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Register a new userQuantum transport of atomic matterwaves in anisotropic 2D and 3D disorder
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Authors
Marie Piraud
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The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich of counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic 2D and 3D speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate a disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalize energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are revelant for current matter wave experiments, where the disorder is created with a laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.
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We study quantum transport in anisotropic 3D disorder and show that non rotation invariant correlations can induce rich diffusion and localization properties. For instance, structured finite-range correlations can lead to the inversion of the transport anisotropy. Moreover, working beyond the self-consistent theory of localization, we include the disorder-induced shift of the energy states and show that it strongly affects the mobility edge. Implications to recent experiments are discussed.
We describe non-conventional localization of the midband E=0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to display multifractal fluctuations, having many sparse peaks, and by scaling the participation ratio we obtain its disorder-dependent fractal dimension $D_{2}$. A logarithmic average correlation function grows as $g(r) sim eta ln r$ at distance $r$ from the maximum amplitude and is consistent with a typical overall power-law decay $|psi(r)| sim r^{-eta}$ where $eta $ is proportional to the strength of off-diagonal disorder.
A random lattice model with dilute interlayer bonds of density $p$ is proposed to describe the underdoped high--$T_c$ cuprates. We show analytically via an appropriate perturbation expansion and verify independently by numerical scaling of the conductance that for any finite $p$ the states remain extended in all directions, despite the presence of interlayer disorder. However, the obtained electronic transport is highly anisotropic with violent conductance fluctuations occuring in the layering direction, which can be responsible for the experimentally observed metallic in-plane and semiconducting out-of-plane resistivity of the cuprates.
We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed back-scattering are formed in this model in the direction of the lines. The system reveals Levy-flight transport in stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent $T$-matrix approximation.
Effect of short-range disorder on the excited states of the exciton is studied. Disorder causes an obvious effect of broadening. Microscopically, an exciton, as an entity, is scattered by the large-scale disorder fluctuations. Much less trivial is that short-scale fluctuations, with a period of the order of the Bohr radius, cause a well-defined down-shift of the exciton levels. We demonstrate that this shift exceeds the broadening parametrically and study the dependence of this shift on the orbital number. Difference of the shifts for neighboring levels leads to effective renormalization of the Bohr energy. Most remarkable effect is the disorder-induced splitting of S and P exciton levels. The splitting originates from the fact that disorder lifts the accidental degeneracy of the hydrogen-like levels. The draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.
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