It is known that there is a wide class of quasi-two-dimensional graphenelike nanomaterials which in many respects can outperform graphene. So, here in addition to graphene, the attention is directed to stanene (buckled honeycomb structure) and phosphorene (puckered honeycomb structure). It is shown that, depending on the doping, these materials can have magnetically ordered edges. Computed diagrams of magnetic phases illustrate that, on the one hand, $n$-type doped narrow zigzag nanoribbons of graphene and stanene have antiferromagnetically aligned magnetic moments between the edges. On the other hand, however, in the case of phosphorene nanoribbons the zigzag edges can have ferromagnetically aligned magnetic moments for the $p$-type doping. The edge magnetism critically influences transport properties of the nanoribbons, and if adequately controlled can make them attractive for spintronics.

The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multiband $k·p$ theory, showing the presence of nonzero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture $b^2$ as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number $Z$, as expected for valence electrons in atoms. For isolated bands, it is found that $b^2$ follows a scaling law close to $b^2\sim Z^4$. The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for $b^2$ can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.

Ab initio calculations in the framework of many-body perturbation theory (MBPT) are performed to calculate the electronic and optical properties of monolayer and bilayer blue phosphorene with different stacking configurations. It is found that the stacking configuration of bilayer blue phosphorene strongly affects the electronic band gap of the material. By solving the Bethe-Salpeter equation (BSE) on top of the $G_0{W}_0$ calculation, the binding energies, spectral positions, and band decomposition of excitons of monolayer and bilayer configurations are investigated. The most prominent two excitonic peaks of bilayers are examined in detail. Our calculations show that different stacking configurations lead to distinct interlayer interaction characteristics which lead to substantial change in the optical spectrum of bilayer blue phosphorene. Mostly intralayer and mixed interlayer excitons with quite high binding energies are obtained in bilayer blue phosphorene. Our results show that excitonic properties of ultrathin materials play an important role in tuning and improving the optoelectronic performance of two-dimensional materials.

The dynamics of chaotic systems are, by definition, exponentially sensitive to the initial conditions and may appear rather random. In this work, we establish rigorous relations between the chaotic dynamics of an observable in a dissipative system and the dynamics of information (entropy) contained in this observable, focussing on a disordered metal coupled to a dissipative, e.g., phononic, bath. The chaotic dynamics is characterized by Lyapunov exponents $\lambda$, the rates of growth of out-of-time order correlators (OTOCs), quantities of the form $\langle {[\widehat{A}\left(t\right),\widehat{B}\left(0\right)]}^2\rangle \propto exp\left(2\lambda t\right)$, where $\widehat{A}$ and $\widehat{B}$ are the operators of, e.g., the total current of electrons in a metallic quantum dot. We demonstrate that the Lyapunov exponent $\lambda$ matches, in appropriate units, the rate of decay of information stored in the observable $\langle \widehat{A}\left(t\right)\rangle$ after applying a small perturbation with a small classical uncertainty. This relation suggests a way to measure Lyapunov exponents in experiment. We compute both the Lyapunov exponent and the rate of decay of information microscopically in a disordered metal in the presence of a bosonic bath, which may, in particular, represent interactions in the system. For a sufficiently short range of the correlations in the bath, the exponent has the form $\lambda ={\lambda }_0-1/\tau$, where ${\lambda }_0$ is the (temperature-independent) Lyapunov exponent in the absence of the bath and $1/\tau$ is the inelastic scattering rate of the electrons. Our results demonstrate also the existence of a transition between chaotic and nonchaotic behavior at ${\lambda }_0=1/\tau$, which may be triggered, e.g., by changing the temperature of the bath. Also, we provide arguments for the validity of the established relation between chaos and the dynamics of information in a generic system.

In iron-based superconductors, band inversion of $d$ and $p$ orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$ and $p$ orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov–de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is found that there appear various types of Majorana fermions such as surface flat band, Majorana quartet, and Möbius twisted surface states. Our theoretical results show that iron-based superconductors are promising platforms to realize rich topological crystalline phases.

