By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state, and a variational approach à la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $\alpha$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $\alpha$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out to be practically independent on $N$, allowing to identify a finite range of values of $\alpha$ where spin phase coherence is preserved also for large $N$. Then, by using matrix product state simulations, and the Mori formalism and the variational approach à la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a nonmonotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.

In the vicinity of the insulator-to-superfluid quantum phase transition in its core, a dislocation in a ${}^4\mathrm{He}$ crystal supports particle-hole excitations with arbitrary small gaps. These exotic analogs of Frenkel interstitial-vacancy pairs should manifest themselves in various threshold and thermoactivation effects. In worm algorithm simulations, we reveal the presence of corresponding small gaps via the anomalous thermoactivation behavior of particle number fluctuations, which we unambiguously associate with dislocations by the “visualization” technique. Experimentally, the related threshold and thermoactivation dependencies could be observed in the ultrasound and the microwave absorption.

We engineer a system of two strongly confined quantum dots to gain reproducible electrostatic control of the even-electron spin at zero magnetic field. Coupling the dots in a tight ring-shaped potential with two tunnel barriers, we demonstrate that an electric field can switch the electron ground state between a singlet and a triplet configuration. Comparing our experimental cotunneling spectroscopy data to a full many-body treatment of interacting electrons in a double-barrier quantum ring, we find excellent agreement in the evolution of many-body states with electric and magnetic fields. The calculations show that the singlet-triplet energy crossover, not found in conventionally coupled quantum dots, is made possible by the ring-shaped geometry of the confining potential.

We demonstrate the existence of a special chiral “phantom” mode with some analogy to a Goldstone mode in the anisotropic quantum $XXZ$ Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum $k_0$. The mode exists not due to symmetry principles, but results from nontrivial scattering properties of magnons with momentum $k_0$ given by the anisotropy via $cos{k}_0=\mathrm{\Delta }$. Different occupations of the phantom mode lead to energetical degeneracies between different magnetization sectors in the periodic case. This mode originates from special string-type solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots (PBRs). We derive criteria under which the spectrum contains eigenstates with PBRs, both in open and periodically closed integrable systems, for spin-$1/2$ and higher spins, and discuss the respective chiral eigenstates. The simplest of such eigenstates, the spin helix state, which is a periodically modulated state of chiral nature, is built up from the phantom excitations exclusively. Implications of our results for experiments are discussed.

The three-dimensional charge density wave (CDW) compound ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ undergoes a first-order CDW phase transition at around 200 K. An atypical CDW state is found, that is characterized by an incommensurate CDW with $\mathbf{q}=\left[0.2499\right(3),0.4843(4),0.2386(2\left)\right]$ at 60 K, and a large orthorhombic-to-triclinic lattice distortion with $\beta =91.945{\left(2\right)}^{\circ }$. We present the modulated crystal structure of the incommensurate CDW state. Structural analysis shows that the CDW resides on the zigzag chains of iridium atoms along $\mathbf{c}$. The structural distortions are completely similar between nonmagnetic ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ and previously studied isostructural magnetic ${\mathrm{Er}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ with the small differences explained by the different values of the atomic radii of Lu and Er. Such a similarity is unique to $R_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ $(R=\mathrm{rare}\mathrm{earth})$. It differs from, for example, the rare-earth CDW compounds $R_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ for which ${\mathrm{Lu}}_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ possess entirely different CDW states. We argue that the mechanism of CDW formation, thus, is different for $R_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ and $R_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$.

The existence of photonic band gap (PBG) in amorphous networks has been associated with structural short-range order and internal similarity. In this study we present amorphous networks that possess low degrees of orderness and similarity, yet still exhibit decent PBG forming ability. The robustness of PBG is found to be related to less-deviated ring distributions. We develop regional ring disorder to quantify variations of rings, revealing the complementary roles of regional ring uniformity and local similarity in PBG formation. The evolution of PBG with respect to structural deformation is also presented to elucidate the effect of regional characters on PBG formation. Our study brings new insights towards the understanding of PBG formation in amorphous structures, paving the way for novel design and manipulation of amorphous PBG materials.

