Time delay matrix at the spectrum edge and the minimal chaotic cavities

Using the concept of minimal chaotic cavities, we give the distribution of the proper delay times of $Q=-i\hbar S^\dagger \frac{\partial S}{\partial E}$ at the spectrum edge with a scattering matrix $S$ belonging to circular ensembles CE. The three classes of symmetry ($\beta=1$, 2 and 4) will be analyzed to show how it differs from the distribution obtained in the bulk of the spectrum. In this new class of universality at the spectrum edge, more attention will be given to the Wigner time $\tau_w=tr(Q)$ and its distribution will be given analytically in the case of 2 modes scattering. The results will be presented exactly at all the Fermi energies without any approximation. All this will be tested numerically with an excellent precision.Comment: 7 pages, 4 figure

Thermal Enhancement of Interference Effects in Quantum Point Contacts

We study an electron interferometer formed with a quantum point contact and a scanning probe tip in a two-dimensional electron gas. The images giving the conductance as a function of the tip position exhibit fringes spaced by half the Fermi wavelength. For a contact opened at the edges of a quantized conductance plateau, the fringes are enhanced as the temperature T increases and can persist beyond the thermal length l_T. This unusual effect is explained assuming a simplified model: The fringes are mainly given by a contribution which vanishes when T -> 0 and has a decay characterized by a T-independent scale

Tunneling phase diagrams in anisotropic Multi-Weyl semimetals

Motivated by the exciting prediction of Multi-Weyl topological semimetals that are stabilized by point group symmetries [Phys. Rev. Lett. 108 (2012) 266802], we study tunneling phenomena for a class of anisotropic Multi-Weyl semimetals. We find that a distant detector for different ranges of an anisotropy parameter $\lambda$ and incident angle $\theta$ will measure a different number of propagating transmitted modes. We present these findings in terms of phase diagrams that is valid for an incoming wave with fixed wavenumber $k$--energy is not fixed. To gain a deeper understanding of this phenomenon we then focus on the simplest case of an anisotropic quadratic Weyl-semimetal and analyze tunneling coefficients analytically and numerically to confirm the observations from the phase diagram. Our results show non-analytical behavior, which is the hallmark of a phase transition. This serves as a motivation to make a formal analogy with phase transitions that are known from statistical mechanics. Specifically, we argue that the long distance limit in our tunneling problem takes the place of the thermodynamic limit in statistical mechanics. More precisely, find a direct formal connection to the recently developed formalism for dynamical phase transitions [Reports on Progress in Physics 81 (5) (2018) 054001]. We propose that this analogy to phase transitions can help classify transport properties in exotic semimetals

Pseudo Electric Field and Pumping Valley Current in Graphene Nano-bubbles

The extremely high pseudo-magnetic field emerging in strained graphene suggests that an oscillating nano-deformation will induce a very high current even without electric bias. In this paper, we demonstrate the sub-terahertz (THz) dynamics of a valley-current and the corresponding charge pumping with a periodically excited nano-bubble. We discuss the amplitude of the pseudo-electric field and investigate the dependence of the pumped valley current on the different parameters of the system. Finally, we report the signature of extra-harmonics generation in the valley current that might lead to potential modern devices development operating in the nonlinear regimeComment: 7 page

Transport thermoélectrique dans des contacts quantiques ponctuels et de cavités chaotiques: effets thermiques et fluctuations

Scanning Gate Microscopy (SGM) is a technique of imaging quantum transport coefficients due to the presence of an AFM charged tip. The interference pattern of the conductance change of a quantum point contact, obtained with this technique will be explained. The decay law of the fringes is obtained assuming a resonant level model we exactly solve. Moreover, the result of the analytical formulation of the problem suggests an unusual effect of thermal enhancement of the fringes that we explain analytically and verify numerically. We propose also, the SGM of the Seebeck coefficient of a QPC. Here again, we give the analytical decay law of the fringes and discuss the Cuttler-Mott formula of thermopower. To finish, we look at the statistics of thermopower in chaotic cavities. We give the exact expression of the probability density function of the Seebeck coefficient and discuss the energy dependence of this probability distribution.Dans cette thèse, on s'intéresse au transport quantique des électrons dans des nano-systèmes et des cavités chaotiques . En particulier, on apporte dans un premier temps la base théorique qui permet d'expliquer les expériences de microscopie à effet de grille dans des contacts quantiques ponctuels

Thermoelectric transport in quantum point contacts and chaotic cavities (thermal effects and fluctuations)

Dans cette thèse, on s'intéresse au transport quantique des électrons dans des nano-systèmes et des cavités chaotiques. En particulier, on apporte dans un premier temps la base théorique qui permet d'expliquer les expériences de microscopie à effet de grille dans des contacts quantiques ponctuels. Dans ces expériences, on étudie la conductance d'un contact quantique ponctuel (QPC). À l'aide d'une pointe chargée d'un AFM, quelques nanomètres au dessus d'un gaz bidimensionnel d'électrons, on crée une région de déplétion de la charge électronique. Cette déplétion modifie la conductance du QPC et permet de tracer en changeant la position de la pointe chargée, des figures de franges d'interférence espacées de la moitié de la longueur d'onde de Fermi. En se basant sur des constatations numériques obtenues à l'aide de programmes écrits en utilisant des algorithmes de fonctions de Green récursives, on propose un modèle simple que l'on résout exactement.Ce modèle nous permet de prévoir un effet contre intuitif d'accroissement des franges d'interférences avec la temperature. Dans une deuxième partie, on s'intéresse aux fluctuations du coefficient Seebeck d'une cavité chaotique. On se base sur la theorie des matrices aléatoires afin d'obtenir la probabilité de distribution du coefficient Seebeck dans le cas où la matrice de diffusion de la cavité est uniformément distribuée selon les ensembles circulaires de Dyson. On propose dans cette démarche une procédure de décimation-renormalisation afin de réduire les degrés de liberté de la cavité. Le résultat obtenu montre une singularité de la distribution et un coefficient Seebeck bornéPARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF