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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

The Anderson Transition in Two-Dimensional Ultracold Gases

David A. W. Hutchinson, Ehsan Arabahmadi, Dániel Schumayer, Maarten D. Hoogerland, Benoît Grémaud, Christian Miniatura

Published Aug 4, 2024• 0 citations
Publisher

Abstract

We study Anderson localization in two-dimensional, disordered, spin-orbit systems belonging to the symplectic symmetry class. The critical exponent and mobility edge of the metal-insulator transition are obtained via finite-time analysis of the coherent backscattering width. © 2024 The Author(s)
DOI
10.1109/cleo-pr60912.2024.10676797

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Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation symmetry is broken. The critical exponent $\ensuremath{\nu}$ that characterizes the diverging localization length and the bulk multifractal scaling exponents that characterize the amplitudes of the critical wave functions at the metal-insulator transition do not depend on the topological nature of the insulating state, i.e., whether it is topologically trivial (ordinary insulator) or nontrivial (a Z2{\mathbb{Z}}_{2}Z2​ insulator supporting a quantum spin Hall effect). This is not true of the boundary multifractal scaling exponents, which we show (numerically) to depend on whether the insulating state is topologically trivial or not.
We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.
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We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models that take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases obtained in the moderate interaction regime.