Based on the recently established parafermionic matrix product states, we study the classification of one-dimensional gapped phases of parafermions with time-reversal (TR) symmetry satisfying $T^2=1$. Without extra symmetry, it has been found that ${\mathbb{Z}}_p$ parafermionic gapped phases can be classified as topological phases, spontaneous symmetry breaking (SSB) phases, and a trivial phase, which are uniquely labeled by the divisors $n$ of $p$. In the presence of TR symmetry, however, the enriched classification is characterized by three indices $n$, $\kappa$, and $\mu$, where $\kappa \in {\mathbb{Z}}_2$ denotes the linear or projective TR actions on the edges, and $\mu \in {\mathbb{Z}}_2$ indicates the commutation relations between the TR and (fractionalized) charge operator. For the ${\mathbb{Z}}_r$-symmetric parafermionic ground states, where $r=p$ for trivial or topological phases, and $r=p/n$ for SSB phases, each original gapped phase with odd $r$ is divided into two phases, while each phase with even $r$ is further separated into four phases. The gapped parafermionic phases with the TR symmetry include the symmetry protected topological phases, symmetry enriched topological phases, and the SSB coexisting symmetry protected topological phases. From analyzing the structures and symmetries of their reduced density matrices of these resulting topological phases, we can obtain the topologically protected degeneracies of their entanglement spectra.

We investigate the electronic and optical properties of twisted bilayer graphene with arbitrary twist angles $\theta$. Our results are based on a method of evolving in time quantum states in lattice space. We propose an efficient scheme of sampling lattice nodes that helps to reduce significantly computational cost, particularly for tiny twist angles. We demonstrate the continuous variation of the density of states and the optical conductivity with respect to the twist angle. It indicates that the commensurability between the two graphene layers does not play an essential role in governing the electronic and optical properties. We point out that, for the twist angles roughly in the range $0.1^{\circ }<\theta <3^{\circ }$, the density of states in the vicinity of the Fermi energy exhibits the typical W shape with a small peak locating at the Fermi energy. This peak is formed as the merging of two van Hove peaks and reflects the appearance of states strongly localized in the AA-like region of moiré zones. When decreasing the twist angle to zero, the W shape is gradually transformed to the U shape, which is seen as the behavior of the density of states in the limit of $\theta \to 0^{\circ }$.

Electron spins in a two-dimensional electron gas can be manipulated by spin-orbit (SO) fields originating from either Rashba or Dresselhaus interactions with independent isotropic characteristics. Together, though, they produce anisotropic SO fields with consequences on quantum transport through spin interference. Here we study the transport properties of modeled mesoscopic rings subject to Rashba and Dresselhaus [001] SO couplings in the presence of an additional in-plane Zeeman field acting as a probe. By means of one- and two-dimensional quantum transport simulations we show that this setting presents anisotropies in the quantum resistance as a function of the Zeeman field direction. Moreover, the anisotropic resistance can be tuned by the Rashba strength up to the point to invert its response to the Zeeman field. We also find that a topological transition in the field texture that is associated with a geometric phase switching is imprinted in the anisotropy pattern. We conclude that resistance anisotropy measurements can reveal signatures of SO textures and geometric phases in spin carriers.

Starting from the simplified linear combination of atomic orbitals method in combination with first-principles calculations, we construct a tight-binding (TB) model in the two-centre approximation for borophene and hydrogenated borophene (borophane). The Slater and Koster approach is applied to calculate the TB Hamiltonian of these systems. We obtain expressions for the Hamiltonian and overlap matrix elements between different orbitals for the different atoms and present the SK coefficients in a nonorthogonal basis set. An anisotropic Dirac cone is found in the band structure of borophane. We derive a Dirac low-energy Hamiltonian and compare the Fermi velocities with that of graphene.

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nanomechanical lattices in the classical regime, i.e., essentially “masses and springs.” We show that the thermal conductance factorizes into topological and nontopological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.

We study the linear polarization properties of the photoluminescence of ensembles of neutral and negatively charged nitrogen vacancies and neutral vacancies in diamond crystals as a function of their symmetry and their response to strong external magnetic fields. The linear polarization degree, which exceeds 10% at room temperature, and rotation of the polarization plane of their zero-phonon lines significantly depend on the crystal rotation around specific axes demonstrating anisotropic angular evolutions. The sign of the polarization plane rotation is changed periodically through the crystal rotation, which indicates a switching between electron excited states of orthogonal linear polarizations. At external magnetic fields of up to 10 T, the angular dependencies of the linear polarization degree experience a remarkable phase shift. Moreover, the rotation of the linear polarization plane increases linearly with rising magnetic field at 6 K and room temperature, for the negatively charged nitrogen vacancies, which is attributed to magneto-optical Faraday rotation.

The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson's equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed.

