We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.

We report on quantum-interference measurements in top-gated Hall bars of monolayer graphene epitaxially grown on the Si face of SiC, in which the transition from negative to positive magnetoresistance was achieved varying temperature and charge density. We perform a systematic study of the quantum corrections to the magnetoresistance due to quantum interference of quasiparticles and electron-electron interaction. We analyze the contribution of the different scattering mechanisms affecting the magnetotransport in the $-2.0\times {10}^{10}$ cm${}^{-2}$ to $3.75\times {10}^{11}$ cm${}^{-2}$ density region and find a significant influence of the charge density on the intravalley scattering time. Furthermore, we observe a modulation of the electron-electron interaction with charge density not accounted for by present theory. Our results clarify the role of quantum transport in SiC-based devices, which will be relevant in the development of a graphene-based technology for coherent electronics.

We study theoretically and experimentally the infrared (IR) spectrum of an adamantane monolayer on a Au(111) surface. Using a STM-based IR spectroscopy technique (IRSTM) we are able to measure both the nanoscale structure of an adamantane monolayer on Au(111) as well as its infrared spectrum, while DFT-based ab initio calculations allow us to interpret the microscopic vibrational dynamics revealed by our measurements. We find that the IR spectrum of an adamantane monolayer on Au(111) is substantially modified with respect to the gas-phase IR spectrum. The first modification is caused by the adamantane-adamantane interaction due to monolayer packing, and it reduces the IR intensity of the 2912 cm${}^{-1}$ peak (gas phase) by a factor of 3.5. The second modification originates from the adamantane-gold interaction, and it increases the IR intensity of the 2938 cm${}^{-1}$ peak (gas phase) by a factor of 2.6 and reduces its frequency by 276 cm${}^{-1}$. We expect that the techniques described here can be used for an independent estimate of substrate effects and intermolecular interactions in other diamondoid molecules and for other metallic substrates.

We propose the most general classification of pointlike and linelike extrinsic topological defects in $(2+1)$-dimensional Abelian topological states. We first map generic extrinsic defects to boundary defects, and then provide a classification of the latter. Based on this classification, the most generic point defects can be understood as domain walls between topologically distinct boundary regions. We show that topologically distinct boundaries can themselves be classified by certain maximal subgroups of mutually bosonic quasiparticles, called Lagrangian subgroups. We study the topological properties of the point defects, including their quantum dimension, localized zero modes, and projective braiding statistics.

We study the conductance through an Aharonov-Bohm ring, containing a quantum dot in the Kondo regime in one arm, at finite temperature and arbitrary electronic density. We develop a general method for this calculation based on changing the basis to the screening and nonscreening channels. We show that an unusual term appears in the conductance, involving the connected four-point Green's function of the conduction electrons. However, this term and the terms quadratic in the $\mathrm{T}$ matrix can be eliminated at sufficiently low temperatures, leading to an expression for the conductance linear in the Kondo T matrix. Explicit results are given for temperatures that are high compared to the Kondo temperature.

We study transport at finite bias, i.e., beyond the linear regime, through two interacting resonant levels connected by a Fermi sea, by means of time-dependent density-matrix renormalization group. We first consider methodological issues, such as the protocol that leads to a current-carrying state and the characterization of the steady state. At finite sizes, both the current and the occupations of the interacting levels oscillate as a function of time. We determine the amplitude and period of such oscillations as a function of bias. We find that the occupations on the two dots oscillate with a relative phase which depends on the distance between the impurities and on the Fermi momentum of the Fermi sea, as expected for Rudermann-Kittel-Kasuya-Yosida interactions. Also, the approximant to the steady-state current displays oscillations as a function of the distance between the impurities. Such a behavior can be explained by resonances in the free case. We then discuss the incidence of interaction on such a behavior. We conclude by showing the effect of the bias on the current, making connection with the one-impurity case.

We devise a dimensional regularization scheme for quantum field theories with a Fermi surface to study scaling behavior of non-Fermi liquid states in a controlled approximation. Starting from two space dimensions, the co-dimension of the Fermi surface is extended to a general value while its dimension is fixed. When the Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension $d_c=5/2$. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.

Coherent large-wave-vector phonons in graphene layers were excited by using a 7.5-fs ultrashort laser, and observed by wavelength-resolved pump-probe transient reflectivity spectroscopy. Inter-Dirac-cone electron scattering mediated by edges and defects in graphene layers drives large-wave-vector coherent $D$-mode phonons near the Dirac point ($K$ point) of the Brillouin zone. In contrast to the normal coherent phonons generated with first-order Raman process, phonon chirp is observed, and amplitude and frequency strongly change depending on the probed wavelength. The results are discussed on the basis of doubly resonant Raman scattering process, demonstrating that generated $D$-mode coherent phonons can propagate as nanoscale optical-phonon wave packets.

