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Two-Particle Collisional Coordinate Shifts and Hydrodynamic Anomalous Hall Effect in Systems without Lorentz
1Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA.
Physical Review Letters
|December 15, 2018
Summary
Electrons in crystals shift coordinates during two-particle collisions. This shift, influenced by electron wave functions, impacts the anomalous Hall conductivity in Weyl fermions.
Area of Science:
- Condensed matter physics
- Solid-state physics
- Quantum mechanics
Background:
- Electrons in crystalline solids exhibit complex behaviors governed by quantum mechanics.
- Understanding electron interactions is crucial for predicting material properties.
- Bloch wave functions describe electron states in periodic potentials.
Purpose of the Study:
- To derive a general, gauge-invariant expression for the coordinate shift experienced by electrons during two-particle collisions in crystals.
- To investigate the application of this theory to Weyl fermions in three spatial dimensions.
- To determine the contribution of these coordinate shifts to the anomalous Hall conductivity.
Main Methods:
- Derivation of a gauge-invariant expression for two-particle coordinate shifts.
- Analysis of electron collisions within arbitrary band structures and interaction potentials.
- Application to Weyl fermions in 3D space.
Main Results:
- Electrons in two-particle collisions within a crystal experience a coordinate shift.
- This shift is dependent on single-particle Bloch wave functions.
- The derived expression for the coordinate shift is gauge-invariant and broadly applicable.
- Coordinate shifts contribute to the anomalous Hall conductivity of Weyl fermions.
Conclusions:
- The study provides a fundamental theoretical framework for understanding electron collision-induced coordinate shifts in crystals.
- The findings elucidate a new mechanism contributing to the anomalous Hall conductivity, particularly in systems like Weyl semimetals.
- This work offers insights into electron dynamics and transport phenomena in condensed matter systems.
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