Effects of discrete topology on quantum transport across a graphene $n-p-n$ junction: A quantum gravity analogue

Abstract

In this article, we investigate the effect of next-to-the-nearest atom hopping on Klein tunnelling in graphene. An effective quantum dynamics equation is obtained based on an emergent generalized Dirac structure by analyzing the tight-binding model beyond the linear regime. We show that this structure has some interesting theoretical properties. First, it can be used to simplify quantum transport calculations used to characterize Klein tunnelling; second, it is not Chirally symmetric as hinted by previous work. Finally, it is reminiscent of theories on a space with a discrete topology. Exploiting these properties, we show that the discrete topology of the crystal lattice has an effect on the Klein tunnelling, which can be experimentally probed by measuring the transmittance through $n-p-n$ junctions. We argue that this simulates quantum gravitational analogues using graphene and we propose an experiment to perform such measurements.

9 pages, 2 figures

References in corpus (23)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Quantum interference and Klein tunneling in graphene heterojunctions
• Evidence of Klein tunneling in graphene p-n junctions
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• Very Special Relativity
• The Schwinger mechanism and graphene
• Conductance asymmetry of graphene pn junction
• High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy
• Supercritical Coulomb Impurities in Gapped Graphene
• Zero Landau level in folded graphene nanoribbons
• Modeling Klein tunneling and caustics of electron waves in graphene
• Tunable Klein-like tunneling of high-temperature superconducting pairs into graphene
• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Relativistic electron transport through an oscillating barrier: wave packet generation and Fano-type resonances
• Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions
• Testing Short Distance Anisotropy in Space
• Chiral tunneling in single layer graphene with Rashba spin-orbit coupling: spin currents
• Klein Bound States in Single-Layer Graphene
• Plunging in the Dirac sea using graphene quantum dots
• Klein Paradox in Chaotic Dirac Billiards

Cited by in corpus (7)

• Hunting Quantum Gravity with Analogs: the case of graphene
• Turning graphene into a lab for noncommutativity
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Effective information bounds in modified quantum mechanics
• Effects of underlying topology on quantum state discrimination
• Deformation of Nanowires and Nanotubes
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence