Transport features of electron and hole quantum wires with Rashba coupling

Abstract

[eng] This thesis studies the effects of the Rashba spin-orbit coupling on the transport properties of electron and hole quantum wires. For each case, a specific physical system is considered: the first one is a quantum wire with inhomogeneous Rashba coupling while the second is a quantum wire with homogeneous Rashba intensity and with external magnetic field; they are studied in the first (electrons) and the second (holes) parts of this work, respectively. Both systems are examples of the effects of the Rashba spin-orbit coupling on the physics of transport. In Part I, for electron systems, we study the conductance and polarization of the outgoing current for an incident unpolarized electron beam. The electron conductance of a quantum wire has a staircase dependence with energy, where each step is a conductance plateau. With the Rashba inhomogeneity a Fano dip appears at the end of each plateau, at specific energies, and we observe how the outgoing current is spin polarized. This current polarization occurs only above the first plateau, since it is due to the interference of two propagating modes with opposite spin. We also study how two conductance dips, in the first plateau, interfere when we have two tunable Rashba regions. We show how this interference evolves from crossing to anticrossing behavior when the distance between the two regions increases. Transport through evanescent states is responsible for this behavior, as we will see. Continuing Part I, we study the generalization of the Datta-Das transistor for a quasi-one-dimensional system —the original device corresponds to a purely one-dimensional system with a Rashba region attached to polarized leads and its main feature is an oscillatory behavior of the conductance with Rashba strength. In our system we observe how that sinusoidal behavior is strongly affected by the multichannel transport, i.e., transport in a quasi one-dimensional system having a transverse confinement. As a consequence, increasing the number of propagating channels the effect of spin precession is destroyed. Finishing this first part, the limit from quasi one-dimensional to two-dimensional system is considered, when the quantum wire becomes a two-dimensional electron gas with a Rashba stripe. In the hole-system study, Part II, we present calculations of the g factors for the lower conductance steps of three dimensional quantum wires. We define the g factors from the anomalous half-steps appearing in the conductance in the presence of magnetic field. Our results prove that the anisotropy of g factors for different magnetic field orientations originates in the Rashba spin-orbit coupling. We also analyze the relevance of the deformation, as the wire evolves from 3D towards a flat 2D geometry. For high enough wire deformations, the perpendicular g factors are greatly quenched by the Rashba interaction. On

the contrary, parallel g factors are rather insensitive to the Rashba interaction, resulting in a high g factor anisotropy. Finally, we study the purely onedimensional hole system.

[cat] En aquesta tesi s’estudien els efectes de l’acoblament d’esp´ı-`orbita sobre les propietats de transport de fils qu`antics d’electrons i forats. Per a cada cas s’ha considerat un sistema f´ısic diferent: per als primers (electrons) ´es un fil qu`antic amb una zona inhomog`enea d’acoblament de Rashba mentre que en els segons (forats) l’interacci´o de Rashba ´es homog`enia a l’espai on, a m´es, s’ha aplicat un camp magn`etic uniforme extern. Aix´ı la tesi est`a separada clarament en dues parts, la primera pel cas del transport electr`onic i la segona pel transport fet per forats. Els dos sistemes s´on exemples del efectes que fa l’acoblament d’esp´ı-`orbita de Rashba sobre el transport. A la Part I, per al sistema d’electrons, estudiam la conduct`ancia i la polaritzaci´o del corrent resultant quan el feix incident d’electrons ´es no polaritzat. La conduct`ancia per un fil qu`antic t´e una depend`encia escalonada amb l’energia, on cada gra´o ´es un plateau de conduct`ancia. Amb la inhomogene¨ıtat de Rashba, apareix un m´ınim de Fano al final de cada plateau a energies espec´ıfiques i, a m´es, el corrent de sortida est`a polaritzat en esp´ı. Aquest corrent polaritzat nom´es el trobam a partir d’energies del segon plateau, ja que ´es la conseq¨u`encia de la interfer`encia de dos modes propagants amb espins oposats. Tamb´e estudiam, en aquesta part, com interfereixen aquests dos m´ınims de conduct`ancia quan tenim dues zones seguides d’intearcci´o de Rashba. Observam com els dos deeps passen d’un comportament de creuament a anticreuament quan la dist`ancia entre les dues regions augmenta. Els responsables d’aquest comportament no s´on m´es que els estats evanescents. Continuant en aquesta Part I, estudiam la generalitzaci´o del transistor de Datta i Das per a un sistema quasi-unidimensional –el dispositiu original correspon a un sistema purament 1D amb una regi´o de Rashba acoblada a uns contactes polaritzats, on la seva principal caracter´ıstica ´es la del comportament oscil·latori de la conduct`ancia en funci´o de la intensitat del Rashba. En el nostre sistema observam que aquest comportament sinuso¨ıdal es veu fortament afectat pel transport multicanal, ´es a dir, transport en un sistema quasi-unidimensional el qual t´e un confinament transversal. Conseq¨uentment, augmentant el nombre de canals propagants, l’efecte de precessi´o d’esp´ı es veu destruit. Per acabar aquesta part d’electrons, es considera el l´ımit d’un sistema quasi-unidimensional a un de bidimensional, on el fil qu`antic passa a ser un gas d’electrons bidimensional amb una franja de Rashba. Per al sistema de forats, Part II, presentam c`alculs dels factors giromagn`etics per als primers escalons de la conduct`ancia per fils qu`antics tridimensionals. Definint els factors g com a mitjos escalons “an`omals” que apareixen en la conduct`ancia quan s’hi aplica un camp magn`etic extern, trobam que l’anisotropia del factors g per a diferents orientacions del camp magn`etic ´es conseq¨u`encia

de l’acoblament de Rashba. Tamb´e analitzam la rellev`ancia de la deformaci´o, quan el fil passa d’una geometria tridimensional a bidimensional. En un fil molt deformat, el factor g perpendicular disminueix fortament amb l’increment de la interacci´o de Rashba. D’altra banda, per un camp magn`etic paral·lel al fil, els factors g s´on considerablement insensibles al Rashba. Finalment, estudiam el l´ımit d’un sisema purament unidimensional pel cas de forats.