Dynamics of spin relaxation in finite-size two-dimensional systems: An exact solution

Abstract

We find an exact solution for the problem of electron spin relaxation in a two-dimensional (2D) circle with Rashba spin-orbit interaction. Our analysis shows that the spin relaxation in finite-size regions involves three stages and is described by multiple spin relaxation times. It is important that the longest spin relaxation time increases with the decrease in system radius but always remains finite. Therefore, at long times, the spin polarization in small 2D systems decays exponentially with a size-dependent rate. This prediction is supported by results of Monte Carlo simulations.

Spin dynamics of cold fermions with synthetic spin-orbit coupling

“…[7]. This corresponds to n = (0, 0, 1), q = (q, 0, 0), and B = (B, 0, 0), which translates to the following helicoidal structure [26][27][28][29] of the transformed Zeeman field…”

Decay of persistent spin helix due to the spin relaxation at boundaries

“…It has been shown by us recently [9][10][11] that the system boundaries significantly modify the dynamics of process. For example, we have demonstrated 10 that in finite size 2D systems, the spin polarization density decays much slower than in the bulk and the exponential spin polarization decay rate is defined by both the system size and strength of spin-orbit interaction.…”

“…It has been shown by us recently [9][10][11] that the system boundaries significantly modify the dynamics of process. For example, we have demonstrated 10 that in finite size 2D systems, the spin polarization density decays much slower than in the bulk and the exponential spin polarization decay rate is defined by both the system size and strength of spin-orbit interaction. In finite length wires 9 and channels 11 (oriented in a specific direction), changes in the electron spin relaxation are even more pronounced: instead of relaxing to zero, the homogeneous electron spin polarization relaxes into a persistent spin polarization structure known as the spin helix [12][13][14][15] -a spin polarization configuration in which the direction of spin polarization density rotates along the wire.…”

“…In this paper, we use both spin kinetic 11 and diffusion [15][16][17][18][19] equations to investigate the dynamics of elec-tron spin polarization in semiconductor wires of finite length. Specifically, we consider dynamics of spin relaxation in one-dimensional (1D) finite length systems with Bychkov-Rashba 20 spin-orbit interaction and boundary spin relaxation.…”

“…Specifically, we consider dynamics of spin relaxation in one-dimensional (1D) finite length systems with Bychkov-Rashba 20 spin-orbit interaction and boundary spin relaxation. Since it is easier to incorporate the boundary spin relaxation into the boundary conditions for spin kinetic equations 11 , below, we use the spin kinetic equation approach first. Next, based on boundary conditions for the spin kinetic equations, we derive boundary conditions for spin diffusion equation which is easier to solve.…”