arXiv subjects

G. Montambaux

Publications and source records attributed to G. Montambaux.

At least 37 records · Page 2Linked to original sources

arXiv2010

A semi-Dirac point in the Hofstadter spectrum

The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair of Dirac points may merge into a single one, with a topological transition towards a gapped phase. At the transition, the spectrum is linear in one direction and quadratic in the other one (a spectrum recently named "hybrid" or "semi-Dirac"). This transition is studied in the framework of a general Hamiltonian describing the merging of Dirac points. The possibility of creating gauge fields for cold atoms in optical lattices may offer the first opportunity to observe this merging of Dirac points and the hybrid dispersion relation.

cond-mat.mes-hall↗

arXiv2009

Merging of Dirac points in a two-dimensional crystal

We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological transition between a semi-metallic phase and a band insulator. We derive a universal Hamiltonian that describes the physical properties of the transition, which is controlled by a single parameter, and analyze the Landau-level spectrum in its vicinity. This merging may be observed in the organic salt alpha-(BEDT-TTF)_2 I_3 or in an optical lattice of cold atoms simulating deformed graphene.

cond-mat.mes-hall↗

arXiv2009

A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal

We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac cones from an insulating phase with a gap. We calculate the density of states and the specific heat. The spectrum in a magnetic field B is related to the resolution of a Schrodinger equation in a double well potential. They obey the general scaling law e_n \propto B^{2/3} f_n(Delta /B^{2/3}. They evolve continuously from a sqrt{n B} to a linear (n+1/2)B dependence, with a [(n+1/2)B]^{2/3} dependence at the transition. The spectrum in the vicinity of the topological transition is very well described by a semiclassical quantization rule. This model describes continuously the coupling between valleys associated with the two Dirac points, when approaching the transition. It is applied to the tight-binding model of graphene and its generalization when one hopping parameter is varied. It remarkably reproduces the low field part of the Rammal-Hofstadter spectrum for the honeycomb lattice.

cond-mat.mes-hall↗

arXiv2009

Electric-field-induced lifting of the valley degeneracy in alpha-(BEDT-TTF)_2I_3 Dirac-like Landau levels

The relativistic Landau levels in the layered organic material alpha-(BEDT-TTF)_2I_3 [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] are sensitive to the tilt of the Dirac cones, which, as in the case of graphene, determine the low-energy electronic properties under appropriate pressure. We show that an applied inplane electric field, which happens to be in competition with the tilt of the cones, lifts the twofold valley degeneracy due to a different level spacing. The scenario may be tested in infrared transmission spectroscopy.

cond-mat.mes-hall↗

arXiv2008

Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3

We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a strong magnetic field, the relativistic form of which is reminiscent to that of graphene, with a renormalized Fermi velocity due to the tilt of the Dirac cones. These relativistic Landau levels, experimentally accessible via spectroscopy or even a quantum Hall effect measurement, may be used as a direct experimental verification of Dirac cones in alpha-(BEDT-TTF)_2I_3.

cond-mat.mes-hall↗

arXiv2008

Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network

We investigate weak localization in metallic networks etched in a two dimensional electron gas between $25\:$mK and $750\:$mK when electron-electron (e-e) interaction is the dominant phase breaking mechanism. We show that, at the highest temperatures, the contributions arising from trajectories that wind around the rings and trajectories that do not are governed by two different length scales. This is achieved by analyzing separately the envelope and the oscillating part of the magnetoconductance. For $T\gtrsim0.3\:$K we find $\Lphi^\mathrm{env}\propto{T}^{-1/3}$ for the envelope, and $\Lphi^\mathrm{osc}\propto{T}^{-1/2}$ for the oscillations, in agreement with the prediction for a single ring \cite{LudMir04,TexMon05}. This is the first experimental confirmation of the geometry dependence of decoherence due to e-e interaction.

cond-mat.mes-hall↗

arXiv2007

Proximity DC squids in the long junction limit

We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence, notably the low and high field dependence of the maximum switching current. In contrast with the well-known Fraunhoffer-type oscillations typical of short wide junctions, we find a monotonous gaussian extinction of the critical current at high field. As shown in [15], this monotonous dependence is typical of long and narrow diffusive junctions. We also find in some cases a puzzling reentrance at low field. In contrast, the temperature dependence of the critical current is well described by the proximity effect theory, as found by Dubos {\it et al.} [16] on SNS wires in the long junction limit. The switching current distributions and hysteretic IV curves also suggest interesting dynamics of long SNS junctions with an important role played by the diffusion time across the junction.

cond-mat.mes-hall↗

arXiv2007

Conservation of energy in coherent backscattering of light

Although conservation of energy is fundamental in physics, its principles seem to be violated in the field of wave propagation in turbid media by the energy enhancement of the coherent backscattering cone. In this letter we present experimental data which show that the energy enhancement of the cone is balanced by an energy cutback at all scattering angles. Moreover, we give a complete theoretical description, which is in good agreement with these data. The additional terms needed to enforce energy conservation in this description result from an interference effect between incident and multiply scattered waves, which is reminiscent of the optical theorem in single scattering.