The properties of many intrinsic defects in the wide-band-gap semiconductor LaAlO${}_3$ are studied using the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE) [J. Chem. Phys. 118, 8207 (2003)]. As in pristine structures, exact exchange included in the screened hybrid functional alleviates the band-gap underestimation problem, which is common to semilocal functionals; this allows accurate prediction of defect properties. We propose correction-free defect energy levels for bulk LaAlO${}_3$ computed using HSE that might serve as a guide in the interpretation of photoluminescence experiments.

We present a theory of local electric polarization in crystalline solids and apply it to study the case of wurtzite group-III nitrides. We show that a local value of the electric polarization, evaluated at the atomic sites, can be cast in terms of a summation over nearest-neighbor distances and Born effective charges. Within this model, the local polarization shows a direct relation to internal strain and can be expressed in terms of internal strain parameters. The predictions of the present theory show excellent agreement with a formal Berry-phase calculation for random distortions of a test-case CuPt-like InGaN alloy and InGaN supercells with randomly placed cations. While the present level of theory is appropriate for highly ionic compounds, such as III-N materials, we show that a more complex model is needed for less ionic materials, such as GaAs, in which the strain dependence of Born effective charges has to be taken into account. Moreover, we provide ab initio parameters for GaN, InN, and AlN, including hybrid functional values for the piezoelectric coefficients and the spontaneous polarization, which we use to accurately implement the local theory expressions. In order to calculate the local polarization potential, we also present a point dipole method. This method overcomes several limitations related to discretization and resolution which arise when obtaining the local potential by solving Poisson's equation on an atomic grid. Finally, we perform tight-binding supercell calculations to assess the impact of the local polarization potential arising from alloy fluctuations on the electronic properties of InGaN alloys. In particular, we find that the large upward bowing with composition of the InGaN valence-band edge is strongly influenced by local polarization effects. Furthermore, our analysis allows us to extract composition-dependent bowing parameters for the energy gap and valence- and conduction-band edges.

The transition from the microscopic Heisenberg model to the macroscopic elastic theory is carried out for MnSi-type chiral magnetics with $B20$ crystal structure. Both exchange and Dzyaloshinskii-Moriya (DM) interactions are taken into account for the first, second, and third magnetic neighbors. The particular components of the DM vectors of bonds are found, which are responsible for (i) the global magnetic twist and (ii) the canting between four different spin sublattices. A possible mechanism for effective reinforcement of the global magnetic twist is suggested: it is demonstrated that the components of the DM vectors normal to corresponding interatomic bonds become very important for the twisting power. The Ruderman-Kittel-Kasuya-Yosida (RKKY) theory is used for model calculation of exchange parameters. It is found that just the interplay between the exchange parameters of several magnetic shells rather than the signs of DM vectors can be responsible for the concentration-induced reverse of the magnetic chirality recently observed in Mn${}_{1-x}$Fe${}_x$Ge crystals.

We study the simple Hamiltonian, $H=-K(S_{1z}^2+S_{2z}^2)+\lambda {\vec{S}}_1·{\vec{S}}_2$, of two large, coupled spins which are taken equal, each of total spin $s$ with $\lambda$ the exchange coupling constant. The exact ground state of this simple Hamiltonian is not known for an antiferromagnetic coupling corresponding to the $\lambda >0$. In the absence of the exchange interaction, the ground state is fourfold degenerate, corresponding to the states where the individual spins are in their highest weight or lowest weight states, $|\uparrow ,\uparrow \rangle ,|\downarrow ,\downarrow \rangle ,|\uparrow ,\downarrow \rangle ,|\downarrow ,\uparrow \rangle$, in obvious notation. The first two remain exact eigenstates of the full Hamiltonian. However, we show that the two states $|\uparrow ,\downarrow \rangle ,|\downarrow ,\uparrow \rangle$ organize themselves into the combinations $|\pm \rangle =\frac{1}{\sqrt{2}}\left(\right|\uparrow ,\downarrow \rangle \pm |\downarrow \uparrow \rangle )$, up to perturbative corrections. For the antiferromagnetic case, we show that the ground state is nondegenerate, and we find the interesting result that for integer spins the ground state is $|+\rangle$ and the first excited state is the antisymmetric combination $|-\rangle$ while for half odd integer spin, these roles are exactly reversed. The energy splitting, however, is proportional to ${\lambda }^{2s}$, as expected by perturbation theory to the $2s$th order. We obtain these results through the spin coherent state path integral.

We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er${}_2$Ti${}_2$O${}_7$ on its approach to the critical temperature $T_c$. We show that its anisotropic exchange parameters, $\left\{J_e\right\}$, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near $T_c$. While different $\mathit{q}=0$ $XY$ order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear “${\psi }_2$ state” as found in Er${}_2$Ti${}_2$O${}_7$. Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at $T_c$ in this frustrated quantum spin-1/2 antiferromagnetic material.

