arXiv subjects

Gilles Montambaux

Publications and source records attributed to Gilles Montambaux.

At least 37 records · Page 2Linked to original sources

arXiv2012

Inter-band tunneling near the merging transition of Dirac cones

Motivated by a recent experiment in a tunable graphene analog [L. Tarruell et al., Nature 483, 302 (2012)], we consider a generalization of the Landau-Zener problem to the case of a quadratic crossing between two bands in the vicinity of the merging transition of Dirac cones. The latter is described by the so-called universal hamiltonian. In this framework, the inter-band tunneling problem depends on two dimensionless parameters: one measures the proximity to the merging transition and the other the adiabaticity of the motion. Under the influence of a constant force, the probability for a particle to tunnel from the lower to the upper band is computed numerically in the whole range of these two parameters and analytically in different limits using (i) the Stueckelberg theory for two successive linear band crossings, (ii) diabatic perturbation theory, (iii) adiabatic perturbation theory and (iv) a modified Stueckelberg formula. We obtain a complete phase diagram and explain the presence of unexpected probability oscillations in terms of interferences between two poles in the complex time plane. We also compare our results to the above mentioned experiment.

cond-mat.quant-gas↗

arXiv2012

An equivalence between monolayer and bilayer honeycomb lattices

In this brief report, we show the equivalence between the tight-binding descriptions of the monolayer and bilayer honeycomb lattices. With appropriate value of the third nearest neighbors coupling, the Hamiltonian for a monolayer is equivalent to the low energy effective Hamiltonian for bilayer in the presence of trigonal warping. A simple physical argument is provided to explain this correspondance.

cond-mat.mes-hall↗

arXiv2012

Bloch-Zener oscillations across a merging transition of Dirac points

Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition towards a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.

cond-mat.quant-gas↗

arXiv2011

Magnetoresistance in Disordered Graphene: The Role of Pseudospin and Dimensionality Effects Unraveled

We report a theoretical low-field magnetotransport study unveiling the effect of pseudospin in realistic models of weakly disordered graphene-based materials. Using an efficient Kubo computational method, and simulating the effect of charges trapped in the oxide, different magnetoconductance fingerprints are numerically obtained in system sizes as large as 0.3 micronmeter squared, containing tens of millions of carbon atoms. In two-dimensional graphene, a strong valley mixing is found to irreparably yield a positive magnetoconductance (weak localization), whereas crossovers from positive to a negative magnetoconductance (weak antilocalization) are obtained by reducing disorder strength down to the ballistic limit. In sharp contrast, graphene nanoribbons with lateral size as large as 10nm show no sign of weak antilocalization, even for very small disorder strength. Our results rationalize the emergence of a complex phase diagram of magnetoconductance fingerprints, shedding some new light on the microscopical origin of pseudospin effects.

cond-mat.mes-hall↗

arXiv2010

WKB analysis of edge states in graphene in a strong magnetic field

We investigate the fine structure of the edge states energy spectrum for zigzag and armchair ribbons of graphene in a strong magnetic field. At low energy, the spectra can be described by an effective Schrodinger Hamiltonian with a double well potential, symmetric in the zigzag case and asymmetric in the armchair case. We develop a semiclassical formalism based on the WKB approximation to calculate analytically the energy spectrum for the two types of edges, including regions which were not studied earlier. Our results are in very good quantitative agreement with numerical calculations. This approach leads to a qualitative description of the spectra in terms of the quantization of unusual classical orbits in the real space.

cond-mat.mes-hall↗

arXiv2010

Semiclassical quantization of skipping orbits

We propose a simple description of the spectrum of edge states in the quantum Hall regime, in terms of semiclassical quantization of skipping orbits along hard wall boundaries, ${\cal A}=2 π(n+γ) \ell_B^2$, where ${\cal A}$ is the area enclosed between a skipping orbit and the wall and $\ell_B$ is the magnetic length. Remarkably, this description provides an excellent quantitative agreement with the exact spectrum. We discuss the value of $γ$ when the skipping orbits touch one or two edges, and its variation when the orbits graze the edges and the semiclassical quantization has to be corrected by diffraction effects. The value of $γ$ evolves continuously from $1/2$ to $3/4$. We calculate the energy dependence of the drift velocity along the different Landau levels. We compare the structure of the semiclassical cyclotron orbits, their position with respect to the edge, to the wave function of the corresponding eigenstates.

cond-mat.mes-hall↗

arXiv2009

Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_φ$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time $τ_φ$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.

cond-mat.dis-nn↗

arXiv2008

Semiclassical analysis of edge state energies in the integer quantum Hall effect

Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separatly, this problem is equivalent to that of a one dimensional harmonic oscillator centered at x=x_c and an infinite wall at x=0, and appears in numerous physical contexts. The eigenvalues E_n(x_c) for a given quantum number n are solutions of the equation S(E,x_c)=π[n+ γ(E,x_c)] where S is the WKB action and 0<γ<1 encodes all the information on the connection procedure at the turning points. A careful implication of the WKB connection formulae results in an excellent approximation to the exact energy eigenvalues. The dependence of γ[E_n(x_c),x_c] \equiv γ_c (x_c) on x_c is analyzed between its two extreme values 1/2 as x_c goes to -infinity far inside the sample and 3/4 as x_c goes to infinity far outside the sample. The edge-state energies E_n(x_c) obey an almost exact scaling law of the form E_n(x_c)=4 [n+γ_n(x_c)] f(x_c/4 n +3) and the scaling function f(y) is explicitly elucidated