Modeling the behavior of materials composed of elements with different bonding and electronic structure character for large spatial and temporal scales and over a large compositional range is a challenging problem. Cases in point are amorphous alloys of Si, a prototypical covalent material, and Li, a prototypical metal, which are being considered as anodes for high-energy-density batteries. To address this challenge, we develop a methodology based on neural networks that extends the conventional training approach to incorporate pre-trained parts that capture the character of different components, into the overall network; we refer to this model as the “implanted neural network” method. We show that this approach works well for the Si-Li amorphous alloys for a wide range of compositions, giving good results for key quantities like the diffusion coefficients. The method is readily generalizable to more complicated situations that involve two or more different elements.

In a ferroelectric field effect transistor (FeFET), it is generally assumed that the ferroelectric gate plays a purely electrostatic role. Recently it has been shown that in some cases, which could be called “active FeFETs,” electronic states in the ferroelectric contribute to the device conductance as the result of a modulation doping effect in which carriers are transferred from the channel into the ferroelectric layers near the interface. Here we report first-principles calculations and model analysis to elucidate the various aspects of this mechanism and to provide guidance in materials choices and interface termination for optimizing the on-off ratio, using $\mathrm{BaTi}{\mathrm{O}}_3/n-\mathrm{SrTi}{\mathrm{O}}_3$ (electron-doped $\mathrm{SrTi}{\mathrm{O}}_3$) and $\mathrm{PbTi}{\mathrm{O}}_3/n-\mathrm{SrTi}{\mathrm{O}}_3$ as prototypical systems. It is shown that the modulation doping is substantial in both cases, and that the electrostatic model developed in previous work can be used to predict electron transfer. This model can thus be used to suggest additional materials heterostructures for the design of active FeFETs.

We demonstrate midinfrared second-harmonic generation as a highly sensitive phonon spectroscopy technique that we exemplify using $\alpha$-quartz (${\mathrm{SiO}}_2$) as a model system. A midinfrared free-electron laser provides direct access to optical phonon resonances ranging from 350 to $1400{\mathrm{cm}}^{-1}$. While the extremely wide tunability and high peak fields of a free-electron laser promote nonlinear spectroscopic studies—complemented by simultaneous linear reflectivity measurements—azimuthal scans reveal crystallographic symmetry information of the sample. Additionally, temperature-dependent measurements show how damping rates increase, phonon modes shift spectrally and in certain cases disappear completely when approaching $T_c=846\mathrm{K}$ where quartz undergoes a structural phase transition from trigonal $\alpha$-quartz to hexagonal $\beta$-quartz, demonstrating the technique's potential for studies of phase transitions.

Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nanosystems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasilocalized phonons when appropriate. Our results, in addition to confirming a $T^5$ temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.

Spin nematic phase is a quantum magnetic phase characterized by a quadrupolar order parameter. Since the quadrupole operators are directly coupled to neither the magnetic field nor the neutron, currently, it is an important issue to develop a method for detecting the long-range spin nematic order. In this paper, we propose that electron spin resonance (ESR) measurements enable us to detect the long-range spin nematic order. We show that the frequency of the paramagnetic resonance peak in the ESR spectrum is shifted by the ferroquadrupolar order parameter together with other quantities. The ferroquadrupolar order parameter is extractable from the angular dependence of the frequency shift. In contrast, the antiferroquadrupolar order parameter is usually invisible in the frequency shift. Instead, the long-range antiferroquadrupolar order yields a characteristic resonance peak in the ESR spectrum, which we call a magnon-pair resonance peak. This resonance corresponds to the excitation of the bound magnon pair at the wave vector $\mathit{k}=\mathit{0}$. Reflecting the condensation of bound magnon pairs, the field dependence of the magnon-pair resonance frequency shows a singular upturn at the saturation field. Moreover, the intensity of the magnon-pair resonance peak shows a characteristic angular dependence and it vanishes when the magnetic field is parallel to one of the axes that diagonalize the weak anisotropic interactions. We confirm these general properties of the magnon-pair resonance peak in the spin nematic phase by studying an $S=1$ bilinear-biquadratic model on the square lattice in the linear flavor-wave approximation. In addition, we argue applications to the $S=\frac{1}{2}$ frustrated ferromagnets and also the $S=\frac{1}{2}$ orthogonal dimer spin system ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$, both of which are candidate materials of spin nematics. Our theory for the antiferroquadrupolar ordered phase is consistent with many features of the magnon-pair resonance peak experimentally observed in the low-magnetization regime of ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$.

Shot noise reveals spin dependent transport properties in a magnetic tunnel junction. We report measurement of shot noise in CoFeB/MgO/CoFeB/MgO/CoFeB double barrier magnetic tunnel junctions, which shows a strong temperature dependence. The Fano factor used to characterize shot noise increases with decreasing temperature. A sequential tunneling model can be used to account for these results, in which a larger Fano factor results from larger spin relaxation length at lower temperatures.

Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the $\overline{\mathrm{M}}$ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{M}}$ direction order of ten free electron masses and light effective mass in the $\overline{\mathrm{M}}\text{−}\overline{\mathrm{K}}$ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the $\overline{\mathrm{M}}$ point.