We study quench dynamics in an interacting spin chain with a quasiperiodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to $L=50$. We find that the choice of periodicity $\mathrm{\Phi }$ of the quasiperiodic field influences the dynamics. For $\mathrm{\Phi }=(\sqrt{5}-1)/2$ (the inverse golden ratio) and interaction $\mathrm{\Delta }=1$, the model most frequently considered in the literature, we obtain the critical disorder $W_c=4.8\pm 0.5$ in units where the noninteracting transition is at $W=2$. At the same time, for periodicity $\mathrm{\Phi }=\sqrt{2}/2$ we obtain a considerably higher critical value, $W_c=7.8\pm 0.5$. Finite-size effects on the critical disorder $W_c$ are much weaker than in the purely random case. This supports the enhancement of $W_c$ in the case of a purely random potential by rare “ergodic spots,” which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.

The high pressure lattice dynamics of rhombohedral antimony have been studied by a combination of diffuse scattering and inelastic x-ray scattering. The evolution of the phonon behavior as a function of pressure was analyzed by means of two theoretical approaches: density functional perturbation theory and symmetry-based phenomenological phase transition analysis. This paper focuses on the first structural phase transition, SbI-SbIV, and the role of vibrations in leading the transition. The phonon dispersion exhibits complex behavior as one approaches the structural transition, with the branches, corresponding to the two transitions happening at high pressure in the Va elements (A7-to-BCC and A7-to-PC) both showing softening.

The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disorder-temperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.

We report systematic magnetotransport measurements and ab initio calculations on single-crystalline ${\mathrm{TaP}}_2$, a member of the transition-metal dipnictides. We observed unsaturated magnetoresistance (MR) reaching ∼700% at a magnetic field ($B$) of 9 T at 2 K when $B$ is perpendicular to the electric current ($I$). We also found negative longitudinal MR ($n$-LMR) when $B$ slightly deviates from the direction of $I$ along with striking Shubnikov–de Haas (SdH) oscillations. Our analysis on the SdH oscillations uncovers three fundamental magnetic oscillation frequencies of 72, 237, and 356 T, slightly different from the theoretical calculations which reveal one hole pocket and two electron pockets at the $L$ point and one electron pocket at the $Z$ point of the Brillouin zone. The inconsistency might be due to that one Fermi pocket is out of the detection capability by our measurements. The analysis also reveals a nonzero Berry phase, indicating nontrivial band topology. The $n$-LMR could be fitted with the Adler-Bell-Jackiw chiral anomaly equation but the origin remains yet ambiguous. The ab initio calculations suggest ${\mathrm{TaP}}_2$ as a weak topological insulator with the $Z_2$ indices of (0; 111), which exhibits topological surface states on the (001) surface.

We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at “generic” incommensurate fillings, with the superconductivity being “interrupted” by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. These features are consistent with experimental observations in magic-angle twisted bilayer graphenes despite the distinct microscopic details. We further study the full phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.

We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector $\mathit{q}$) Hall conductivity of “gapped graphene” (a nontopological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosities and conductivity up to ${\mathit{q}}^2$ at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graphene, the derivation reveals a significant difference between the two systems. First of all, both the Hall viscosity and the Hall conductivity vanish when the Fermi level lies in the gap that separates the lowest Landau level in the conduction band from the highest Landau level in the valence band. It is only when the Fermi level is not in the gap that the familiar formulas of gapless graphene are recovered. Second, in the case of gapped graphene, it is not possible (at least, within our present approach) to define a single-valley Hall viscosity: this quantity diverges with a strength proportional to the magnitude of the gap. It is only when both valleys are included that the diverging terms, having opposite signs in the two valleys, cancel out, and the familiar result is recovered. In contrast to this, the nonlocal Hall conductivity is finite in each valley. These results indicate that the Hoyos-Son formula [Phys. Rev. Lett. 108, 066805 (2012)] connecting the Hall viscosity to the coefficient of $q^2$ in the small-$q$ expansion of the $q$-dependent Hall conductivity cannot be applied to each valley, but only to the system as a whole. The problem of defining a “valley Hall viscosity” remains open.

Monolayer graphene under a strong perpendicular magnetic field exhibits quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry [K. Nomura and A. H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006)]. The approximate SU(4) spin/valley symmetry is broken by small lattice-scale effects in the central Landau level corresponding to filling factors $\nu =0,\pm 1$. Notably, the ground state at $\nu =0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $\nu =\pm 1,0$ by using exact diagonalizations on the spherical geometry. If we neglect anisotropies, we confirm the validity of the standard skyrmion picture generalized to four degrees of freedom. For filling factor $\nu =-1$, the hole skyrmion is an infinite-size valley skyrmion with full spin polarization because it does not feel the anisotropies. The electron skyrmion is also always of infinite size. In the F phase it is always fully polarized, while in the AF phase it undergoes continuous magnetization under increasing Zeeman energy. In the case of $\nu =0$, the skyrmion is always maximally localized in space both in F and AF phases. In the F phase it is fully polarized, while in the AF phase it has also progressive magnetization with Zeeman energy. The magnetization process is unrelated to the spatial profile of the skyrmions, contrary to the SU(2) case. In all cases, the skyrmion physics is dominated by the competition between anisotropies and Zeeman effect but not directly by the Coulomb interactions, breaking universal scaling with the ratio Zeeman to Coulomb energy.

