Variable-range hopping in 2D quasi-1D electronic systems

A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, $g(\epsilon)$, where $\epsilon$ is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), {\it i.e.} $\sigma(T) \sim \exp[-(T_L/T)^{\gamma_L}]$, and current in the non-linear (NL), {\it i.e.} $j({\mathcal E}) \sim \exp[-({\mathcal E}_{NL} / \mathcal{E})^{\gamma_{NL}}]$, response regimes (${\mathcal E}$ is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, {\it i.e.} with respect to the disorder-dependence of $T_L$ and ${\mathcal E}_{NL}$ and the values of $\gamma_L$ and $\gamma_{NL}$.Comment: (v2) Entirely re-written (some notations changed, new presentation and new structure). Part on the Wigner crystal taken off for short. Minor changes in results. 16 RevTex4 pages, 5 figures. (v3) Published versio

One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem

We consider one-dimensional (1D) interacting electrons beyond the Dzyaloshinskii-Larkin theorem, i.e., keeping forward scattering interactions among the electrons but adding a non-linear correction to the electron dispersion relation. The latter generates multi-loop corrections to the polarization operator and electron self-energy thereby providing a variety of inelastic processes affecting equilibrium as well as non-equilibrium properties of the 1D system. We first review the computation of equilibrium properties, e.g., the high frequency part of the dynamical structure factor and corrections to the electron-electron scattering rate. On this basis, microscopic equilibration processes are identified and a qualitative estimate of the relaxation rate of thermal carriers is given.Comment: 4 pages, 5 figure

Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene

The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the BPHZ prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via density-density or via current-current correlation functions, a single well-defined value is obtained: $\mathcal{C}= (19-6\pi)/12) = 0.01$ in agreement with the result first obtained by Mishchenko and which is compatible with experimental uncertainties.Comment: LaTeX file with feynMF package. (v2) Footnotes and references added to answer referee's questions and comments. No change in results. 23 pages (JHEP format), 4 figures (v1) 12 pages, 4 figure

Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene

We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field is four-dimensional, our formula involves only recursively one-loop integrals and can therefore be evaluated exactly. From this formula, we deduce the anomalous scaling dimension of the fermion field as well as the renormalized fermion propagator up to two loops. The results are then applied to the ultra-relativistic limit of graphene and compared with similar results obtained for four-dimensional and three-dimensional quantum electrodynamics.Comment: (v2) Accepted for publication in PRD. Footnote with reference added per referee's comment, other minor modifications. No change in results. 23 pages, 4 figures. (v1) LaTeX file with feynMF package. 23 pages, 4 figure

Interaction corrections to the minimal conductivity of graphene via dimensional regularization

We compute the two-loop interaction correction to the minimal conductivity of disorder-free intrinsic graphene with the help of dimensional regularization. The calculation is done in two different ways: via density-density and via current-current correlation functions. Upon properly renormalizing the perturbation theory, in both cases, we find that: \sigma = \sigma_0\,( 1 + \al\,(19-6\pi)/12) \approx \sigma_0 \,(1 + 0.01\, \al), where \al = e^2 / (4 \pi \hbar v) is the renormalized fine structure constant and $\sigma_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theoretical dispute.Comment: (v2) 5 pages, 2 figures, ref [19] added, minor typos corrected, no change in results. (v1) 5 pages, 2 figure

Statistical properties of charged interfaces

We consider the equilibrium statistical properties of interfaces submitted to competing interactions; a long-range repulsive Coulomb interaction inherent to the charged interface and a short-range, anisotropic, attractive one due to either elasticity or confinement. We focus on one-dimensional interfaces such as strings. Model systems considered for applications are mainly aggregates of solitons in polyacetylene and other charge density wave systems, domain lines in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature, we find a shape instability which lead, via phase transitions, to tilted phases. Depending on the regime, elastic or confinement, the order of the zero-temperature transition changes. Thermal fluctuations lead to a pure Coulomb roughening of the string, in addition to the usual one, and to the presence of angular kinks. We suggest that such instabilities might explain the tilting of stripes in cuprate oxides. The 3D problem of the charged wall is also analyzed. The latter experiences instabilities towards various tilted phases separated by a tricritical point in the elastic regime. In the confinement regime, the increase of dimensionality favors either the melting of the wall into a Wigner crystal of its constituent charges or a strongly inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure