In the framework of the kinetic approach based on the Boltzmann equation for the phonon distribution function, we analyze phonon heat transfer in a heterostructure containing a layer of a normal metal ($N$) and a layer of a ferromagnetic insulator ($F$). Two realistic methods for creating a temperature gradient in such a heterostructure are considered: by heating the $N$ layer by an electric current and by placing the $N/F$ bilayer between massive dielectrics with different temperatures. The electron temperature $T_e$ in the $N$ layer and the magnon temperature $T_m$ in the $F$ layer are calculated. The difference in these temperatures determines the voltage $V_{\text{ISHE}}$ on the $N$ layer in the Seebeck spin effect regime. The dependence of $V_{\text{ISHE}}$ on the bath temperature and on the thickness of the $N$ and $F$ layers is compared with the available experimental data.

The magnetocaloric effect of gadolinium has been measured directly in pulsed magnetic fields up to $62\mathrm{T}$. The maximum observed adiabatic temperature change is $\mathrm{\Delta }{T}_{\mathrm{ad}}=60.5\mathrm{K}$, the initial temperature $T_0$ being just above $300\mathrm{K}$. The field dependence of $\mathrm{\Delta }{T}_{\mathrm{ad}}$ is found to follow the usual $H^{2/3}$ law, with a small correction in $H^{4/3}$. However, as $H$ is increased, a radical change is observed in the dependence of $\mathrm{\Delta }{T}_{\mathrm{ad}}$ on $T_0$, at $H=\mathrm{const}$. The familiar caret-shaped peak situated at $T_0=T_{\mathrm{C}}$ becomes distinctly asymmetric, its high-temperature slope becoming more gentle and evolving into a broad plateau. For yet higher magnetic fields, ${\mu }_{0}H\gtrsim 140\mathrm{T}$, calculations predict a complete disappearance of the maximum near $T_{\mathrm{C}}$ and an emergence of a new very broad maximum far above $T_{\mathrm{C}}$.

Unconventional superconductivity often arises from Cooper pairing between neighboring atomic sites, stipulating a characteristic pairing symmetry in the reciprocal space. The twisted bilayer graphene (TBG) presents a new setting where superconductivity emerges on the flatbands whose Wannier wave functions spread over many graphene unit cells, forming the so-called moiré pattern. To unravel how Wannier states form Cooper pairs, we study the interplay between electronic, structural, and pairing instabilities in TBG. For comparisons, we also study graphene on boron-nitride (GBN) possessing a different moiré pattern, and single-layer graphene (SLG) without a moiré pattern. For all cases, we compute the pairing eigenvalues and eigenfunctions by solving a linearized superconducting gap equation, where the spin-fluctuation mediated pairing potential is evaluated from materials-specific tight-binding band structures. We find an extended $s$ wave as the leading pairing symmetry in TBG, in which the nearest-neighbor Wannier sites form Cooper pairs with same phase. In contrast, GBN assumes a $p+ip$-wave pairing between nearest-neighbor Wannier states with odd-parity phase, while SLG has the $d+id$-wave symmetry for intersublattice pairing with even-parity phase. Moreover, $p+ip$ and $d+id$ pairings are chiral, and nodeless, but the extended $s$-wave channel possesses accidental nodes. The nodal pairing symmetry makes it easily distinguishable via power-law dependencies in thermodynamical entities, in addition to their direct visualization via spectroscopies.

Many of the macroscopic properties of a glass are determined by the degree of structural relaxation. When the nonequilibrium system ages toward a thermodynamically more favorable state, the accompanying densification leads to an increase of the activation energies found for the $\alpha$ and especially the $\beta$ relaxation processes. In this work we experimentally quantify the low-energy mechanical relaxation spectrum of a metallic glass at cryogenic temperatures, and show that these relaxation processes intriguingly show the opposite trend. The energy scale as well as the relaxation strength decrease during the aging process below the glass transition temperature with a surprisingly strong dependence on the annealing time. The experimental results are analyzed in the framework of established models and the temporal behavior of the typical energy $V_0$ is assessed. We compare the derived values to the values of the thermal energy available at the estimated fictive temperature of the given state and find that the absolute values as well as their temporal behavior show a high degree of correlation for the studied metallic glass. The decreasing characteristic energy values found in the present experiment directly depict the evolution of the structure toward a hypothetical lowest entropy state before the glass becomes structurally indistinguishable from a crystalline material.

