Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

Abstract

We obtain the spin-orbit interaction and spin-charge coupled transport equations of a twodimensional heavy hole gas under the influence of strain and anisotropy. We show that a simple two-band Hamiltonian can be used to describe the holes. In addition to the well-known cubic hole spin-orbit interaction, anisotropy causes a Dresselhaus-like term, and strain causes a Rashba term. We discover that strain can cause a shifting symmetry of the Fermi surfaces for spin up and down holes. We predict an enhanced spin lifetime associated with a spin helix standing wave similar to the Persistent Spin Helix which exists in the two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit interactions. These results may be useful both for spin-based experimental determination of the Luttinger parameters of the valence band Hamiltonian and for creating long-lived spin excitations.PACS numbers: 72.25. Dc, 73.63.Hs Systems with spin-orbit interactions have generated great academic and practical interest [1-5] because they allow for purely electric manipulation of the electron spin [6][7][8], which could be of use in areas ranging from spintronics to quantum computing. However spin-orbit interactions have also the undesired effect of causing spin decoherence [9]. Recently a new mechanism by which a system can sustain both strong spin-orbit interactions and long spin relaxation times has been proposed [10]. In properly tuned systems a non-decaying spin density standing wave can be excited. This Persistent Spin Helix (PSH) has been observed through spin transient experiments in electron doped GaAs quantum wells. [11,12] In electron doped samples the PSH occurs when the Rashba and Dresselhaus spin-orbit interaction strengths are tuned to match each other. At equal strength the spin dynamics conserve an SU (2) triplet of spin operators, two of which describe spin standing waves, while the third describes a uniform spin density that is selected and preserved by the tuned spin-orbit interaction. The triplet's infinite lifetime is obtained by tuning the spinorbit interaction to have a constant phase independent of electron momentum, in which case the electron spin structure is independent of momentum and conserved under scattering. In particular, the Rashba and linear Dresselhaus terms are proportional to k − = k x − ık y and to k + = k x + ık y respectively, so when they are at equal strength the total spin-orbit interaction has constant phase, producing long-lived spin excitations.The experimental discovery of the PSH in the 2-D electron gas raises the question of whether it exists in other systems. Recently one of us predicted that tuned topological insulators can host PSHs with very long lifetimes [13]. Here we examine 2-D hole gases under strain, calculate the spin orbit interaction of the heavy holes, and find Rashba and Dresselhaus-like terms caused respectively by applied strain and anisotropy. When fine-tuned properly the spin orbit term has constant phase, producing long-lived spin helices aligned with the strai...

Spin response to localized pumps: Exciton polaritons versus electrons and holes

“…However, unlike polaritons, they possess real spin and therefore must reverse their spin dynamics when their momentum is rotated by 180 degrees. Moreover, in holes (without strain or anisotropy 10,11 ) rotating the momentum by 60 degrees also reverses the spin dynamics. This is a consequence of the crystal symmetry, in combination with the four-fold degeneracy of the valence band.…”

Conserved spin quantity in strained hole systems with Rashba and Dresselhaus spin-orbit coupling

“…Here, we follow Ref. [20]. Thus the potentials b and d are positive whereas a can be positive or negative.…”

“…We note that there are discrepancies in the perturbative determination of the coefficients b 8v8v i as outlined in Appendix B 2. Furthermore, the effect of strain is described by the BirPikus strain Hamiltonian H S [20,29]:…”

“…In Ref. [20], the PSH was found in the presence of finite strain and Rashba SOC where the condition for the Luttinger parameters is restricted by a different, however, also unusual condition γ 2 = −γ 3 .…”

“…[20,21]. However, these publications presuppose materials with strongly restricted and unusual band structures.…”