Coherent Transport in Two-Dimensional Disordered Potentials under Spatially Uniform SU(2) Gauge Fields

We study interference effects in the dynamics of a spin $1/2$ particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.

💡 Research Summary

In this work the authors investigate quantum interference in the transport of a spin‑½ particle moving in two dimensions under the combined influence of a spatially uniform non‑Abelian SU(2) gauge field and a short‑range random potential. The clean Hamiltonian is written as ˆH₀=(ˆp+ˆA)²/2m with ˆA=M·σ, where the 2×3 matrix M can be reduced by spatial and spin rotations to two parameters: a strength κ and an angle η that interpolates between pure Rashba (η=π/4) and pure Dresselhaus (η=0) spin‑orbit couplings. Diagonalising the spin part yields two energy branches E±(k) that form anisotropic Fermi contours depending on η.

The system is initialized in a spin‑polarized plane wave on the (+) branch. Using split‑step numerical simulations averaged over 4000 disorder realizations, the authors compute the momentum distribution n(k,t) for times ranging from a few scattering times τ up to the diffusive regime. In the weak‑disorder limit (mean free path ℓ≈10 Lκ) they observe two hallmark features: (i) a conventional coherent back‑scattering (CBS) dip at –k₀ on the same branch, caused by destructive interference of time‑reversed paths and a π Berry phase; (ii) a transient peak on the opposite (–) branch, displaced from the exact back‑scattering direction by a small angle δθ≈0.08 rad, i.e. located at –k₀–2κₓ. The peak appears only at short times (t∼τ) and decays as the system equilibrates between the two branches.

To explain the offset, the authors perform a non‑Abelian gauge transformation ˆU=exp(iκₓxσ₁). In the transformed frame the x‑component of the gauge field disappears, the Hamiltonian becomes that of a spin‑less particle plus a residual term ˆH_A that couples the spin states with strength ∝sin²η. For η=0 the residual term vanishes, the transformed system respects T²=+1 time‑reversal symmetry, and a CBS peak (instead of a dip) appears at –k₀–2κₓ. Transforming back to the original frame reproduces the observed offset. When η≠0, ˆH_A acts as a perturbation that induces dephasing, turning the CBS peak into a transient feature that decays exponentially with a characteristic time τ_γ.

The dephasing time is derived analytically using a diagrammatic Cooperon (maximally‑crossed) approach. The Bethe‑Salpeter equation for the Cooperon yields γ₀Π_C(q,ω)≈1+iτω−Dτ(q+2κₓ)²−τ/τ_γ, where D is the diffusion constant and τ_γ=τ/