Finite size effects, super-and sub-poissonian noise in a nanotube connected to leads

The injection of electrons in the bulk of carbon nanotube which is connected to ideal Fermi liquid leads is considered. While the presence of the leads gives a cancellation of the noise cross-correlations, the auto-correlation noise has a Fano factor which deviates strongly from the Schottky behavior at voltages where finite size effects are expected. Indeed, as the voltage is increased from zero, the noise is first super-poissonian, then sub-poissonian, and eventually it reaches the Schottky limit. These finite size effects are also tested using a diagnosis of photo-assisted transport, where a small AC modulation is superposed to the DC bias voltage between the injection tip and the nanotube. When finite size effects are at play, we obtain a stepwise behavior for the noise derivative, as expected for normal metal systems, whereas in the absence of finite size effects, due to the presence of Coulomb interactions, a smoothed staircase is observed. The present work shows that it is possible to explore finite size effects in nanotube transport via a zero frequency noise measurement

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: I. Spectral properties

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when $K_c>1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunnel density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength

Etudes des effets de taille finie et de l'écrantage causé par une pointe de STM dans les liquides de Lüttinger

This thesis takes place in the field of condensed matter. More precisely, we focus on the finite size effects and the screening effects caused by a STM tip in a quantum wire. For that, we use, first, the Luttinger liquid theory, which allows to describe strongly correlated systems and secondly, the Keldysh formalism, which is necessary to treat the out-of-equilibrium systems. For these studies, we consider, the current, the noise and the conductance.The noise presents a non-poissonian behaviour, when finite size effects appear. Through the photo-assisted transport, it is shown that those effects hide the effects of the Coulomb interactions. Considering the proximity between the STM tip, used as a probe or as an injector, and a quantum wire, screening effects appear. We can conclude that they play a similar role to those of Coulomb interactions.Cette thèse s'inscrit dans le domaine de la physique mésoscopique. Plus particulièrement, on s'est intéressé aux effets de taille finie et aux effets de l'écrantage causé par une pointe de STM dans un fil quantique, ceci à travers les comportements du courant, du bruit non-symétrisé et de la conductance. Ces études reposent sur, d'une part, la théorie des liquides de Luttinger qui permet de décrire les systèmes 1D d'électrons fortement corrélés et d'autre part, le formalisme Keldysh permettant de considérer des situations hors équilibre. Le bruit présente un comportement non poissonien, résultant des effets de taille finie. A travers le transport photo-assisté, il est également montré que ces effets masquent ceux des interactions coulombiennes. En considérant la proximité entre la pointe de STM, qui sert de sonde comme d'injecteur d'électrons, et un fil quantique, des effets d'écrantage apparaissent. Il est montré qu'ils jouent un rôle similaire à ceux des interactions coulombiennes

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: II. Transport properties

International audienceWe study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations non perturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the amplitude of the tunnel transfer: the tunnel current is strongly reduced by the presence of screening. The zero-frequency noise is modified in a similar way, but the Fano factor remains unchanged. We also consider the effect of the screening on the asymmetry of the finite-frequency non-symmetrized noise and on the conductance

Majorana fermions in honeycomb lattices

We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a one-dimensional chain, for which the existence of Majorana fermions has been extensively discussed. Consequently we can find the conditions for the emergence of Majorana fermions in such a ribbon for particular values of the chemical potential such as the top or the bottom of the band, and the Van Hove singularities, and relate the existence of Majoranas to a band inversion in the bulk band structure. Moreover we find that similar situations arise in anisotropic lattices and we give some examples which show the formation of Majorana fermions in these structures