We explore the emergence of spin-polarized flat bands at head-to-head domain walls (DWs) in topological insulator heterostructures with in-plane magnetization and interlayer antiferromagnetic coupling. We show in the framework of quantum well physics that, by tuning the width of a DW, one can control the functional form of the bound states appearing across it. Furthermore, we demonstrate the effect that the parity of the number of layers in a multilayer sample has on the electronic dispersion. The alignment of the magnetization vectors on the top and bottom surfaces of odd-layer samples affords particle-hole symmetry, leading to the presence of linearly dispersing topologically nontrivial states around $E=0$. By contrast, the lack of particle-hole symmetry in even-layer samples results in a gapped system, with spin-polarized flat bands appearing on either side of a band gap, with a characteristic energy well within terahertz energy scales. Such a system is a versatile platform for the development of spintronic devices and proposes one use in reconfigurable magnetic memory.

In conventional magnetometry, exchange bias training (EBT) is mostly evaluated through the major magnetization hysteresis loops (MHLs). We here report a study of EBT by using the first-order reversal curves (FORCs) in the heterostructures of ${\mathrm{SrTiO}}_3\left(001\right)/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{FeO}}_3\left(\mathrm{LSFO}\right)/{\mathrm{Ni}}_{79}{\mathrm{Fe}}_{21}\left(\mathrm{Py}\right)/{\mathrm{PyO}}_x$. It was unraveled that the training effect occurs once after exceeding the left coercivity of the first MHL, while the magnetic coupling from the ultrathin native oxide (${\mathrm{PyO}}_x$) mainly contributes to an exchange springlike behavior. Besides for the first MHL, the FORCs corresponding to the second MHL and the quasiequilibrium stage were collected, respectively, which provide a detailed picture of how the magnetization reversal evolves in the training process.

In this paper, we present a consolidated equation for all low-field transport coefficients, based on a reservoir approach developed for noninteracting quasiparticles. This formalism allows us to treat the two distinct types of charged (fermionic and bosonic) quasiparticles that can be simultaneously present, as, for example, in superconductors. Indeed, in the underdoped cuprate superconductors, these two types of carriers result in two onset temperatures with distinct features in transport: $T^{*}$, where the fermions first experience an excitation (pseudo)gap, and $T_c$, where bosonic conduction processes are dominant and often divergent. This provides the central goal of this paper, which is to address the challenges in thermoelectric transport that stem from having two characteristic temperatures as well as two types of charge carriers whose contributions can in some instances enhance each other and in others compete. We show how essential features of the cuprates (their bad-metal character and the presence of Fermi arcs) provide an explanation for the classic pseudogap onset signatures at $T^{*}$ in the longitudinal resistivity, ${\rho }_{xx}$. Based on the fits to the temperature-dependent ${\rho }_{xx}$, we present the implications for all of the other thermoelectric transport properties.

We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such two-dimensional exponentially localized—yet valley polarized—Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-site fashion. We also analyze the gap and the dispersion of single particle and single hole excitations above a strong coupling ground state at integer fillings, which we find to be dominated by the on-site and the nearest-neighbor terms of a triangular lattice hopping model, with a minimum at the center of the moiré Brillouin zone. Finally, we use the insight gained from this real-space description to understand the dependence of the gap and the effective mass on the range of the screened Coulomb interaction.

Angle disorder is an intrinsic feature of twisted bilayer graphene and other moiré materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-Büttiker transmission through an angle disorder barrier with a width comparable to the moiré period, using a decimation technique based on a real-space description. We find that barriers which separate regions where the widths of the bands differ by $50\%$ or more lead to a minor suppression of the transmission and that the transmission is close to 1 for normal incidence, which is reminiscent of Klein tunneling. These results suggest that transport in twisted bilayer graphene is weakly affected by twist angle disorder.

Magnetic impurities deposited on topological superconductor candidate ${\mathrm{PbTaSe}}_2$ can introduce a nonsplitting zero-energy state inside the superconducting gap, which has been proposed as a field-free platform for topological zero modes. However, it is still unclear how robust the topological state in ${\mathrm{PbTaSe}}_2$ is against magnetic impurities, which is related to the topological nature of the zero-energy state as well as its potential for quantum computation. In this paper, we use scanning tunneling microscopy to study the topological surface state in the normal state of ${\mathrm{PbTaSe}}_2$ under the perturbation of magnetic impurities. We visualize the quasiparticle interference (QPI) arising from the topological surface state. We then deposit Fe impurities on the surface to form atomic Fe adatoms. We find that each Fe adatom sits at a unique interstitial position on the surface and features a local state at high energies, both of which are consistent with our first-principles calculation that further reveals its large magnetic moment. Our systematic Fe deposition and subsequent measurements show that the arclike QPI pattern at the Fermi energy is robust with up to 3% Fe coverage where the atomic nature of Fe adatoms still holds. Our results provide evidence that the topological surface state at the Fermi energy in ${\mathrm{PbTaSe}}_2$ is robust against dilute magnetic impurities.

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic $d$-dimensional lattice Hamiltonian for which fermion-number conservation is broken down to the conservation of fermion parity. We show that when the internal symmetry group $G_f^{}$ is realized locally (in a repeat unit cell of the lattice) by a nontrivial projective representation, then the ground state cannot be simultaneously nondegenerate, symmetric (with respect to lattice translations and $G_f^{}$), and gapped. We also show that when the repeat unit cell hosts an odd number of Majorana degrees of freedom and the cardinality of the lattice is even, then the ground state cannot be simultaneously nondegenerate, gapped, and translation symmetric.

Hydrodynamic flow of charge carriers in graphene is an energy flow unlike the usual mass flow in conventional fluids. In neutral graphene, the energy flow is decoupled from the electric current, making it difficult to observe the hydrodynamic effects and measure the viscosity of the electronic fluid by means of electric current measurements. In particular, we show that the hallmark Poiseuille flow in a narrow channel cannot be driven by the electric field irrespective of boundary conditions at the channel edges. Nevertheless, one can observe nonuniform current densities similarly to the case of the well-known ballistic-diffusive crossover. The standard diffusive behavior with the uniform current density across the channel is achieved under the assumptions of specular scattering on the channel boundaries. This flow can also be made nonuniform by applying weak magnetic fields. In this case, the curvature of the current density profile is determined by the quasiparticle recombination processes dominated by the disorder-assisted electron-phonon scattering—the so-called supercollisions.

The potential energy surface (PES) of interlayer interaction of twisted bilayer graphene with vacancies in one of the layers is investigated via density functional theory (DFT) calculations with van der Waals corrections. These calculations give a non-negligible magnitude of PES corrugation of 28 meV per vacancy and barriers for relative sliding of the layers of 7–8 meV per vacancy for the moiré pattern with coprime indices (2,1) (twist angle $21.8^{\circ }$). At the same time, using the semiempirical potential fitted to the DFT results, we confirm that twisted bilayer graphene without defects exhibits superlubricity for the same moiré pattern and the magnitude of PES corrugation for the infinite bilayer is below the calculation accuracy. Our results imply that atomic-scale defects restrict the superlubricity of two-dimensional layers and can determine static and dynamic tribological properties of these layers in a superlubric state. We also analyze computationally cheap approaches that can be used for modeling of tribological behavior of large-scale systems with defects. The adequacy of using state-of-the-art semiempirical potentials for interlayer interaction and approximations based on the first spatial Fourier harmonics for the description of interaction between graphene layers with defects is discussed.

We study the transport properties of silicene in a perpendicular magnetic field by evaluating the Hall and longitudinal conductivities and resistivities when the acoustic phonon correction to the Landau level (LL) energy is taken into account. The acoustic phonons are considered by three modes: the transverse (TA), longitudinal, and out-of-plane ones. Under the influence of the acoustic phonon correction, the quantum Hall effect plateaus occur at higher values of the magnetic field, where the TA phonon displays the strongest effect. The combined effects of the strong spin-orbit coupling in silicene, the external electric field, and the Zeeman field on the transport parameters are investigated. These combined effects lift the spin and valley degeneracy of the LLs, leading to the additional plateaus in the Hall conductivity with the sequence being found as ${\sigma }_{yx}=(4e^2/h)(n/4+1/2)$. The temperature has a significant effect on the width of the Hall conductivity plateaus. We also appraise the longitudinal conductivity ${\sigma }_{xx}$ and the Hall, ${\rho }_{xy}$, and longitudinal, ${\rho }_{xx}$, resistivities and show the difference between the present results and those for graphene as well as for silicene without the Zeeman field effect. The combined effects of the electric and Zeeman fields lead to the quadrupled peaks of ${\rho }_{xx}$ and the sequence of $(h/e^2)/(n+2)$ in the height of the plateaus in ${\rho }_{xy}$.

