Spin-Orbit Interaction in Symmetric Wells with Two Subbands

Abstract

We investigate the spin-orbit (SO) interaction in two-dimensional electron gases in quantum wells with two subbands. From the 8 8 Kane model, we derive a new intersubband-induced SO term which resembles the functional form of the Rashba SO but is nonzero even in symmetric structures. This follows from the distinct parity of the confined states (even or odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new SO coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new SO term gives rise to a nonzero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy (" F ) and can induce an unusual Zitterbewegung with cycloidal trajectories without magnetic fields. The rapidly developing field of spintronics has generated a great deal of interest in spin-orbit (SO) coupling in semiconductor nanostructures [1]. For an n-doped zincblende semiconductor quantum well with only the lowest subband occupied, i.e., in a strictly 2D situation, there are two main contributions to the interaction of the spin and orbital degrees of freedom of electrons. One contribution is the Dresselhaus term, which results from the lack of inversion symmetry of the underlying zinc-blende lattice [2] and is to lowest order linear in the crystal momentum [3]. This linearity is shared by the other contribution known as the Rashba term [4], which is due to structural inversion asymmetry and can be tuned by an electric gate across the well [5]. These two contributions can lead to an interesting interplay in spintronic systems [6].In this Letter we consider yet another type of electronic SO coupling which, as we show, occurs in III-V (or II-VI) zinc-blende semiconductor quantum wells with more than one subband. We derive a new intersubband-induced SO interaction which resembles that of the ordinary Rashba model; however, in contrast to the latter, ours is nonzero even in symmetric structures (Fig. 1). We self-consistently determine the strength of this new SO coupling for realistic single and double wells and find it comparable to the Rashba constant [Figs. 2(a) and 2(b)]. We have investigated the spin-Hall effect and the dynamics of spinpolarized electrons due to this new SO term. We find (i) a nonzero ballistic spin-Hall conductivity which changes sign as a function of " F and (ii) an unusual Zitterbewegung [7] with cycloidal trajectories without magnetic fields (Fig. 3). As derived below, for a symmetric well with two subbands our 4 4 electron Hamiltonian is

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

“…(13) into Eq. (14) we obtain the following exact result (up to the order indicated) for the Hamiltonian…”

“…As shown experimentally, the Rashba coupling strength can be tuned via proper gating of the structure 12,13 , which makes the Rashba interaction very appealing for potential technological applications involving spin control. More recently, yet a new type of spin-orbit interaction has been found in symmetric two-dimensional quantum structures with two subbands: the inter-subbandinduced spin-orbit coupling 14,15 . Interestingly, this new spin-orbit interaction gives rise to non-zero intrinsic spin Hall effect 16 .…”

Toward high-frequency operation of spin lasers

“…[87][88][89] Our own implementation of the k·p method in this work has been previously tested in calculating the luminescence spectra in δ-doped GaAs, 90 confirming experimental and theoretical electronic structure for GaAs QWs, 91 and (Al,Ga)N/GaN superlattices, 92 identifying fully spin-polarized semiconductor heterostructures, based on (Zn,Co)O, 93 as well exploring polytypic systems consisting of zinc-blende and wurtzite crystal phases in the same nanostructure. 94,95 Before considering confined systems, it is important to investigate the corresponding bulk crystal structure and construct the functional form of the Hamiltonian.…”

Acoplamento spin-órbita inter-subbanda em heteroestruturas semicondutoras

“…Como recentemente proposto [1,2], ao obter o hamiltoneano de um sistema com duas sub-bandas na aproximação de massa efetiva, constata-se a presença de um acoplamento inter-subbanda que não se anula mesmo em heteroestruturas simétricas. Apresentamos aqui as deduções teóricas que levaramà proposição desse novo acoplamento e mostramos o cálculo autoconsistente da intensidade do acoplamento e a comparamos com a intensidade do acoplamento Rashba, já amplamente estudado.…”

“…Recentemente foi proposto por Bernardes et al [1,2] um novo tipo de acoplamento spin-órbita em estruturas semicondutoras com mais de um estado confinado na direção de 4 Segundo a nomenclatura difundida naárea, a palavra bulk -do inglês, 'volume' -denota um material uniforme, de tamanho macroscópico, sem interfaces.…”