The magnetic penetration depth anisotropy ${\gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}$ (${\lambda }_{ab}$ and ${\lambda }_c$ are the in-plane and the out-of-plane components of the magnetic penetration depth) in a ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ single crystal sample (the critical temperature $T_{\mathrm{c}}\simeq 35$ K) was studied by means of muon-spin rotation ($\mu \mathrm{SR}$). ${\gamma }_{\lambda }$ is almost temperature independent for $T\lesssim 20$ K (${\gamma }_{\lambda }\simeq 1.9$) and it reaches $\simeq 3.0$ by approaching $T_{\mathrm{c}}$. The change of ${\gamma }_{\lambda }$ induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL $\mu \mathrm{SR}$ response. A comparison of ${\gamma }_{\lambda }$ with the anisotropy of the upper critical field (${\gamma }_{H_{\mathrm{c}2}}$) studied by Meier et al. [Phys. Rev. B 94, 064501 (2016)] reveals that ${\gamma }_{\lambda }$ is systematically higher than ${\gamma }_{H_{\mathrm{c}2}}$ at low temperatures and approaches ${\gamma }_{H_{\mathrm{c}2}}$ for $T\to T_{\mathrm{c}}$. The anisotropic properties of $\lambda$ are explained by the multigap nature of superconductivity in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density.

The vibrational excitations in ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ thin-film metallic glasses are investigated using molecular dynamics simulations. A strong density layering parallel to surfaces is formed in the glassy thin films. This layering behavior results in a layerlike arrangement of soft regions through films. The vibrational excitations in the periodic soft layers are proved to be harmonic and in analog y with the simple one-dimensional lattice vibration. A low-frequency and optical-like phonon mode features the soft-mode excitations. The soft-mode excitations enhance the vibrational density of states in the low-frequency side, depending on the softness of layers. Our results provide direct evidence supporting the low-frequency and nonacoustic vibrational excitations of soft domains in glasses.

${\mathrm{Fe}}_{69}{\mathrm{Co}}_{26}{\mathrm{Si}}_5$ alloy thin films of various thicknesses were deposited on MgO(100) single crystal substrates by magnetron sputtering at $230{}^{\circ }\mathrm{C}$ substrate temperature. The thickness dependence of the dynamic magnetic properties was investigated using broadband ferromagnetic resonance (FMR). The x-ray diffraction results indicate that all films are of the bcc structure with an in-plane epitaxial alignment of ${\left[100\right]}_{\mathrm{FeCoSi}}//{\left[110\right]}_{\mathrm{MgO}}$. The exchange constant was determined from the field shift between the uniform precession FMR mode and the first order perpendicular standing spin wave resonance mode in the FMR spectra. The effective damping parameter decreases dramatically with increasing film thickness up to 16 nm due to the decrease of the spin pumping contribution and then remains relatively constant as the film thickness increases. In-plane angle dependent FMR measurements reveal that the in-plane anisotropy of these films is dominated by a fourfold magnetic anisotropy, which increases sharply with increasing film thickness up to 16 nm and then shows a slightly decreasing trend as the film thickness increases. In-plane angular dependence of the FMR linewidth shows a strong two-magnon scattering contribution.

The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds $A_2{\mathrm{CoTeO}}_6$ ($A=\text{Ca}$, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in the model, indicating the possibility to observe supersolid phases in these compounds. We also find that one of the supersolid phases is similar to the nonclassical coplanar phase obtained in the $XXZ$ model on the triangular lattice.

