In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a finite thermal correlation length $\xi$, such that for system sizes $L\gg \xi$ finite-size calculations actually simulate the thermodynamic limit. In this paper, we focus on the square lattice Heisenberg antiferromagnet (SLH) and quantum Ising models (QIM) on open and cylindrical geometries up to width $W=10$. We explore various one-dimensional mapping paths in the matrix product operator (MPO) representation, whose performance is clearly shown to be geometry dependent. We benchmark against quantum Monte Carlo (QMC) data, yet also the series-expansion thermal tensor network results. Thermal properties including the internal energy, specific heat, and spin structure factors, etc. are computed with high precision, obtaining excellent agreement with QMC results. XTRG also allows us to reach remarkably low temperatures. For SLH, we obtain an energy per site $u_g^{*}\simeq -0.6694\left(4\right)$ and a spontaneous magnetization $m_S^{*}\simeq 0.30\left(1\right)$ already consistent with the ground-state properties, which is obtained from extrapolated low-$T$ thermal data on $W\le 8$ cylinders and $W\le 10$ open strips, respectively. We extract an exponential divergence versus $T$ of the structure factor $S\left(M\right)$, as well as the correlation length $\xi$, at the ordering wave vector $M=(\pi ,\pi )$, which represents the renormalized classical behavior and can be observed over a narrow but appreciable temperature window, by analyzing the finite-size data by XTRG simulations. For the QIM with a finite-temperature phase transition, we employ several thermal quantities, including the specific heat, Binder ratio, as well as the MPO entanglement to determine the critical temperature $T_c$.

We study the zero-temperature many-body properties of twisted bilayer graphene with a twist angle equal to the so-called “first magic angle.” The system low-energy single-electron spectrum consists of four (eight, if spin label is accounted) weakly dispersing partially degenerate bands, each band accommodating one electron per Moiré cell per spin projection. This weak dispersion makes electrons particularly susceptible to the effects of interactions. Introducing several excitonic order parameters with spin-density-wave-like structure, we demonstrate that (i) the band degeneracy is partially lifted by the interaction and (ii) the details of the low-energy spectrum become doping dependent. For example, at or near the undoped state, interactions separate the eight bands into two quartets (one quartet is almost filled; the other is almost empty), while for two electrons per Moiré cell, the quartets are pulled apart, and doublets emerge. When the doping is equal to one or three electrons per cell, the doublets split into singlets. Hole doping produces similar effects. As a result, electronic properties (e.g., the density of states at the Fermi energy) demonstrate oscillating dependence on the doping concentration. This allows us to reproduce qualitatively the behavior of the conductance observed recently in experiments [Cao et al., Nature (London) 556, 80 (2018)]. Near half-filling, the electronic spectrum loses hexagonal symmetry indicating the appearance of a many-body nematic state.

We extend the notion of the eigenstate thermalization hypothesis (ETH) to open quantum systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation. We present evidence that the eigenstates of nonequilibrium steady-state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is nonintegrable, just as eigenstates of Gibbs density matrices are conjectured to do in equilibrium. This generalized ETH, which we call NESS ETH, can be used to obtain representative pure states that reproduce the expectation values of few-body operators in the NESS. The density matrices of these representative pure states can be further interpreted as weak solutions of the GKLS master equation. Additionally, we explore the validity and breakdown of NESS-ETH in the presence of symmetries, integrability, and many-body localization in the bulk Hamiltonian.

We theoretically study the diamagnetic levitation and the thermal driven motion of graphite. Using the quantum mechanically derived magnetic susceptibility, we compute the equilibrium position of levitating graphite over a periodic arrangement of magnets, and investigate the dependence of the levitation height on the susceptibility and the geometry. We find that the levitation height is maximized at a certain period of the magnets, and the maximum height is then linearly proportional to the susceptibility of the levitating object. We compare the ordinary AB-stacked graphite and a randomly stacked graphite, and show that the latter exhibits a large levitation length particularly in low temperatures, because its diamagnetism is inversely proportional to the temperature. Finally, we demonstrate that the temperature gradient moves the levitating object towards the high-temperature side, and estimate the generated force as a function of susceptibility.