Nonlinear isolators have attracted significant attention for their ability to break reciprocity and provide isolation without the need of an external bias. A popular approach for the design of such devices is based on Fano resonators, which, due to their sharp frequency response, can lead to very large isolation for moderate input intensities. Here, we show that, independent of their specific implementation, these devices are subject to fundamental bounds on the transmission coefficient in the forward direction versus their quality factor, input power, and nonreciprocal intensity range. Our analysis quantifies a general tradeoff between forward transmission and these metrics, stemming directly from time-reversal symmetry, and that unitary transmission is only possible for vanishing nonreciprocity. Our results also shed light on the operation of resonant nonlinear isolators, reveal their fundamental limitations, and provide indications on how it is possible to design nonlinear isolators with optimal performance.

We investigated the lock-in transition of charge density waves (CDWs) in quasi-one-dimensional conductors, based on McMillan's free energy. The higher-order umklapp terms play an essential role in this study. McMillan's theory was extended by Nakanishi and Shiba to treat multiple CDW vectors. Although their theories were aimed at understanding CDWs in quasi-two-dimensional conductors, we applied them to the quasi-one-dimensional conductors, including ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_3, {\mathrm{NbSe}}_3$, and $m-{\mathrm{TaS}}_3$, and confirmed its validity for these cases. Then we discussed our previous experimental result of $o-{\mathrm{TaS}}_3$, which revealed the coexistence of commensurate and incommensurate states. We found that the coexistence of multiple CDW vectors is essential for the lock-in transition to occur in $o-{\mathrm{TaS}}_3$. The even- and odd-order terms in the free energy play roles for amplitude development and phase modulation, respectively. Moreover, consideration of the condition of being commensurate CDWs allowed us to relate it with that of the weak localization in random media.

The electron affinity and surface states are of utmost importance for designing the potential landscape within (heterojunction) nanowires and hence for tuning conductivity and carrier lifetimes. Therefore, we determined for stoichiometric nonpolar $\mathrm{GaN}\left(10\overline{1}0\right)$ $m$-plane facets, i.e., the dominating sidewalls of GaN nanowires, the electron affinity to $4.06\pm 0.07\mathrm{eV}$ and the energy of the empty Ga-derived surface state in the band gap to $0.99\pm 0.08\mathrm{eV}$ below the conduction band minimum using scanning tunneling spectroscopy. These values imply that the potential landscape within GaN nanowires is defined by a surface state-induced Fermi-level pinning, creating an upward band bending at the sidewall facets, which provides an electronic passivation.

We explore the impact of strain on charge carrier mobility of monolayer $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-P, the four well-known atomically thin allotropes of phosphorus, using density functional theory. Owing to the highly anisotropic band dispersion, the charge carrier mobility of the pristine allotropes is significantly higher (more than 5 times in some cases) in one of the principal directions (zigzag or armchair) compared to the other. Uniaxial strain (up to 6% compressive/tensile) leads to band gap alteration in each of the allotropes, especially a direct to indirect band gap semiconductor transition in $\gamma$-P and a complete closure of the band gap in $\gamma$- and $\delta$-P. We find that the charge carrier mobility is enhanced typically by a factor of ∼5–10 in all the allotropes due to uniaxial strain; notably, among them an ∼250 (30) times increase of the hole (electron) mobility along the armchair (zigzag) direction is observed in $\beta$-P ($\gamma$-P) under a compressive strain, acting in the armchair direction. Interestingly, the preferred electronic conduction direction can also be changed in the case of $\alpha$- and $\gamma$-P by applying strain.

Conventional wisdom has long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave function. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. While the dissipationless viscosity is the Chern-Simons field counterpart for the Wigner crystal, the Berry curvature is a feature not presented in the conventional composite fermion theory. Hence, contrary to general belief, composite particles follow the more general Sundaram-Niu dynamics instead of the ordinary Newtonian one. We show that the presence of the Berry curvature is an inevitable feature for a dynamics conforming to the dipole picture of composite particles and Kohn's theorem. Based on the dynamics, we determine the dispersions of magnetophonon excitations numerically. We find an emergent magnetoroton mode which signifies the composite-particle nature of the Wigner crystal. It occurs at frequencies much lower than the magnetic cyclotron frequency and has a vanishing oscillator strength in the long-wavelength limit.

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015)], we introduced the “fluctuation diagnostics” approach to extract the dominant wave-vector-dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes to render its connection with resonance valence bond (RVB) fluctuations more transparent. Second, by using a large-$U$ expansion, where $U$ is the Coulomb interaction, we relate the fluctuations to real-space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity, and RVB-like real-space correlations, broadening the analysis of an earlier work [J. Merino and O. Gunnarsson, Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent $\mathbf{K}$ points at the Fermi surface. We find that as $U$ is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously, a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-type state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.