cond-mat.mes-hall↗

arXiv2007

Remarks on the tight-binding model of graphene

We address a simple but fundamental issue arising in the study of graphene, as well as of other systems that have a crystalline structure with more than one atom per unit cell. For these systems, the choice of the tight-binding basis is not unique. For monolayer graphene two bases are widely used in the literature. While the expectation values of operators describing physical quantities should be independent of basis, the form of the operators may depend on the basis, especially in the presence of disorder or of an applied magnetic field. Using the inappropriate form of certain operators may lead to erroneous physical predictions. We discuss the two bases used to describe monolayer graphene, as well as the form of the most commonly used operators in the two bases. We repeat our analysis for the case of bilayer graphene.

cond-mat.mes-hall↗

arXiv2007

A new magnetic field dependence of Landau levels on a graphene like structure

We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as E_n(B) ~ [(n+γ)B]^{2/3}. This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value $γ=1/2$ is found to result from the cancellation of a Berry phase.

cond-mat.mes-hall↗

arXiv2007

Interference pattern of a long diffusive Josephson junction

We calculate the modulation by a magnetic field of the critical current of a long disordered Josephson junction in the diffusive limit, i.e. when the dimensions of the junction are larger that the elastic mean free path, and when the length $L$ is much larger than the width $w$. Due to the averaging of the gauge invariant phase factor over diffusive trajectories, the well-known oscillations of the Fraunhofer pattern are smoothed out and replaced by an exponential decay at large field. The predicted pattern is universal, i.e., it is independent of the disorder strength. We point out an interesting relation with the physics of speckle correlations in optics of turbid media.

cond-mat.mes-hall↗

arXiv2007

Magnetoconductance oscillations in metallic rings and decoherence due to electron-electron interaction

We study weak localization in chains of metallic rings. We show than nonlocality of quantum transport can drastically affect the behaviour of the harmonics of magnetoconductance oscillations. Two different geometries are considered: the case of rings separated by long wires compared to the phase coherence length and the case of contacted rings. In a second part we discuss the role of decoherence due to electron-electron interaction in these two geometries.

cond-mat.dis-nn↗

arXiv2007

Al'tshuler-Aronov correction to the conductivity of a large metallic square network

We consider the correction $Δσ_\mathrm{ee}$ due to electron-electron interaction to the conductivity of a weakly disordered metal (Al'tshuler-Aronov correction). The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of $Δσ_\mathrm{ee}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $Δσ_\mathrm{WL}(L_ϕ)$ as a function of the phase coherence length. Our result for $Δσ_\mathrm{ee}$ interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of $Δσ_\mathrm{ee}$ keeps a 1d behaviour. Quite surprisingly, the result is very close to the 2d logarithmic behaviour already for $L_T\sim{a}/2$, where $a$ is the lattice parameter.

cond-mat.dis-nn↗

arXiv2006

Coherence and interactions in diffusive systems

This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak localization correction or universal conductance fluctuations. I show how these physical properties of phase coherent conductors can be simply related to the classical return probability for a diffusive particle. The diffusion equation is then solved in various appropriate geometries and in the presence of a magnetic field. The important notion of quantum crossing is developed, which is at the origin of the quantum effects. The analogy with optics is exploited and the relation between universal conductance fluctuations and speckle fluctuations in optics is explained. The last part concerns the effect of electron-electron interactions. Using the same simple description, I derive qualitatively the expressions of the Altshuler-Aronov anomaly of the density of states, and of the correction to the conductivity. The last part, slightly more technical, adresses the question of the lifetime of a quasiparticle in a disordered metal.

cond-mat.mes-hall↗

arXiv2006

Dimensional crossover in quantum networks: from macroscopic to mesoscopic Physics

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to $10^{6}$ plaquettes, with anisotropic aspect ratio. Both Altshuler-Aronov-Spivak (AAS) $h/2e$ periodic oscillations and Aharonov-Bohm (AB) $h/e$ periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length $L_ϕ$, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.

cond-mat.mes-hall↗

arXiv2006

Dephasing due to electron-electron interaction in a diffusive ring

We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.

cond-mat.mes-hall↗

arXiv2005

Non exponential quasiparticle decay and phase relaxation in low dimensional conductors

We show that in low dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one dimensional case, both behave at small time as $e^{- (t/τ_{in})^{3/2}}$ where the inelastic time $τ_{in}$, identical for both processes, is a power $T^{2/3}$ of the temperature. This result implies the existence of an unusual distribution of relaxation times that we obtain.

cond-mat.mes-hall↗

arXiv2005

Direct measurement of the phase coherence length in a GaAs/GaAlAs square network

The low temperature magnetoconductance of a large array of quantum coherentloops exhibits Altshuler-Aronov-Spivak oscillations which periodicitycorresponds to 1/2 flux quantum per loop.We show that the measurement of the harmonics content in a square networkprovides an accurate way to determine the electron phase coherence length$L\_ϕ$ in units of the lattice length without any adjustableparameters.We use this method to determine $L\_ϕ$ in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs heterojunction. The temperaturedependence follows a power law $T^{-1/3}$ from 1.3 K to 25 mK with nosaturation, as expected for 1D diffusive electronic motion andelectron-electron scattering as the main decoherence mechanism.

cond-mat.mes-hall↗