Structure searches of beryllium chalcogenides (BeS, BeSe, and BeTe) at high pressures using a swarm intelligence algorithm, in conjunction with density functional theory, reveal modulated polymorphs, unusual for such simple binary compounds. Apart from the well-known cubic (space group $F\overline{4}3m$, zinc-blende structure) to hexagonal closed-packed (space group $P{6}_3/mmc$, nickel-arsenide structure) structural transition, a further transition at higher pressure to an orthorhombic structure is predicted for BeS and BeSe. The orthorhombic phase is space group Cmca in BeS and Pnma before finally adopting Cmca in BeSe, each accompanied by the onset of modulation of the atomic arrangement. The amplitude of displacements associated with the modulation increases with increasing pressure and molecular dynamics simulations show the modulated structure to become stable at least to 300 GPa and 2000 K. This unusual structural modulation is not seen, however, in BeTe, which instead transforms to a $C2/m$ phase. Links are drawn between the modulated phases of BeS and BeSe and the high-pressure modulated phases of their parent chalcogens. Our results provide key insights into understanding the modulation in binary compounds at high pressure.

We investigate the migration mechanism of the carbon vacancy $\left(V_{\text{C}}\right)$ in silicon carbide (SiC) using a combination of theoretical and experimental methodologies. The $V_{\text{C}}$, commonly present even in state-of-the-art epitaxial SiC material, is known to be a carrier lifetime killer and therefore strongly detrimental to device performance. The desire for $V_{\text{C}}$ removal has prompted extensive investigations involving its stability and reactivity. Despite suggestions from theory that $V_{\text{C}}$ migrates exclusively on the C sublattice via vacancy-atom exchange, experimental support for such a picture is still unavailable. Moreover, the existence of two inequivalent locations for the vacancy in 4H-SiC [hexagonal, $V_{\text{C}}\left(h\right)$, and pseudocubic, $V_{\text{C}}\left(k\right)]$ and their consequences for $V_{\text{C}}$ migration have not been considered so far. The first part of the paper presents a theoretical study of $V_{\text{C}}$ migration in 3C- and 4H-SiC. We employ a combination of nudged elastic band (NEB) and dimer methods to identify the migration mechanisms, transition state geometries, and respective energy barriers for $V_{\text{C}}$ migration. In 3C-SiC, $V_{\text{C}}$ is found to migrate with an activation energy of $E_{\text{A}}=4.0$ eV. In 4H-SiC, on the other hand, we anticipate that $V_{\text{C}}$ migration is both anisotropic and basal-plane selective. The consequence of these effects is a slower diffusivity along the axial direction, with a predicted activation energy of $E_{\text{A}}=4.2$ eV, and a striking preference for basal migration within the $h$ plane with a barrier of $E_{\text{A}}=3.7$ eV, to the detriment of the $k$-basal plane. Both effects are rationalized in terms of coordination and bond angle changes near the transition state. In the second part, we provide experimental data that corroborates the above theoretical picture. Anisotropic migration of $V_{\text{C}}$ in 4H-SiC is demonstrated by deep level transient spectroscopy (DLTS) depth profiling of the ${\mathrm{Z}}_{1/2}$ electron trap in annealed samples that were subject to ion implantation. Activation energies of $E_{\text{A}}=(4.4\pm 0.3)$ eV and $E_{\text{A}}=(3.6\pm 0.3)$ eV were found for $V_{\text{C}}$ migration along the $c$ and $a$ directions, respectively, in excellent agreement with the analogous theoretical values. The corresponding prefactors of $D_0=0.54{\mathrm{cm}}^2/\mathrm{s}$ and 0.$017{\mathrm{cm}}^2/\mathrm{s}$ are in line with a simple jump process, as expected for a primary vacancy point defect.

Structural and magnetic transitions in the distorted inverse trirutile $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ have been studied between 1.5 and 300 K using magnetization, dielectric permittivity, and specific heat measurements combined with synchrotron x-ray- and neutron-diffraction techniques on polycrystalline samples. A first-order structural transition, strongly hysteretic, occurs progressively over a large temperature span and is characterized by a broad maximum peaking at 53 K in the specific heat data. This structural transition is followed by two antiferromagnetic transitions, to commensurate and incommensurate magnetic orders, at 48 and 26 K, respectively. This succession of structural and magnetic transitions is interpreted as originating from a delicate balance between Jahn-Teller distortion of $\mathrm{Mn}{\mathrm{O}}_6$ octahedra, rigid $\mathrm{Te}{\mathrm{O}}_6$ units, and their consequences on orbital and spin orderings.