Recently, the experimental realization of Dirac fermions in ${\beta }_{12}$- and ${\chi }_3$-boron sheets has attracted tremendous attention and simulated a broad exploration for the novel topologically nontrivial states in two-dimensional materials. Herein, by combining first-principles and tight-binding calculations, we discover a coexistence of open nodal arc and closed nodal loop produced by three-band touching in the recently synthesized $\beta$-boron sheet [Q. Zhong et al., Phys. Rev. Mater. 1, 021001 (2017)]. The symmetry analysis reveals that the nodal lines are protected by both time-reversal symmetry (TRS) and mirror-reflection symmetry (MRS). Intriguingly, when TRS is broken, e.g., via introducing magnetic proximity effect, a topological phase transition occurs, namely, the original spin-degenerate nodal line (loop) decays into fully spin-polarized nodal line (loop). Furthermore, when Rashba spin-orbit coupling (SOC) is turned on to break the MRS, spin-up and -down states are shifted toward opposite momentum directions, leading to the emergence of two new nodal loops around the $\mathrm{\Gamma }$ point. In addition, inclusion of both Rashba SOC and exchange field leads to band-gap opening of the Dirac points and nodal lines. Our findings not only reveal a form of nodal line in the $\beta$-boron sheet, but also offer an alternative approach to realize spin-polarized nodal line semimetals with promising applications in spintronic devices.

Detailed theoretical studies of the electronic structure of (InGa)(AsSb)/GaAs/GaP quantum dots are presented. This system is unique since it exhibits concurrently direct and indirect transitions both in real and momentum space and is attractive for applications in quantum information technology, showing advantages as compared to the widely studied (In,Ga)As/GaAs dots. We proceed from the inspection of the confinement potentials for $\mathbf{k}\ne 0$ and $\mathbf{k}=0$ conduction and $\mathbf{k}=0$ valence bands, through the formulation of $\mathbf{k}·\mathbf{p}$ calculations for $\mathbf{k}$-indirect transitions, up to the excitonic structure of $\mathrm{\Gamma }$ transitions. Throughout this process we compare the results obtained for dots on both GaP and GaAs substrates, enabling us to make a direct comparison to the (In,Ga)As/GaAs quantum dot system. We also discuss the realization of quantum gates.

Silicon thin film with both remarkable stability and graphenelike properties attract many research interests in materials science and condensed matter physics. In this paper, two new two-dimensional silicon allotropes (Si-Cmma and Si-Pmma) with excellent energetic stability and positive dynamical stability are proposed and investigated by first-principles calculations. Si-Pmma possesses the energy of about 203 meV/atom lower than that of silicene and it is a normal metallic phase. Si-Cmma is of about 198 meV/atom lower than silicene in energy and it is confirmed to be a nodal loop semimetallic material. Symmetry analysis reveals that the nodal loop in Si-Cmma is protected by the glide mirror and it belongs to class AI $+$ R of Altland-Zirnbauer symmetry classes. A further three-band $k·\mathrm{p}$ model is constructed to understand the formation of the nodal loop and its strong anisotropy.

Motivated by the recent observation of correlated insulator states and unconventional superconductivity in twisted bilayer graphene, we study the dependence of electron correlations on the twist angle and reveal the existence of strong correlations over a narrow range of twist angles near the magic angle. Specifically, we determine the on-site and extended Hubbard parameters of the low-energy Wannier states using an atomistic quantum-mechanical approach. The ratio of the on-site Hubbard parameter and the width of the flat bands, which is an indicator of the strength of electron correlations, depends sensitively on the screening by the semiconducting substrate and the metallic gates. Including the effect of long-ranged Coulomb interactions significantly reduces electron correlations and explains the experimentally observed sensitivity of strong-correlation phenomena on twist angles.

