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S. Teber

Publications and source records attributed to S. Teber.

32 records · Page 2Linked to original sources
arXiv2017

New results for a two-loop massless propagator-type Feynman diagram

We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations.

hep-th↗
arXiv2016

Critical behaviour of reduced QED$_{4,3}$ and dynamical fermion gap generation in graphene

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component fermions ($N=2$ for graphene), where photons are $(3+1)$-dimensional and mediate a fully retarded interaction among $(2+1)$-dimensional fermions. A correspondence between reduced QED$_{4,3}$ and QED$_3$ allows us to derive an exact gap equation for QED$_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $α> α_c$ where $1.03 < α_c < 1.08$ in the case $N=2$ or for $N < N_c$ where $N_c$ is such that $α_c \to \infty$ and takes the values $3.24 < N_c < 3.36$. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction. At the fixed point: $α= 1/137 \ll α_c$, and the system is therefore in the semi-metallic regime in accordance with experiments.

hep-th↗
arXiv2016

Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge

Dynamical chiral symmetry breaking (D$χ$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $1/N$ expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, $N_c(ξ)$ where $ξ$ is the gauge fixing parameter, which is such that D$χ$SB takes place for $N<N_c(ξ)$. Neglecting the weak gauge-dependent terms yields $N_c = 2.8469$ while, in the general case, it is found that: $N_c(1) = 3.0084$ in the Feynman gauge, $N_c(0) = 3.0844$ in the Landau gauge and $N_c(2/3)= 3.0377$ in the $ξ=2/3$ gauge where the leading order fermion wave function is finite. These results suggest that D$χ$SB should take place for integer values $N \leq 3$.

hep-th↗
arXiv2016

Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge

The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N<N_c where N_c=3.29, that is only about $1\%$ larger than its value at leading order.

hep-th↗
arXiv2016

The method of uniqueness and the optical conductivity of graphene: new application of a powerful technique for multi-loop calculations

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation of a two-loop massless propagator Feynman diagram with a non-integer index on the central line. The result is applied to the computation of the optical conductivity of graphene at the infra-red Lorentz invariant fixed point. The effect of counter-terms is analysed. A brief comparison with the non-relativistic case is included.

hep-th↗
arXiv2014

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: $σ= σ_0\,( 1 + \al\,(19-6π)/12) \approx σ_0 \,(1 + 0.01\, \al)$, where $\al = e^2 / (4 π\hbar v)$ is the renormalized fine structure constant and $σ_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theoretical dispute.

cond-mat.mes-hall↗
arXiv2014

Two-loop fermion self-energy and propagator in reduced QED$_{3,2}$

We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics (RQED) for an arbitrary gauge in the case where the photon field is three-dimensional and the fermion field two-dimensional: super-renormalizable RQED$_{3,2}$ with $N_F$ fermions. We find that the theory is infrared finite at two-loop and that finite corrections to the fermion propagator have a remarkably simple form.

hep-ph↗
arXiv2014

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.

hep-ph↗
arXiv2012

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.

cond-mat.str-el↗
arXiv2012

Electromagnetic current correlations in reduced quantum electrodynamics

We consider a theory of massless reduced quantum electrodynamics (RQED$_{d_γ,d_e}$), e.g., a quantum field theory where the U(1) gauge field lives in $d_γ$-spacetime dimensions while the fermionic field lives in a reduced spacetime of $d_e$ dimensions ($d_e \leqslant d_γ$). In the case where $d_γ=4$ such RQEDs are renormalizable while they are super-renormalizable for $d_γ<4$. The 2-loop electromagnetic current correlation function is computed exactly for a general RQED$_{d_γ,d_e}$. Focusing on RQED$_{4,3}$, the corresponding $β$-function is shown to vanish which implies the scale invariance of the theory. Interaction correction to the 1-loop vacuum polarization, $Π_1$, of RQED$_{4,3}$ is found to be: $Π= Π_1 (1 + 0.056 \al)$ where $\al$ is the fine structure constant. The scaling dimension of the fermion field is computed at 1-loop and is shown to be anomalous for RQED$_{4,3}$.