The bulk Rashba semiconductors $\mathrm{BiTe}X$ ($X=\mathrm{I},\mathrm{Cl}$, and Br) with intrinsically enhanced Rashba spin-orbit coupling provide a new platform for investigation of spintronic and magnetic phenomena in materials. We theoretically investigate the interlayer exchange interaction between two ferromagnets deposited on opposite surfaces of a bulk Rashba semiconductor BiTeI in its trivial and topological insulator phases. In the trivial phase BiTeI, we find that for ferromagnets with a magnetization orthogonal to the interface, the exchange coupling is reminiscent of that of a conventional three-dimensional metal. Remarkably, ferromagnets with a magnetization parallel to the interface display a magnetic exchange qualitatively different from that of conventional three-dimensional metal due to the spin-orbit coupling. In this case, the interlayer exchange interaction acquires two periods of oscillations and decays as the inverse of the thickness of the BiTeI layer. For topological BiTeI, the magnetic exchange interaction becomes mediated only by the helical surface states and acts between the one-dimensional spin chains at the edges of the sample. The surface-state-mediated interlayer exchange interaction allows for the coupling of ferromagnets with noncollinear magnetization and displays a decay power different from that of trivial BiTeI, allowing the detection of the topological phase transition in this material. Our work provides insights into the magnetic properties of these newly discovered materials and their possible functionalization.

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Néel order is included as a special case. Close to half filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasiparticle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest- and next-to-nearest-neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side and smaller for electron doping. Hence, in the hole-doped regime near half filling, the ground-state pairing gap sets the scale for the Kosterlitz-Thouless temperature $T_c^{\mathrm{KT}}$, while in the slightly electron-doped regime, $T_c^{\mathrm{KT}}$ is determined essentially by the ground-state phase stiffness.

In a process called parametric down-conversion, a dc-biased Josephson junction coupled to two microwave resonators emits photon pairs when the Josephson frequency matches the sum of the two resonance frequencies. Recent experiments have shown that such a setup permits analyzing the correlation of the radiation. Motivated by these results, we study theoretically the full counting statistics of a nondegenerate parametric oscillator below the threshold of instability. Furthermore, we analyze the second-order coherences of the radiation and discuss thermal effects on the radiation statistics. We provide results for the driving strength at which the Cauchy-Schwarz inequality is most strongly violated. Additionally, we study the impact of asymmetry in the linewidth of the modes—a distinctive property of the nondegenerate resonance effect. In particular, we find that the radiation from the mode with the larger linewidth preferably takes the total detuning, while the other mode emits photons at its resonance frequency.

Magnetic excitations and magnetic structure of ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$ were investigated by inelastic neutron scattering (INS), neutron diffraction, and random phase approximation (RPA) calculations. Below the superconducting transition temperature $T_{\text{c}}=36.5$ K, the INS spectra exhibit the neutron spin resonances at $Q_{\text{res}}=1.27\left(2\right)$ and $1.79\left(3\right){\AA }^{-1}$. They correspond to the $\mathbf{Q}=(0.5,0.5,1)$ and (0.5,0.5,3) nesting wave vectors, showing three-dimensional nature of the band structure. The characteristic energy of the neutron spin resonance is $E_{\text{res}}=17.7\left(3\right)$ meV corresponding to $5.7\left(1\right)k_{\text{B}}{T}_{\text{c}}$. Observation of the neutron spin resonance mode and our RPA calculations in conjunction with the recent optical conductivity measurements are indicative of the $s_{\pm }$ superconducting pairing symmetry in ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$. In addition to the neutron spin resonance mode, upon decreasing temperature below the magnetic transition temperature $T_{\text{N}}=15$ K, the spin wave excitation originating in the long-range magnetic order of the Eu sublattice was observed in the low-energy inelastic channel. Single-crystal neutron diffraction measurements demonstrate that the magnetic propagation vector of the Eu sublattice is $\mathbf{k}=(0,0,0.25)$, representing the three-dimensional antiferromagnetic order. Linear spin wave calculations assuming the obtained magnetic structure with the intra- and interplane nearest neighbor exchange couplings of $J_1/k_{\text{B}}=-1.31$ K and $J_c/k_{\text{B}}=0.08$ K can reproduce quantitatively the observed spin wave excitation. Our results show that superconductivity and long-range magnetic order of Eu coexist in ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$, whereas the coupling between them is rather weak.

We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kilohertz. We demonstrate that the pair breaking is caused by the backaction of the single-electron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time.

The behavior of H isotopes in crystals is a fundamental and recurrent theme in materials physics. Especially, the information on H diffusion over a wide temperature range provides a critical insight into the quantum mechanical nature of the subject; however, this is not yet fully explored. From state-of-the-art ab initio calculations to treat both electrons and nuclei quantum mechanically, we found that the temperature dependence of H isotope diffusivities in face-centered-cubic (fcc) Pd has an unconventional “reversed S” shape on Arrhenius plots. Such irregular behavior is ascribed to the competition between different nuclear quantum effects with different temperature and mass dependencies, which leads to a peculiar situation, where the heavier tritium (${}^3\mathrm{H}$) diffuses faster than the lighter protium (${}^1\mathrm{H}$) in the limited temperature range of 80–400 K. This unveils the mechanism of anomalous crossovers between the normal and reversed isotope effects observed in the experiments at high and low temperatures.