The pseudofermion functional renormalization group (pf-FRG) has been put forward as a semianalytical scheme that, for a given microscopic spin model, allows to discriminate whether the low-temperature states exhibit magnetic ordering or a tendency toward the formation of quantum spin liquids. However, the precise nature of the putative spin-liquid ground state has remained hard to infer from the original (single-site) pf-FRG scheme. Here, we introduce a cluster pf-FRG approach, which allows for a more stringent connection between a microscopic spin model and its low-temperature spin-liquid ground states. In particular, it allows to calculate spatially structured fermion bilinear expectation values on spatial clusters, which are formed by splitting the original lattice into several sublattices, thereby allowing for the positive identification of a family of bilinear spin-liquid states. As an application of this cluster pf-FRG approach, we consider the $J_1\text{−}{J}_2\mathrm{SU}(N)$ Heisenberg model on a square lattice, which is a paradigmatic example for a frustrated quantum magnet exhibiting quantum spin-liquid behavior for intermediate coupling strengths. In the well-established large-$N$ limit of this model, we show that our approach correctly captures the emergence of the $\pi$-flux spin-liquid state at low temperatures. For small $N$, where the precise nature of the ground state remains controversial, we focus on the widely studied case of $N=2$, for which we determine the low-temperature phase diagram near the strongly frustrated regime after implementing the fermion-number constraint by the flowing Popov-Fedotov method. Our results suggest that the $J_1\text{−}{J}_2$ Heisenberg model does not support the formation of a fermion bilinear spin-liquid state.

Variational wave functions have enabled exceptional scientific breakthroughs related to the understanding of novel phases of matter. Examples include the Bardeen-Cooper-Schrieffer theory of superconductivity, the description of the fractional quantum Hall effect through the Laughlin state, and Feynman's variational understanding of large-scale quantum effects in liquid helium. More recently, Gutzwiller-projected wave functions, typically constructed from fermionic degrees of freedom, have been employed to examine quantum spin models in the presence of competing interactions, where exotic phases with no spontaneous symmetry breaking and fractional excitations may exist. In this work, we investigate the aforementioned fermionic wave functions supplemented with neural networks, specifically with the so-called restricted Boltzmann machine (RBM), to boost their accuracy and obtain reliable approximations to the ground state of generic spin models. In particular, we apply our neural augmented fermionic construction to the description of both magnetically ordered and disordered phases of increasing complexity, including cases where the ground state displays a nontrivial sign structure. Even though the RBM state is by far more effective for Néel states endowed with a particularly simple sign structure, it provides a significant improvement over the original fermionic state in highly frustrated regimes where a complex sign structure is anticipated, thus marking the path to an understanding of strongly correlated spin models on the lattice via neural Gutzwiller-projected variational wave functions.

Although many-body localization has primarily been studied in systems with a single local degree of freedom, experimental studies of many-body localization in cold atom systems motivate exploration of the disordered Hubbard model. With two coupled local degrees of freedom, it is natural to ask how localization in spin relates to disorder in charge and vice versa. Most prior work has addressed disorder in only one of these sectors and often has not used measures of localization which distinguish between charge and spin. Here, we explore localization in the Hubbard model with a wide range of independent values of charge and spin disorder using measures of localization based on charge and spin-specific integrals of motion. Our results demonstrate symmetry between the response of the spin to charge disorder and vice versa, and we find very weak disorder in one channel, so long as the disorder in the other channel is sufficiently strong, results in localization in both channels. The strength of disorder required in the less-disordered channel declines as the system size increases. Furthermore, the weaker the disorder in the less-disordered channel, the longer the timescale at which localization appears in the dynamics of this degree of freedom.

Using first-principles calculations we have previously shown that placing graphene on a (111)-oriented perovskite $\mathrm{SrTi}{\mathrm{O}}_3$ (STO) surface provides a possible doping mechanism [D. Shin and A. A. Demkov, Phys. Rev. B 97, 075423 (2018)]. Further theoretical analysis presented here suggests that coupling of electrons in graphene to interfacial hybrid plasmon/optical modes via remote-phonon scattering may result in an effective attractive electron-electron interaction that, in turn, could lead to electron pairing and superconductivity. Specifically, we consider top-gated graphene supported by STO. Using the full dynamic polarizability within the random phase approximation for the entire system (including the hybrid modes arising from the coupling of the graphene plasmons to the optical phonons of the STO substrate and gate insulator), we estimate the superconducting transition temperature in the strong-coupling limit.