Absence of Weak Localization on Negative Curvature Surfaces

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Geometry

Background:

• Anderson localization describes the absence of diffusive transport in disordered systems due to quantum interference.
• In two dimensions, disorder is generally believed to induce localization of all states at sufficient length scales.
• Quantum interference effects are crucial in understanding electron transport in disordered materials.

Purpose of the Study:

• To investigate mechanisms for disrupting Anderson localization in two dimensions.
• To explore the role of manifold curvature in quantum interference and transport phenomena.
• To determine if negative curvature can prevent weak localization.

Main Methods:

• Theoretical analysis of quantum interference and particle trajectories on curved manifolds.
• Calculation of the Cooperon in hyperbolic space to assess weak-localization corrections.
• Investigation of the impact of negative and mixed curvature on diffusive transport.

Main Results:

• Negative curvature manifolds exhibit an infrared cutoff for self-returning paths, suppressing localization.
• Hyperbolic space leads to a proliferation of quantum trajectories, diminishing interference effects and restoring diffusion.
• Intermittency in variable curvature manifolds causes hyperbolic regions to dominate, arresting weak localization.

Conclusions:

• Manifold curvature offers a novel mechanism to counteract Anderson localization in two dimensions.
• Negative curvature and specific mixed-curvature surfaces can prevent weak localization, potentially relevant for 2D materials and disordered films.
• The findings suggest experimental verification using quantum simulators and offer insights into realistic material properties.