the understanding of the power transfer from source to load. We derive a general expression for the power conversion efficiency in terms of material parameters, external load resistance, and input power. As the Hall current is perpendicular to the electric field and does not generate Joule heating by itself, we obtain high power conversion efficiency when the Hall angle (which increases with the input power) is large and the load resistance is optimized. Promising materials for high-efficiency Hall rectifiers are also discussed.

The strong-field approximation (SFA) model proposed originally for a gaseous phase has been extended to explain the high-harmonic generation (HHG) in solids. In most of the previous works using the SFA model, only two bands near the Fermi energy are included. From another viewpoint, the form of the SFA model is similar to the first-order perturbation expansion with respect to the Rabi frequency, which triggered us to explore whether a higher-order expansion can work. In this paper, we extend the semiperturbative expansion to multiband electron dynamics in solids. We employ higher-order expansions to include more complex electron transition paths involving more than two bands. The high-harmonic spectrum from each perturbative order describes a different electron transition pathway and is verified by comparing with the numerical solution of one-dimensional semiconductor Bloch equations. Our extended approach, which is called the semiperturbation model, offers the distinct advantage for distinguishing contributions to HHG from various transition channels.

The coupling between the molecule-localized electronic states and continuum of the electronic states of the metal surface is of paramount importance for adsorption dynamics, surface reactivity, as well as for the electron- and photon-induced processes at metal surfaces. Here, using the model one-active-electron description and wave-packet propagation approach, we study the resonant electron transfer between the perylene-tetracarboxylic-dianhydride (PTCDA) molecule and metal substrate from 0.5 nm separations down to the adsorption distances. We also address the situation where the molecule is lifted up from the substrate using the scanning tunneling microscope. A detailed comparison with the large amount of available experimental data and ab initio calculations allows us to discuss the validity of the method and the main robust effects driving the lifetimes of molecule-localized states that it reveals. Thus we show that the symmetry of molecule-localized states strongly impacts the dependence of the electron transfer rates on the metal band structure and molecule-surface distance. In addition, in full agreement with recent experimental data on scanning tunneling microscopy manipulation where an adsorbed molecule is lifted into the vertical geometry, we find an order of magnitude reduction of the adsorbate-substrate coupling.

We propose selection rules for four-phonon (4ph) scattering that clarify the predominance of the redistribution process. The cutoff frequencies for specific scattering channels are identified, with their feasibility determined by the magnitude of the a-o gap. We obtain substantive evidence to support the fact that the enhancement of 4ph scattering is due to the flat phonon dispersion. An extremely strong intraband scattering in the ZA branch is identified beyond expectation. The same enhancing effect can manifest between homothetic branches as an enhancement mechanism of interband scattering. The homothety is associated with the distribution trend of phonon group velocity, which can anticipate the intensity of 4ph scattering. Our work provides insights and perspectives into 4ph interaction.

We study nonlocal thermoelectricity in a superconducting wire subject to spin-orbit coupling and a magnetic field with a relative orientation $\theta$ between them. We calculate the current flowing in a normal probe attached to the bulk of a superconducting wire, as a result of a temperature difference applied at the ends of the wire. We focus on the linear response regime, corresponding to a small temperature bias. We find that the nonlocal thermoelectric response is strongly dependent on the angle $\theta$ and occurs in ranges which correspond to the emergence of Bogoliubov-Fermi points in the energy spectrum of the superconducting wire.

The competition between the Kondo screening and indirect magnetic exchange in systems with two magnetic impurities coupled to a conventional $s$-wave superconductor gives rise to a nontrivial ground-state phase diagram. Here, we utilize the density matrix renormalization group (DMRG) method and exploit the non-Abelian spin-SU(2) symmetry to study the phase diagram for two quantum spin-$\frac{1}{2}$ impurities locally exchange coupled to large one-dimensional chains. The nonlocal interimpurity exchange is treated as an emergent Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling. We find qualitatively different phase diagrams for impurity spins coupled to sites with odd or even distances $d$ on the chain and a partial Kondo-screened spin-doublet phase that extends over the whole range of local exchange couplings $J$ in the limit of weak superconducting pairing strength $\mathrm{\Delta }$. Our numerical DMRG studies are complemented by exact diagonalization of small (quantum-box) systems and by perturbative-in-$J$ computations of the $d$- and $\mathrm{\Delta }$-dependent RKKY interaction. It is thereby demonstrated that the specific system geometry is essential for our understanding of magnetic impurity interactions in superconducting hosts, and thus for insights into the control of quantum-state properties in nanoparticle systems and topological superconductivity.

In quantum anomalous Hall (QAH) systems, the Hall conductance is quantized, and the corresponding effective topological theory of the system is the Chern-Simons theory. The conductance quantum is given by the universal constant $e^2/h$—the inverse von Klitzing constant—that is independent of the bulk gap, as well as the size of the system. This picture relies on the assumption that the edge modes are sharply localized at the edge, i.e., they have zero width. We show that, considering the physical case where the edge modes have finite localization length $b$, the effective action would not be topological in the bulk direction anymore. Because of nonzero $b$ the conductance quantum will be corrected as $(1-\varepsilon )e^2/h$ where $\varepsilon$ encompasses the nonuniversal (i.e., material/sample dependent) part that is determined by the dimensionless ratios $\frac{gb}{\hslash v_F}$ and $\frac{b}{L}$ where $g,v_F,L$ are the bulk gap, Fermi velocity, and sample length. To compute the nonuniversal correction $\varepsilon$ we use anomaly inflow framework according to which the bulk action produces the correct amount of anomaly inflow that would cancel the anomaly of the chiral edge modes. These corrections place limits on the precision of measurable quantization in units of the inverse von Klitzing constant for QAH systems with smaller sizes and/or smaller bulk gaps. Our result suggests that the failure of precision measurements to reproduce the exact conductance quantum $e^2/h$ is not an annoying sample quality issue, but it contains the quantitative physics of anomaly inflow that can be inferred by the systematic study of such corrections.

