Unusual spin-orbit control in AlInAs/GaInAs triple wells triggered by band crossing and anticrossing

Abstract

Additional orbital degrees of freedom in multiband quantum systems may offer more intriguing possibilities for spin-orbit (SO) control. Here we explore the Rashba and Dresselhaus SO couplings in realistic AlInAs/GaInAs triple wells subjected to top $({V}_{\mathrm{T}})$ and back $({V}_{\mathrm{B}})$ gate potentials, allowing for flexible triple-occupancy control for electrons. By performing a self-consistent Poisson-Schr\"odinger calculation, we determine all the relevant Rashba (Dresselhaus) SO terms of both intraband ${\ensuremath{\alpha}}_{\ensuremath{\nu}}$ $({\ensuremath{\beta}}_{\ensuremath{\nu}})$ and interband ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}$ $({\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}\ensuremath{\nu}})$ types. For a structurally symmetric triple well, we achieve a crossing of energy levels between the first and second subbands and sequentially an anticrossing between the second and third subbands, accompanied with a double band swapping, simply via adjusting ${V}_{\mathrm{B}}$. As a consequence, when ${V}_{\mathrm{B}}$ varies, an emerging interchange of the first-subband ${\ensuremath{\alpha}}_{1}$ $({\ensuremath{\beta}}_{1})$ and second-subband ${\ensuremath{\alpha}}_{2}$ $({\ensuremath{\beta}}_{2})$ SO terms, and of ${\ensuremath{\alpha}}_{2}$ $({\ensuremath{\beta}}_{2})$ and ${\ensuremath{\alpha}}_{3}$ $({\ensuremath{\beta}}_{3})$ respectively for the second and third subbands, i.e., double SO interchange, occurs, greatly fascinating for selective SO control among distinct subbands in spintronic devices. Further, near the two-band swapping points, across which electron transfer among the three local wells (triple well) takes place, detailed interchanging features of nonlinear SO control are also contrasting. Remarkably, in addition to Rashba terms, we also realize a wide-range control of Dresselhaus couplings, which are usually immune to electrical manipulation. Regarding the interband Rashba and Dresselhaus SO contributions, ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}\ensuremath{\nu}}$ exhibit either a resonant behavior or a steplike jump across band-swapping points, depending on the parity and spatial distribution of electron wave functions. By varying the barrier height of the two inner barriers in the triple-well configuration, dependence of relevant SO terms on engineered structures, which are either structurally symmetric or asymmetric, is also discussed. Interestingly, in the latter asymmetric case, we realize a seemingly symmetric configuration by adjusting ${V}_{\mathrm{B}}$, in which ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ essentially vanish while ${\ensuremath{\alpha}}_{3}$ is nonzero, providing a handle for suppressing electron spin relaxation of chosen subbands. Our results will stimulate more experiments probing unusual SO features in multiband and multiwell quantum systems and act as a guide for more proposals designed for spintronic devices.