Rashba-coupling modelling for two-dimensional and high-order Rashba Hamiltonian for one-dimensional confined heavy holes

Abstract

Based on standard k·p (8 × 8) multiband Hamiltonian, we have deduced an explicit analytical expression for the Rashba-coupling parameter which clarifies its anomalous behavior for heavy holes (hh), gated in quasi-two-dimensional (Q2D) systems, by letting grow the density. Our modelling remarkable better agrees with experimental results in comparison with earlier theoretical models, while recovers the expected cubic dependence on the quasi-momentum. For quasi-one-dimensional (Q1D) hh systems, we have formally derived an effective Rashba Hamiltonian with two competitive terms on the quasi-momentum, a linear term and a cubic one as predicted from suitable approximations to the Q2D scope. The Rashba-coupling parameters also behave anomalously and qualitatively support recent experiments in core/shell nanowires. Furthermore, they exhibit an essential asymptotic discontinuity in the low density regime as a function of the lateral confinement length. For hh, we present closed schemes to accurately quote the Rashba-coupling parameters both for the Q2D and Q1D systems, which become unprecedented for holes.PACS numbers: 71.70. Ej, 73.21.Hb, 73.21.Fg, One of the biggest challenges in Spintronics [1] is to manipulate efficiently spin currents in semiconductors systems without external magnetic fields. Rashba spinorbit interaction (SOI-R) [2,3] is among the most promising mechanisms for achieve this [4][5][6][7]. SOI-R for the heavy holes (hh) case is different from that for electrons or light holes (lh). In quasi-two-dimensional (Q2D) systems, observed in experiments since 1984 [8], the SOI-R coupling Hamiltonian exhibits an atypical cubic dependence in the quasi-momentum (k 3 ) obtained by Gerchikov and Subashiev [9], and Winkler et al. [10][11][12] using group theory arguments.The long data assumption that the induced SOI-R spin splitting in Q2D systems at zero magnetic field rises with electric field, responsible for the inversion asymmetry of the confining potential, firmly validated for electrons [13], was definitely abated when the opposite was demonstrated for holes [10]. Importantly, it has been reported, both numerically and experimentally, the SOI-R coupling parameter anomalous decreasing with a non-zero electric field for Q2D hh in accumulation-layer-like single heterostructures [10,11]. Recently, Habib et al. [12] have shown interesting measurements, with a similar behavior at fixed density, but tuning the external electric field perpendicular to the Q2D gas. Notwithstanding these achievements, several features in the anomalous SOI-R coupling effect remains cumbersome and inspired us to address a complementary study.On the other hand, despite the efforts focused to study SOI-R in quasi-one-dimensional (Q1D) holes systems, due to their appealing applications and phenomenology [14][15][16][17][18][19], some relevant topics remains incomplete still or deserve further attention. SOI-R model for Q1D-hh systems suggested by Governale and Zülicke [15], and intuitively based on the behavior of the Dresselhaus term for Q...

Spin-Orbit Interactions (SOIs) related to super-symmetry and pseudo-super-symmetry: Time-reversed generators and

“…(which can well be phenomenological [26] in nature) more flexible as compared to the approximation process usually done under special relativistic ground [8] and hence speaks in favour of greater experimental viability. The present method may be useful to construct some of the recently proposed SOIs like higher-order Rashba interaction [27][28][29]. II) It generalizes Hertz's contention related to the "kinetic origin of the potential" [30] even in nonclassical interactions involving spin.…”

Electrical tuning of helical edge states in topological multilayers

“…In this work we used the eight-band k • p model including the conduction band states, the three valence bands, the explicit coupling between them and the Luttinger corrections for the effective masses [44,46,47]. This model has been successfully applied in describing the electronic and spintronic properties of low dimensional semiconductor for decades [48,51,[64][65][66][67], including the InAs/GaSb AQWs [5,6,[68][69][70][71][72][73][74][75][76][77].…”

Generating a topological anomalous Hall effect in a non-magnetic conductor

“…Since the equilibrium system is not magnetized the effect is tunable in situ by altering the magnetic field orientation. It is observable in state-of-theart hole samples, which are developing at a brisk pace, motivated in part by quantum computing applications [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], where holes are actively investigated [58][59][60], by their large spin-orbit coupling [61][62][63], interesting transport properties [64][65][66][67][68], and by unconventional properties stemming from their spin-3/2 nature [69][70][71][72][73][74][75][76][77][78][79][80][81][82]. We consider a two-dimensional hole gas grown along (113).…”