We present a density matrix renormalization group study of an extended $t\text{−}J$ model with hopping to the first and second neighbors—the one-dimensional $t_1\text{−}{t}_2\text{−}J$ model. The full phase diagram as a function of the density $n$ and exchange strength $J$, for both positive and negative values of $t_2$, is obtained. For $t_2=-0.5$ we observe that, in the strongly interacting region, Nagaoka ferromagnetism is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange $J$ increases, a charge density wave phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When $t_2=0.5$, the physics is basically reminiscent of the conventional $t\text{−}J$ model, undergoing a transition from a metallic to a SC phase as a function of $J$.

We study the magnetic heat capacity of a series of magnetically ordered Ce-based heavy-fermion materials, which show an anomalous $T^3$ heat capacity in excess of the phonon contribution in many materials. For compounds for which magnon models have been worked out, we show that the local-moment magnon heat capacity derived from the measured magnon spectra underestimates the experimental specific heat. The excess heat capacity reveals increasing density of states with increasing energy, akin to a pseudogap. We show that this anomalous temperature-dependent term is not associated with proximity to a quantum critical point, but is strongly correlated with $T_N$, indicating the anomalous excitations are governed by the magnetic exchange interaction. This insight may hold key information for understanding magnetically ordered heavy fermions.

We describe the mean-field model of a one-dimensional topological superconductor with two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry, involving a translation by a fraction of the unit cell, mimics the role of time-reversal symmetry. As a result, the topological superconductor has ${\mathbb{Z}}_4$ topological phases, two that support Majorana bound states and two that do not, in agreement with a prediction based on K-theory classification [K. Shiozaki, M. Sato, and K. Gomi, Phys. Rev. B 93, 195413 (2016)]. As with the Kitaev chain, the presence of Majorana bound states gives rise to the $4\pi$-periodic Josephson effect. A random matrix with nonsymmorphic time-reversal symmetry may be block diagonalized, and every individual block has time-reversal symmetry described by one of the Gaussian orthogonal, unitary, or symplectic ensembles. We show how this is manifested in the energy level statistics of a random system in the ${\mathbb{Z}}_4$ class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size.

We study magnon transmission across gate-controlled junctions in the $n=0$ manifold of Landau levels in monolayer graphene in the presence of both spin and valley Zeeman fields. Specifically, we consider the $1|-1|1$ sandwich geometry. The nature of the interfaces between regions of different filling turns out to be crucial for magnon transmission. Using the Hartree-Fock approximation, we find that either the spin or the valley degrees of freedom of the occupied one-body states rotate across the interfaces. If the interfaces exhibit spin rotation, then magnon transmission is suppressed at high energies, while if the interfaces have valley rotation, then magnon transmission becomes perfect at high energies. The valley Zeeman coupling, which arises from partial alignment with the encapsulating boron nitride, is independent of perpendicular magnetic field $B$, while the spin Zeeman and other anisotropic couplings scale linearly with $B$. This allows the tuning of the relative strength of the valley Zeeman coupling in situ by varying $B$, which can drive phase transitions of the interfaces between spin-rotated and valley-rotated phases, leading to magnon transmission being either vanishing or perfect at high energies. Our analysis, along with the experimental measurements, can be used to determine the anisotropic couplings in the sample.

We explore the superconducting pairing mechanism in the trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ material through self-consistent mean-field calculations. Our findings demonstrate that the intralayer pairing is substantially weaker compared to the interlayer one. Remarkably, in the superconducting state characterized by the interlayer pairing, our results indicate the presence of a partially gapped Fermi surface, a fascinating occurrence attributable to the inequivalence between the inner and outer conducting layers of ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. Moreover, this Letter provides valuable insights into the lower superconducting transition temperature observed in the ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ compound, thereby deepening our understanding of its distinctive superconducting properties.

A novel spin texture formed by Cooper pair spins is found theoretically with a phase string attached by half-quantized vortices at both ends in a unit cell and characterized by its topologically rich vortex structure in a spin-triplet pairing. It is stable at an intermediate field below a conventional singular vortex phase. The $d$-vector direction of this spin texture is tilted from the principal crystal axes, whose spin susceptibility is neither the normal Pauli one ${\chi }_{\mathrm{N}}$ nor zero, describing microscopically the process of the $d$-vector rotation phenomena observed recently in ${\mathrm{UTe}}_2$. We compare the spin texture and singular vortex state in relation to the quasiparticle structure with Majorana zero modes for STM, the nuclear spin resonance spectral line width for NMR and $\mu \mathrm{SR}$, and the vortex form factors for SANS to facilitate the identification of the pairing symmetry in ${\mathrm{UTe}}_2$.