We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature-dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\times 10$ speedup on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make predictions on the thermodynamics of substoichiometric ${\mathrm{ZrC}}_x$, including vacancy concentration and heat capacity.

We theoretically investigate the dynamics of atomic domain walls (DWs) in antiferromagnets driven by a spin-orbit field. For a DW with a width of a few lattice constants, we identify a Peierls-like pinning effect, with the depinning field exponentially decaying with the DW width, so that a spin-orbit field moderately larger than the threshold can drive the propagation of an atomic DW in a stepwise manner. For a broad DW, the Peierls pinning is negligibly small. However, the external spin-orbit field can induce a fast DW propagation, accompanied by a significant shrinking of its width down to atomic scales. Before stepping into the pinning region, noticeable spin waves are emitted at the tail of the DW. The spin-wave emission event not only broadens the effective width of the DW but also pushes the DW velocity over the magnonic barrier, which is generally believed to be the relativistic limit of the DW speed. While the existing dynamic theory based on the continuum approximation fails in the atomic scale, we develop an energy conversion theory to interpret the DW dynamics beyond the relativistic limit.

In the cubic chiral magnet ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ a metastable state comprising topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating that surface pinning plays a crucial role. Increasing the magnetic field allows an increasing number of skyrmions to overcome the potential barrier and hence to transform into the ground state. Most notably, we find that the unwinding of individual skyrmions may be triggered by the magnetic tip sample interaction itself, however, only when its magnetization is aligned parallel to the external field. This implies that the stray field of the tip is key for locally overcoming the topological protection. Both the control of the position of topologically nontrivial states and their creation and annihilation on demand pose important challenges in the context of potential skyrmionic applications.

${\mathrm{Mn}}_5{\mathrm{Si}}_3$ crystallizes in hexagonal ${\mathrm{D}8}_8$ type structure (space group $P{6}_3/mcm$) with two distinct crystallographic sites for Mn atoms. It undergoes two first-order phase transitions during cooling from paramagnetic to collinear antiferromagnetic phase around 100 K and subsequently to noncollinear antiferromagnetic phase around 66 K. Detailed investigation by dc magnetic measurements probe the presence of inverted hysteresis loop below 66 K. In addition, thermomagnetic and field-induced arrest are the two key features of this alloy. Such arrest of high temperature phase plays the pivotal role toward the observation of inverted hysteresis loop behavior. The robustness of the arrested states was checked by magnetic relaxation measurements.

The superconducting current has been observed in mesa-heterostructures Nb/$\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$/$\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_x$ with a $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$ interlayer having strong spin-orbit interaction. The superconducting critical current density $j_C\approx 0.3\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$ for $d=7$ nm was registered at $T=4.2\mathrm{K}$. Magnetic-field dependence of superconducting critical current $I_C\left(H\right)$ showed a sharp central peak and minor oscillating behavior for sidelobes indicated the absence of pinholes. Integer and fractional Shapiro steps were observed at voltages $V_{m,n}=\left(m/n\right)\left(h/2e\right)f_e$ under microwave radiation at frequencies $f_e=38$ GHz and $f_e=50$ GHz. Fractional Shapiro steps ($m/n=1/2$, 3/2) point on the presence of the second harmonic in the superconducting current-phase relation. The zero-bias conductance peak was observed hinting on existence of low-energy states at $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$/$\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_x$ interface at temperatures higher than the superconducting critical temperature of Nb.

Motivated by the recently discovered time-reversal symmetry-breaking superconductivity in the epitaxial Bi/Ni bilayer system with transition temperature $T_c\approx 4.2\mathrm{K}$ and the observation of a zero-bias anomaly in a background of gap-filling states in tunneling measurements, we show that gap-filling states can appear in the fully gapped $d_{xy}\pm i{d}_{x^2-y^2}$ superconducting states. We consider a model of helical electron states with $d$-wave pairing. In particular, we show that both magnetic and nonmagnetic impurities can create states within the superconducting gap. Alternatively, we show that the coupling of the electron spins to the in-plane Zeeman field provided by nickel can also create gap-filling states by producing Bogoliubov Fermi surfaces.