Effective Dynamics for Bloch Electrons: Peierls Substitution and Beyond
By Gianluca Panati, Herbert Spohn, Stefan Teufel. 2002
196 citations recorded by the source corpus.
AbstractWe consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, φ(ɛx), and vector potential A(ɛx), with xℝd and ɛ≪1. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of L2(ℝd) and an effective Hamiltonian governing the evolution inside this subspace to all orders in ɛ. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/26cd3f1588a241ff150c1c2052ad38cd0f65f0f1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Berry phase effects on electronic properties (2009, background): “In this section we present the general theory of electron dynamics in slowly perturbed crystals (Panati et al., 2003; Shindou and Imura, 2005; Sundaram and Niu, 1999).”
- Triviality of Bloch and Bloch–Dirac Bundles (2006, methodology): “Acknowledgments. I am gratefully indebted with H. Spohn and S. Teufel for suggesting to me to investigate this problem during the preparation of [ PST3 ], and for many useful discussions.”