cond-mat.dis-nn↗

arXiv2005

Mesoscopic scattering of spin s particles

Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases.

cond-mat.mes-hall↗

arXiv2004

Exchange induced ordinary reflection in a single-channel superconductor-ferromagnet-superconductor junction

The stationnary Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction is revisited for arbitrarily large spin polarizations. The quasiclassical calculation of the supercurrent assumes that the Andreev reflection is complete for all channels. However, De Jong and Beenakker have shown that the Andreev reflection at a clean FS interface is incomplete, due to the exchange interaction in the ferromagnet. Taking into account this incomplete Andreev reflection, we investigate the quasiparticle spectrum, the Josephson current and the $0-π$ transition in a ballistic single channel SFS junction. We find that energy gaps open in the phase dependent spectrum. Although the spectrum is strongly modified when the exchange energy increases, the Josephson current and the $0-π$ transition are only weakly affected by the incomplete Andreev reflection, except when the exchange energy is close to the Fermi energy.

cond-mat.mes-hall↗

arXiv2004

Incomplete Andreev reflection in a clean Superconductor/Ferromagnet/Superconductor junction

We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory.

cond-mat.mes-hall↗

arXiv2002

Isolated hybrid normal/superconducting ring in a magnetic flux: from persistent current to Josephson current

We investigate the ground state current of an isolated hybrid normal/superconducting ring (NS ring), threaded by an Aharonov-Bohm magnetic flux. We calculate the excitation spectrum of the ring for any values of the lengths of the normal metal and of the superconductor. We describe the nonlinear flux dependence of the energy levels above and below the gap edge. Using a harmonics expansion for the current, we isolate the contribution due to these nonlinearities and we show that it vanishes for large normal segment length. The remaining contribution is very easy to evaluate from the linearized low energy spectrum. This decomposition allows us to recover in a controlled way the current-flux relationships for SNS junctions and for NS rings. We also study the crossover from persistent current to Josephson current in a multichannel NS ring at finite temperature.

cond-mat.mes-hall↗

arXiv2001

Aharonov-Bohm cages in the GaAlAs/GaAs system

Aharonov-Bohm oscillations have been observed in a lattice formed by a two dimensional rhombus tiling. This observation is in good agreement with a recent theoretical calculation of the energy spectrum of this so-called T3 lattice. We have investigated the low temperature magnetotransport of the T3 lattice realized in the GaAlAs/GaAs system. Using an additional electrostatic gate, we have studied the influence of the channel number on the oscillations amplitude. Finally, the role of the disorder on the strength of the localization is theoretically discussed.

cond-mat.mes-hall↗

arXiv2001

Coherent multiple scattering in disordered media

These notes contain a rapid overview of the methods and results obtained in the field of propagation of waves in disordered media. The case of Schrödinger and Helmholtz equations are considered that describe respectively electrons in metals and scalar electromagnetic waves. The assumptions on the nature of disorder are discussed and perturbation methods in the weak disorder limit are presented. A central quantity, namely the probability of quantum diffusion is defined and calculated in the same limit. It is then shown that several relevant physical quantities are related to the return probability. Examples are provided to substantiate this, which include the average electrical conductivity, its fluctuations, the average albedo and spectral correlations.

cond-mat.mes-hall↗

arXiv2000

Transmission through quantum networks

We propose a simple formalism to calculate the conductance of any quantum network made of one-dimensional quantum wires. We apply this method to analyze, for two periodic systems, the modulation of this conductance with respect to the magnetic field. We also study the influence of an elastic disorder on the periodicity of the AB oscillations and we show that a recently proposed localization mechanism induced by the magnetic field resists to such a perturbation. Finally, we discuss the relevance of this approach for the understanding of a recent experiment on GaAs/GaAlAs networks.

cond-mat.mes-hall↗

arXiv1999

Pauli and orbital effects of magnetic field on charge density waves

Taking into account both Pauli and orbital effects of external magnetic field we compute the mean field phase diagram for charge density waves in quasi-one-dimensional electronic systems. The magnetic field can cause transitions to CDW states with two types of the shifts of wave vector from its zero-field value. It can also stabilize the field-induced charge density wave. Furthermore, the critical temperature shows peaks at a new kind of magic angles.

cond-mat.str-el↗

arXiv1999

Comment on "Level statistics of quantum dots coupled to reservoirs"

This is a comment to J. Konig, Y. Gefen and G. Schon, Phys. Rev. Lett. 81, 4468 (1998) who consider the coupling of two discrete levels of a dot to the continuum of states in reservoirs. We have generalized this work to the case of several discrete levels.

cond-mat.mes-hall↗

arXiv1999

Persistent currents on graphs

We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix which describes the topology of the graph. In certain limits, they are obtained by simple counting of the nodes and their connectivity. We relate the average current of a disordered graph with interactions and the non-interacting current of the same graph with clean 1D wires. A similar relation exists for orbital magnetism in general.

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