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS) and also the singularity of the flat-band wave function obtained by a Fourier transform of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific symmetry representation in a given lattice. Then, the singularity of FT-CLS indicates whether the resulting flat band exhibits a band crossing point or not. A tight-binding Hamiltonian with the flat band corresponding to the FT-CLS is obtained by introducing a set of basis molecular orbitals, which are orthogonal to the FT-CLS. Our construction scheme can be systematically applied to any lattice so that it provides a powerful theoretical framework to study exotic properties of both gapped and gapless flat bands arising from their wave function singularities.

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local ${\mathbb{Z}}_2$ gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional ${\mathbb{Z}}_2$ lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic $XX$ interaction while keeping the local gauge symmetry intact. We find that the ${\mathbb{Z}}_2$ topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

We present a combined experimental and theoretical study of the longitudinal and transverse thermoelectric properties of ferrimagnetic spinels $\mathrm{Cu}{\mathrm{Cr}}_2{X}_4$ ($X=\mathrm{S}$, Se, Te). The thermoelectric power of all studied phases is positive and consists of two contributions; an almost linear diffusive thermopower observed at high temperature, and a strong enhancement below $T_C$ attributed to magnon drag. The diffusive part of thermopower and resistivity decreases from $X=\mathrm{S}$ to Te, whereas the magnon drag enhancement is the biggest for $X=\mathrm{Se}$, which has also the highest $T_C$. The thermopower was calculated by DFT method using GGA, $\mathrm{GGA}+U, \mathrm{GGA}+\text{oeeHyb}$, and mBJ potentials. A good agreement with the experimental thermopower was achieved using GGA potential for $X=\mathrm{S}$ and with mBJ potential for $X=\mathrm{Te}$. The mBJ potential, which was designed for $sp$-type semiconductors, better describes the valence bands of $\mathrm{Cu}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ that exhibit stronger $sp$-orbitals character than sulfide and selenide. The anomalous Nernst effect (ANE) is negative at room temperature for all phases, the highest absolute value $\sim 1.5 \mu \mathrm{V}$/K is observed for $X=\mathrm{Te}$ and Se around room temperature, whereas ANE for $X=\mathrm{S}$ is much smaller. A sign change of ANE to positive is observed at 285 K for $X=\mathrm{S}$ and at 65 K for $X=\mathrm{Se}$. The trend of anomalous Nernst conductivity is reproduced by Berry phase calculations if the renormalization of the bands due to the strong correlation effects is taken into account.

Higher-order topological phases and real topological phases are two emerging topics in topological states of matter, which have been attracting considerable research interest. However, it remains a challenge to find realistic materials that can realize these exotic phases. Here, based on first-principles calculations and theoretical analysis, we identify graphyne, the representative of the graphyne-family carbon allotropes, as a two-dimensional (2D) second-order topological insulator and a real Chern insulator. We show that graphyne has a direct bulk band gap at the three $M$ points, forming three valleys. The bulk bands feature a double band inversion, which is characterized by the real Chern number enabled by the spacetime-inversion symmetry. The real Chern number is explicitly evaluated by both the Wilson loop method and the parity approach. We demonstrate that a nontrivial real Chern number for a 2D system dictates the existence of Dirac-type edge bands and the topological corner states. Furthermore, we find that the topological phase transition in graphyne from the real Chern insulator to a trivial insulator is mediated by a 2D Weyl semimetal phase. The robustness of the corner states against symmetry breaking and possible experimental detection methods are discussed.