In this work we focus on the magnetic properties of metallacrown complexes as computed by various density functional methods. Using the broken symmetry approach, we determine the exchange-coupling constants and the $g$ tensors and compare them with experimentally determined ones from the temperature-dependent magnetic susceptibilities and by the electronic spin resonance, respectively. Generalization of the Noodleman-Dai-Whangbo approach for systems with multiple magnetic centers that we introduce here allows to make quantitative statements about the nature of these electronic states in density functional theory.

Properties of shock waves and solitons in superfluid ${}^4\mathrm{He}$ were studied by time-resolved shadowgraph experiments and theoretical density functional theory calculations. Pressure estimates for shock waves and the bright soliton limit (0.2 MPa) were provided and compared with the semiclassical Rankine-Hugoniot theory. Overall, the shock wave amplitude-velocity relationship was observed to be linear at least up to 175 kg/${\mathrm{m}}^3$. At high amplitudes, the shock waves decay into sound waves in the wake as well as a bright soliton train in the front. This suggests that the experimental shadowgraph data presented by Ancilotto et al. [Phys. Rev. Lett. 120, 035302 (2018)] correspond to such a train structure rather than an individual bright soliton. With reference to theoretical calculations, a new approach based on an accelerating wall embedded in the liquid is proposed for generating single solitons in superfluid helium. This process is also predicted to produce dark solitons in superfluid helium, which have not yet been observed experimentally. At low soliton amplitudes, collision with an exponentially repulsive wall results in nearly lossless reflection, which is accompanied by soliton inversion from dark to bright or bright to dark.

Some interfaces between two different topologically ordered systems can be gapped. In earlier work it was shown that such gapped interfaces can themselves be effective one-dimensional topological systems that possess localized topological modes in open boundary geometries. Here we focus on how this occurs in the context of an interface between two single-component Laughlin states of opposite chirality, with filling fractions ${\nu }_1=1/p$ and ${\nu }_2=1/p{n}^2$. While one type of interface in such systems was previously studied, we show that allowing for edge reconstruction effects opens up a wide variety of possible gapped interfaces depending on the number of divisors of $n.$ We apply a complementary description of the ${\nu }_2=1/p{n}^2$ system in terms of Laughlin states coupled to a discrete gauge ${\mathbb{Z}}_n$ field. This enables us to identify possible interfaces to the ${\nu }_1$ system based on complete or partial confinement of this gauge field. We determine the tunneling properties, the ground-state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.

A $t_{2g}^5$ system with a honeycomb lattice structure such as ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ was firstly proposed as a topological insulator even though ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and its isostructural materials in nature have been turned out to be a Mott insulator with magnetic order. Here we theoretically revisit the topological property based on a minimal tight-binding Hamiltonian for three $t_{2g}$ bands incorporating a strong spin orbit coupling and two types of the first nearest-neighbor (NN) hopping channel between transition metal ions, i.e., the hopping ($t_1$) mediated by edge-shared ligands and the direct hopping ($t_1^{\prime }$) between $t_{2g}$ orbitals via $dd\sigma$ bonding. We demonstrate that the topological phase transition takes place by varying only these hopping parameters with the relative strength parametrized by $\theta$, i.e., $t_1=tcos\theta$ and $t_1^{\prime }=tsin\theta$. We also explore the effect of the second and third NN hopping channels, and the trigonal distortion on the topological phase for the whole range of $\theta$. Furthermore, we examine the electronic and topological phases in the presence of on-site Coulomb repulsion $U$. Employing the cluster perturbation theory, we show that, with increasing $U$, a trivial or topological band insulator in the absence of $U$ can be transferred into a Mott insulator with nontrivial or trivial band topology. We also show that the main effect of the Hund's coupling can be understood simply as the renormalization of $U$. We briefly discuss the relevance of our results to the existing materials.

