Lévy flights are random walks where the dynamics is dominated by rare events. Even though they have been studied in vastly different physical systems, their observation in a single quantum system has remained elusive. Here we analyze a periodically driven open central spin system and demonstrate theoretically that the dynamics of the spin environment exhibits Lévy flights. For the particular realization in a single-electron charged quantum dot driven by periodic resonant laser pulses, we use Monte Carlo simulations to confirm that the long waiting times between successive nuclear spin-flip events are governed by a power-law distribution; the corresponding exponent $\eta =-3/2$ can be directly measured in real time by observing the waiting time distribution of successive photon emission events. Remarkably, the dominant intrinsic limitation of the scheme arising from nuclear quadrupole coupling can be minimized by adjusting the magnetic field or by implementing spin echo.

Thin ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ single crystals laid on Scotch tape are investigated by Fourier transform infrared spectroscopy at $4\mathrm{K}$ and in a magnetic field up to $35\mathrm{T}$. The magnetotransmittance spectra of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3$/tape composite are analyzed as a stacked-slab system, and the average thickness of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ is estimated to be $6.4\pm 1.7\mu \mathrm{m}$. The optical conductivity of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ at different magnetic fields is then extracted, and we find that the magnetic field modifies the optical conductivity in the following ways: (1) Field-induced transfer of the optical weight from the lower-frequency regime $\left(<250{\mathrm{cm}}^{-1}\right)$ to the higher-frequency regime $\left(>250{\mathrm{cm}}^{-1}\right)$ due to the redistribution of charge carriers across the Fermi surface. (2) Evolving of a Fano-resonance-like spectral feature from an antiresonance to a resonance with increasing magnetic field. Such behavior can be attributed to the electron-phonon interactions between the $E_u^1$ optical phonon mode and the continuum of electronic transitions. (3) Cyclotron resonance resulting from the intervalence band Landau level transitions, which can be described by the electrodynamics of massive Dirac holes.

Common density-matrix functionals, the Müller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows us to model the bond dissociation problem and the transition from the weakly to the strongly correlated limit. Unbiased numerical calculations are combined with analytical results. Despite the well known successes of the Müller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of the Müller functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metal-like behavior. The power functional actually favors the ferromagnetic state for weak interaction. Analogous to the Hartree-Fock approximation, the power functional undergoes a transition beyond a critical interaction strength, in this case, however, to a noncollinear antiferromagnetic state.

The availability of quantitatively accurate total energies $\left(E_{\mathrm{tot}}\right)$ of atoms, molecules, and solids, enabled by the development of density functional theory (DFT), has transformed solid state physics, quantum chemistry, and materials science by allowing direct calculations of measureable quantities, such as enthalpies of formation $\left(\mathrm{\Delta }{H}_f\right)$. Still, the ability to compute $E_{\mathrm{tot}}$ and $\mathrm{\Delta }{H}_f$ values does not, necessarily, provide insights into the physical mechanisms behind their magnitudes or chemical trends. Here, we examine a large set of calculated $E_{\mathrm{tot}}$ and $\mathrm{\Delta }{H}_f$ values obtained from the DFT+$U$-based fitted elemental-phase reference energies (FERE) approach [V. Stevanović, S. Lany, X. Zhang, and A. Zunger, Phys. Rev. B 85, 115104 (2012)] to probe relationships between the $E_{\mathrm{tot}}/\mathrm{\Delta }{H}_f$ of metal-nonmetal compounds in their ground-state crystal structures and properties describing the compound compositions and their elemental constituents. From a stepwise linear regression, we develop a linear model for $E_{\mathrm{tot}}$, and consequently $\mathrm{\Delta }{H}_f$, that reproduces calculated FERE values with a mean absolute error of ∼80 meV/atom. The most significant contributions to the model include calculated total energies of the constituent elements in their reference phases (e.g., metallic iron or gas phase ${\mathrm{O}}_2$), atomic ionization energies and electron affinities, Pauling electronegativity differences, and atomic electric polarizabilities. These contributions are discussed in the context of their connection to the underlying physics. We also demonstrate that our $E_{\mathrm{tot}}/\mathrm{\Delta }{H}_f$ model can be directly extended to predict the $E_{\mathrm{tot}}$ and $\mathrm{\Delta }{H}_f$ of compounds outside the set used to develop the model.

