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4 - The Klein paradox and chiral tunneling
Mikhail I. Katsnelson, Radboud Universiteit Nijmegen
Book:

The Physics of Graphene

Published online:

24 May 2020

Print publication:

19 March 2020, pp 77-107
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Summary

Starting from a detailed explanation of Klein paradox of relativistic quantum mechanics, we consider a motion of massless Dirac fermions through potential barriers. It is shown that chiral properties of these particles guarantee a penetration through arbitrarily high and broad potential barriers. The role of this phenomenon (chiral tunneling) for graphene physics and technology is explained. We discuss analogy between electronic optics of graphene and optical properties of metamaterials, especially, Veselago lensing effect for massless Dirac fermions. Chiral tunneling in bilayer graphene is discussed.

Pure point spectrum for the Maryland model: a constructive proof
SVETLANA JITOMIRSKAYA, FAN YANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 1 / January 2021

Published online by Cambridge University Press:

09 August 2019, pp. 283-294

Print publication:

January 2021
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We develop a constructive method to prove and study pure point spectrum for the Maryland model with Diophantine frequencies.

Discrete Tracy–Widom operators
Part of
- Special classes of linear operators
Gordon Blower, Andrew McCafferty
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 3 / October 2009

Published online by Cambridge University Press:

23 September 2009, pp. 545-559
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Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. We consider discrete Tracy–Widom operators and give sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equation and the Fourier transform of Mathieu's equation.