hep-ph↗
arXiv2010

Non-equilibrium effects in a Josephson junction coupled to a precessing spin

We present a theoretical study of a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin. When an external magnetic field is applied, the classical spin will precess with the Larmor frequency. This magnetically active interface results in a time-dependent boundary condition with different tunneling amplitudes for spin-up and spin-down quasiparticles and where the precession produces spin-flip scattering processes. We show that as a result, the Andreev states develop sidebands and a non-equilibrium population which depend on the precession frequency and the angle between the classical spin and the external magnetic field. The Andreev states lead to a steady-state Josephson current whose current-phase relation could be used for characterizing the precessing spin. In addition to the charge transport, a magnetization current is also generated.This spin current is time-dependent and its polarization axis rotates with the same precession frequency as the classical spin.

cond-mat.supr-con↗
arXiv2010

Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction

We study dc-transport and magnetization dynamics in a junction of arbitrary transparency consisting of two spin-singlet superconducting leads connected via a single classical spin precessing at the frequency $Ω$. The presence of the spin in the junction provides different transmission amplitudes for spin-up and spin-down quasiparticles as well as a time-dependent spin-flip transmission term. For a phase biased junction, we show that a steady-state superconducting charge current flows through the junction and that an out-of-equilibrium circularly polarized spin current, of frequency $Ω$, is emitted in the leads. Detailed understanding of the charge and spin currents is obtained in the entire parameter range. In the adiabatic regime, $\hbar Ω\ll 2Δ$ where $Δ$ is the superconducting gap, and for high transparencies of the junction, a strong suppression of the current takes place around $\vp \approx 0$ due to an abrupt change in the occupation of the Andreev bound-states. At higher values of the phase and/or precession frequency, extended (quasi-particle like) states compete with the bound-states in order to carry the current. Well below the superconducting transition, these results are shown to be weakly affected by the back-action of the spin current on the dynamics of the precessing spin. Indeed, we show that the Gilbert damping due to the quasi-particle spin current is strongly suppressed at low-temperatures, which goes along with a shift of the precession frequency due to the condensate. The results obtained may be of interest for on-going experiments in the field of molecular spintronics.

cond-mat.mes-hall↗
arXiv2003

Variable-range hopping in quasi-one-dimensional electron crystals

We study the effect of impurities on the ground state and the low-temperature dc transport in a 1D chain and quasi-1D systems of many parallel chains. We assume that strong interactions impose a short-range periodicicity of the electron positions. The long-range order of such an electron crystal (or equivalently, a $4 k_F$ charge-density wave) is destroyed by impurities. The 3D array of chains behaves differently at large and at small impurity concentrations $N$. At large $N$, impurities divide the chains into metallic rods. The low-temperature conductivity is due to the variable-range hopping of electrons between the rods. It obeys the Efros-Shklovskii (ES) law and increases exponentially as $N$ decreases. When $N$ is small, the metallic-rod picture of the ground state survives only in the form of rare clusters of atypically short rods. They are the source of low-energy charge excitations. In the bulk the charge excitations are gapped and the electron crystal is pinned collectively. A strongly anisotropic screening of the Coulomb potential produces an unconventional linear in energy Coulomb gap and a new law of the variable-range hopping $-\lnσ\sim (T_1 / T)^{2/5}$. $T_1$ remains constant over a finite range of impurity concentrations. At smaller $N$ the 2/5-law is replaced by the Mott law, where the conductivity gets suppressed as $N$ goes down. Thus, the overall dependence of $σ$ on $N$ is nonmonotonic. In 1D, the granular-rod picture and the ES apply at all $N$. The conductivity decreases exponentially with $N$. Our theory provides a qualitative explanation for the transport in organic charge-density wave compounds.

cond-mat.mes-hall↗