We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid–to–Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.

Employing a recently developed many-body technique that allows for the incorporation of thermal effects, the rich phase diagram of a two-dimensional two-orbital (degenerate $d_{xz}$ and $d_{yz}$) Hubbard model is presented varying temperature and the repulsion $U$. Our main result is the finding at intermediate $U$ of an antiferromagnetic orbital selective state where an effective dimensional reduction renders one direction insulating and the other metallic. Possible realizations of this state are discussed. In addition, we also study nematicity above the Néel temperature. After a careful finite-size scaling analysis, the nematicity temperature window appears to survive in the bulk limit, although it is very narrow.

We have studied the dynamical polarization and collective excitations in an anisotropic two-dimensional system undergoing a quantum phase transition with merging of two Dirac points. Analytical results for the one-loop polarization function are obtained at the finite momentum, frequency, and chemical potential. The evolution of the plasmon dispersion across the phase transition is then analyzed within the random phase approximation. We derive analytically the long-wavelength dispersion of the undamped anisotropic collective mode and find that it evolves smoothly at the critical merging point. The effects of the van Hove singularity on the plasmon excitations are explored in detail.

We demonstrate the occurrence of spatial multistability using laterally confined microcavity exciton-polaritons. By coherently exciting with a blue detuned laser a series of confined polariton modes, we investigate the effects of multistability on the transmitted laser beam as a function of the excitation power. At each threshold of the hysteresis loop, a switching of the mode profile of the laser beam is associated with a significant energy jump of each of the confined polariton modes in the mesa. A simulation of this behavior is achieved with a multimode generalization of the Gross-Pitaevskii equations in the exciton photon basis. The mechanism behind the spatial multistability is identified as a repulsive cross interaction between polaritons in different modes.

With the goal of elucidating the nature of spin-dependent electronic transport in ferromagnetic atomic contacts, we present here a combined experimental and theoretical study of the conductance and shot noise of metallic atomic contacts made of the $3d$ ferromagnetic materials Fe, Co, and Ni. For comparison, we also present the corresponding results for the noble metal Cu. Conductance and shot noise measurements, performed using a low-temperature break-junction setup, show that in these ferromagnetic nanowires, (i) there is no conductance quantization of any kind, (ii) transport is dominated by several partially open conduction channels, even in the case of single-atom contacts, and (iii) the Fano factor of large contacts saturates to values that clearly differ from those of monovalent (nonmagnetic) metals. We rationalize these observations with the help of a theoretical approach that combines molecular dynamics simulations to describe the junction formation with nonequilibrium Green's function techniques to compute the transport properties within the Landauer-Büttiker framework. Our theoretical approach successfully reproduces all the basic experimental results and it shows that all the observations can be traced back to the fact that the $d$ bands of the minority-spin electrons play a fundamental role in the transport through ferromagnetic atomic-size contacts. These $d$ bands give rise to partially open conduction channels for any contact size, which in turn lead naturally to the different observations described above. Thus, the transport picture for these nanoscale ferromagnetic wires that emerges from the ensemble of our results is clearly at variance with the well established conduction mechanism that governs the transport in macroscopic ferromagnetic wires, where the $d$ bands are responsible for the magnetism but do not take part in the charge flow. These insights provide a fundamental framework for ferromagnetic-based spintronics at the nanoscale.

We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.

Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016)], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for nonequilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field, and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of interlead and intralead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.

The interband optical response of a three-dimensional Dirac cone is linear in photon energy $\left(\mathrm{\Omega }\right)$. Here, we study the evolution of the interband response within a model Hamiltonian which contains Dirac, Weyl, and gapped semimetal phases. In the pure Dirac case, a single linear dependence is observed, while in the Weyl phase, we find two quasilinear regions with different slopes. These regions are also distinct from the $\text{large-}\mathrm{\Omega }$ dependence. As the boundary between the Weyl (WSM) and gapped phases is approached, the slope of the $\text{low-}\mathrm{\Omega }$ response increases, while the photon-energy range over which it applies decreases. At the phase boundary, a square root behavior is obtained which is followed by a gapped response in the gapped semimetal phase. The density of states parallels these behaviors with the linear law replaced by quadratic behavior in the WSM phase and the square root dependence at the phase boundary changed to ${\left|\omega \right|}^{3/2}$. The optical spectral weight under the intraband (Drude) response at low temperature $\left(T\right)$ and/or small chemical potential $\left(\mu \right)$ is found to change from $T^2$ $\left({\mu }^2\right)$ in the WSM phase to $T^{3/2}$ $\left(\right|\mu {|}^{3/2})$ at the phase boundary.

Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both signs. Here we investigate phenomena related to localized states associated with a flat band supported by the sawtooth geometry. A localization-delocalization transition emerges in the noninteracting regime as the sign of hopping coefficient is changed. In the presence of interactions, patterns of localized states approach a uniform density distribution for repulsive interactions while interesting localized density patterns can arise in a strongly attractive regime. The density patterns indicate the underlying inhomogeneity of the simulator. Two-particle correlations can further distinguish the nature of the localized states in attractive and repulsive interaction regimes. We also survey possible experimental implementations of the simulator.

Single-layer materials represent a new materials class with properties that are potentially transformative for applications in nanoelectronics and solar-energy harvesting. With the goal of discovering novel two-dimensional (2D) materials with unusual compositions and structures, we have developed a grand-canonical evolutionary algorithm that searches the structure and composition space while constraining the thickness of the structures. Coupling the algorithm to first-principles total-energy methods, we show that this approach can successfully identify known 2D materials and find low-energy ones. We present the details of the algorithm, including suitable objective functions, and illustrate its potential with a study of the Sn-S and C-Si binary materials systems. The algorithm identifies several 2D structures of InP, recovers known 2D structures in the binary Sn-S and C-Si systems, and finds two 1D Si defects in graphene with formation energies below that of isolated substitutional Si atoms.

We present equilibrium and out-of-equilibrium studies of the Verwey transition in magnetite. In the equilibrium optical conductivity, we find a steplike change at the phase transition for photon energies below about 2 eV. The possibility of triggering a nonequilibrium transient metallic state in insulating magnetite by photo excitation was recently demonstrated by an x-ray study. Here we report a full characterization of the optical properties in the visible frequency range across the nonequilibrium phase transition. Our analysis of the spectral features is based on a detailed description of the equilibrium properties. The out-of-equilibrium optical data bear the initial electronic response associated to localized photoexcitation, the occurrence of phase separation, and the transition to a transient metallic phase for excitation density larger than a critical value. This allows us to identify the electronic nature of the transient state, to unveil the phase transition dynamics, and to study the consequences of phase separation on the reflectivity, suggesting a spectroscopic feature that may be generally linked to out-of-equilibrium phase separation.

The magnetic structure of the double perovskite compound ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$ was determined from neutron powder diffraction data. This material is magnetically described as an $S=1/2$ quasi-two-dimensional square-lattice Heisenberg model with antiferromagnetic nearest-neighbor and next-nearest-neighbor interactions. ${\mathrm{Sr}}_2{\mathrm{CuTeO}}_6$ undergoes a magnetic phase transition at $T_{\mathrm{N}}\simeq 29$ K. The spin structure below $T_{\mathrm{N}}$ is Néel antiferromagnetic on the square lattice, which means that the nearest-neighbor interaction $\left(J_1\right)$ is stronger than the next-nearest-neighbor interaction $\left(J_2\right)$, in contrast to other isostructural compounds such as ${\mathrm{Ba}}_2{\mathrm{CuWO}}_6$ and ${\mathrm{Sr}}_2{\mathrm{CuWO}}_6$, for which $|J_1|<|J_2|$ is realized.