Electronic band dispersions in copper oxide superconductors have kinks around 70 meV that are typically attributed to coupling of electrons to a bosonic mode. We performed angle-resolved photoemission spectroscopy experiments on overdoped cuprate high temperature superconductors to test the relationship between the superconducting transition temperature and electron-bosonic mode coupling. Remarkably, the kinks remain strong in the heavily overdoped region of the doping phase diagram of La${}_{2-x}$Sr${}_x$CuO${}_4$, even when the superconductivity completely disappears. This unexpected observation is incompatible with the conventional picture of superconductivity mediated by the sharp bosonic modes that are responsible for the kink unless extra doping strongly suppresses their $d$-wave projection but not the overall spectral weight. Our results favor pairing mediated by a very broad electronic spectrum or an unconventional mechanism without pairing glue.

We present numerical evidence from Monte Carlo simulations that the superfluid-insulator quantum phase transition of interacting bosons subject to strong disorder in one dimension is controlled by the strong-randomness critical point. At this critical point the distribution of superfluid stiffness over disorder realizations develops a power-law tail reflecting a universal distribution of weak links. The Luttinger parameter on the other hand does not take on a universal value at this critical point, in marked contrast to the known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in weakly disordered systems. We develop a finite-size scaling procedure which allows us to directly compare the numerical results from systems of linear size up to 1024 sites with theoretical predictions obtained by Altman et al. [Phys. Rev. Lett. 93, 150402 (2004)] using a strong disorder renormalization group approach. The data shows good agreement with the scaling expected at the strong-randomness critical point.

We theoretically investigate the ground-state properties of a molecular para-hydrogen (p-H${}_2$) film in which crystallization is energetically frustrated by embedding sodium (Na) atoms periodically distributed in a triangular lattice. In order to fully deal with the quantum nature of p-H${}_2$ molecules, we employ the diffusion Monte Carlo method and realistic semiempirical pairwise potentials describing the interactions between H${}_2$-H${}_2$ and Na-H${}_2$ species. In particular, we calculate the energetic, structural, and superfluid properties of two-dimensional Na-H${}_2$ systems within a narrow density interval around equilibrium at zero temperature. In contrast to previous computational studies considering other alkali metal species such as rubidium and potassium, we find that the p-H${}_2$ ground state is a liquid with a significantly large superfluid fraction of ${\rho }_s/\rho =0.29\left(2\right)$. The appearance of p-H${}_2$ superfluid response is due to the fact that the interactions between Na atoms and H${}_2$ molecules are less attractive than between H${}_2$ molecules. This induces a considerable reduction of the hydrogen density which favors the stabilization of the liquid phase.

We report the observation of a mechanism of maser generation in an ensemble of intercoupled, inhomogeneously broadened two-level systems, enhanced by high quality factor electromagnetic cavity modes. In this form of population inversion, an inseparable quantum system leads to cavity-enhanced stimulated emission arising from interactions within an ensemble of two-level systems, as opposed to a traditional ensemble of noninteracting identical three-level systems. The effect is observed in a cryogenically cooled whispering gallery mode sapphire resonator containing dilute Fe${}^{3+}$ impurity ions. These ions exhibit strong spin-lattice interaction, leading to both electron spin resonance broadening and phonon mediated spin-spin coupling. The maser effect is due to a $|1/2\rangle \to |3/2\rangle$ energy transition in an electron spin angular momentum observed at zero external magnetic field. Both continuous and oscillating regimes are observed with corresponding thresholds both in detuning frequency and incident power.

Electrons in monolayer graphene in the presence of an electromagnetic (or electric) wave are considered theoretically. It is shown that the electron motion is a nonlinear combination of Zitterbewegung (ZB, trembling motion) resulting from the periodic potential of graphene lattice and the driving field of the wave. This complex motion is called “multimode Zitterbewegung.” The theory is based on the time-dependent two-band Hamiltonian taking into account the graphene band structure and interaction with the wave. Our theoretical treatment includes the rotating-wave approximation and high-driving-frequency approximation for narrow wave packets, as well as numerical calculations for packets of arbitrary widths. Different regimes of electron motion are found, depending on relation between the ZB frequency ${\omega }_Z$ and the driving frequency ${\omega }_D$ for different strengths of the electron-wave interaction. Frequencies and intensities of the resulting oscillation modes are calculated. The nonlinearity of the problem results in a pronounced multimode behavior. Polarization of the medium is also calculated relating our theoretical results to observable quantities. The presence of driving wave, resulting in frequencies directly related to ${\omega }_Z$ and increasing the decay time of oscillations, should facilitate observations of the Zitterbewegung phenomenon.

The stability and reactivity of steps in the initial stage of the graphene growth by sublimating the SiC(0001) surface is theoretically studied by the first-principles calculation. The steps are not necessarily unstable and reactive during the formation of the zeroth graphene layer. Temperature, Si pressure, and C coverage affect the stability and reactivity of the step. The growth mode shows a phase transition. The step is unstable and reactive after the zeroth graphene layer is formed. These findings are tightly related to the graphene formation mechanism on this surface. They are discussed with experimental results and suggest a way to control the quality of graphene.