Stretching and breaking symmetry of the persistent spin helix in quantum transport

Abstract

As a result of relativistic transformation, electrons moving through an electric field, experience an effective magnetic field, the spin orbit (SO) field, whose direction depends on the momentum and couples to the electron spin. The SO interaction has become a versatile resource in fundamental semiconductor research and is at the heart of semiconductor spintronics. In two dimensional zinc blende structures, the Rashba and Dresselhaus SO field, are the two dominant contributions. While both are linear in momentum, the Dresselhaus SO field also possesses a cubic contribution in momentum. In this thesis, the persistent spin helix (PSH) state is investigated in transport measurements. The PSH results from balancing the strengths of the two dominant contributions to SO coupling, the Rashba parameter alpha and the renormalized Dresselhaus parameter beta. In this case the SO field is uniaxial and spins are robust against momentum scattering. Quantum corrections to conductivity serve as a convenient tool to detect this symmetry, which exhibits weak localization at the PSH symmetry point and weak antilocalization, if the PSH symmetry is broken. In the first part of this thesis we use the transition from weak antilocaliztion to weak localization to detect the PSH state. Using a top gate and back gate we demonstrate control of the Rashba SO coupling and, for the first time, tuning of the renormalized linear Dresselhaus term beta, independently of each other. This allows us to find the PSH state not just for one particular gate configuration but for a continuous set of gate configurations, where the ratio alpha/beta remains to unity but their overall strength varies. This enables a new concept, the stretchable PSH, where the length for a 2pi rotation of the spins becomes tunable. We combine the transport data with numerical self-consistent simulations and can determine all SO coefficients. Stretching of the PSH allows to convey spin polarizations over long distances of up to 25 mum, before their spin gets randomized by the cubic Dresselhaus term. Furthermore, the stretchable PSH allows to coherently control spin rotations at a fixed position. In the second part of this thesis, we break the PSH symmetry to extract the SO coefficients purely from transport experiments. We first derive a closed-form expression for the quantum corrections to the conductivity, in the vicinity of the PSH state, which includes the Rashba and linear, as well as the cubic Dresselhaus term. In symmetrically doped wafers with higher density the cubic Dresselhaus term is strong and breaks the PSH symmetry, which is characterized by the reappearance of weak antilocalization. This allows us to determine the cubic Dresselhaus term from fits to the new expression. In the second stage we tune away from the PSH symmetry and are able to extract the linear SO terms by keeping the cubic term fixed. We are thus able to unambiguously determine fundamental band structure parameters that define the Rashba and Dresselhaus SO strength. The obtained results between the two experiments are in very good agreement and compare very well with recent optical studies.