The influence of the antiferromagnetic (AFM) spin structure of epitaxial ${\mathrm{Ni}}_{0.4}{\mathrm{Mn}}_{0.6}$ films on the magnetic properties of adjacent out-of-plane-magnetized ferromagnetic (FM) Ni layers in $\text{Ni}/{\mathrm{Ni}}_{0.4}{\mathrm{Mn}}_{0.6}/\text{Ni}$ trilayers on Cu(001) is investigated by magneto-optical Kerr-effect experiments. An AFM interlayer coupling between the two FM layers, which emerges below the AFM ordering temperature for an odd number of atomic layers of the antiferromagnet, suddenly disappears at a lower, AFM-thickness-dependent transition temperature. For even numbers of atomic layers of the antiferromagnet, a maximum of the coercivity is observed at a corresponding temperature. This result is interpreted as a transition of the AFM spin structure of the ${\mathrm{Ni}}_{0.4}{\mathrm{Mn}}_{0.6}$ layer that strongly affects the interlayer exchange coupling of the two FM layers by direct exchange through the AFM layer.

Single-layer transition metal dichalcogenides exhibit a variety of atomic structures and associated exotic electronic and magnetic properties. Density-functional calculations using the LDA+$U$ approximation show that single-layer ${\mathrm{VS}}_2$ is a strongly correlated material, where the stability, phonon spectra, and magnetic moments of the octahedral ($1T$) and the trigonal prismatic ($2H$) structures significantly depend on the effective Hubbard $U$ parameter, $U_{\mathrm{eff}}$. Comparison with the HSE06 hybrid density functional used as a benchmark indicates that $U_{\mathrm{eff}}=2.5$ eV, which consistently shows that the $2H$ structure is more stable than the $1T$ structure and a ferromagnetic semiconductor. The magnetic moments are localized on the V atoms and coupled ferromagnetically due to the superexchange interactions mediated by the S atoms. Calculations of the magnetic anisotropy show an easy plane for the magnetic moment. Assuming a classical $\mathit{XY}$ model with nearest neighbor coupling, we determine the critical temperature, $T_{\mathrm{c}}$, for the Berezinsky-Kosterlitz-Thouless transition of $2H$ single-layer ${\mathrm{VS}}_2$ to be about 90 K. Applying biaxial tensile strains can increase $T_{\mathrm{c}}$. Using Wannier interpolation, we evaluate the Berry curvature and anomalous Hall conductivity of $2H$ single-layer ${\mathrm{VS}}_2$. The coexistence of quasi-long-range ferromagnetic ordering and semiconducting behavior enables $2H$ single-layer ${\mathrm{VS}}_2$ to be a promising candidate for spintronics applications.

We report a study of the ${\mathrm{Ca}}_{0.73}{\mathrm{La}}_{0.27}{\mathrm{FeAs}}_2$ single crystals. We unravel a monoclinic to triclinic phase transition at 58 K, and a paramagnetic to stripe antiferromagnetic phase transition at 54 K, below which spins order ${45}^{\circ }$ away from the stripe direction. Furthermore, we demonstrate this material is substantially structurally untwinned at ambient pressure with the formation of spin rotation walls (S walls). Finally, in addition to the central-hole and corner-electron Fermi pockets usually appearing in Fe pnictide superconductors, angle-resolved photoemission measurements resolve a fermiology where an extra electron pocket of mainly As chain character exists at the Brillouin zone edge.