Representation by neural networks, in particular by restricted Boltzmann machines (RBMs), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of quantum states can be efficiently represented with RBMs. Here, we show that RBMs can efficiently represent a wide class of many-body entangled states with rich exotic topological orders. This includes (1) ground states of double semion and twisted quantum double models with intrinsic topological orders, (2) states of the AKLT model and two-dimensional CZX model with symmetry protected topological orders, (3) states of stabilizer Fracton models with fracton topological order, and (4) (generalized) stabilizer states and hypergraph states that are important for quantum information protocols. One twisted quantum double model state considered here harbors non-Abelian anyon excitations. Our result shows that it is possible to study a variety of quantum models with exotic topological orders and rich physics using the RBM computational toolbox.

The logarithmic singularity of the Lindhard linear response function plays an important role in various phenomena, such as the long-range Friedel oscillations and Kohn anomaly in phonon dispersion. Such a weak singularity cannot be captured by the known gradient expansion of the kinetic energy (KE), but it can be somewhat mimicked by the second-order gradient singularity expansion (GSE2) developed in this work. We show that the GSE2 Pauli KE potential of atoms, computed with the Kohn-Sham density, is remarkably accurate, being the best possible approximation provided by any second-order KE gradient expansion. Next, we study the utility of GSE2 for orbital-free density functional theory, and we prove that the GSE2-based KE functionals give an important and systematic improvement over other popular KE functionals.

We propose a hierarchical architecture for building “logical” Majorana zero modes using “physical” Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three “physical” Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekule vortex pattern in the set of hybridization amplitudes yields an emergent “logical” Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, without moving any of the “physical” Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such “logical” Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner.

We characterize the dynamics of electrons in twisted bilayer graphene by analyzing the time evolution of electron waves in an atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomials; this method does not requires any diagonalization of the system Hamiltonian. Our simulations reveal that interlayer electronic coupling induces an exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference in the wavefront dynamics compared to monolayer graphene. The intralayer spreading of electron waves is irregular and progresses as a two-stage process. The first one, characterized by a well-defined wavefront, occurs in a short time—a wavefront forms instead during the second stage. The wavefront takes a hexagonlike shape with the vertices developing faster than the edges. Though the detail spreading form of waves depends on initial states, we observe localization of waves in specific regions of the moiré zone. To characterize the electron dynamics, we also analyze the time autocorrelation functions. We show that these quantities exhibit beating modulation when reducing interlayer coupling.

The recent excitement about Dirac and Weyl fermion systems has renewed interest in magnetotransport properties of multicarrier systems. However, the complexity of their analysis, even in the simplest two-carrier case, has hampered a good understanding of the underlying phenomena. Here we propose a new analysis scheme for two independent conduction channels, that strongly reduces previous ambiguities and allows one to draw robust conclusions. This is demonstrated explicitly for the example of three-dimensional topological insulators. Their temperature and gate voltage-dependent Hall coefficient and transverse magnetoresistance behavior, including the phenomenon of huge linear transverse magnetoresistance, can be traced back to two conduction channels, with fully determined carrier concentrations and mobilities. We further derive an upper limit for the transverse magnetoresistance. Its violation implies field dependencies in the electronic band structure or scattering processes, or the presence of more than two effective carrier types. Remarkably, none of the three-dimensional topological insulators or semimetals with particularly large transverse magnetoresistance violates this limit.

We study topological aspects of a Dirac fermion coupled with a Higgs field associated with the lattice model introduced by Benalcazar et al. [Science 357, 61 (2017)] which has the topological quadrupole phase. Using the index theorem, we show that the index of the Hamiltonian is just given by the winding number of the Higgs field, implying that a corner state of the lattice model belongs to the same class of the Jackiw-Rossi states localized at a vortex. We also calculate the current density of the Dirac fermion with a symmetry-breaking term dependent on time, which is associated with the dipole pump proposed by Benalcazar et al.. We argue that the total pumped charge is given by an integer related with the index.

We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the bandwidth $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the density-matrix renormalization group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.