Inter-band tunneling near the merging transition of Dirac cones

Abstract

Motivated by a recent experiment in a tunable graphene analog [L. Tarruell et al., Nature 483, 302 (2012)], we consider a generalization of the Landau-Zener problem to the case of a quadratic crossing between two bands in the vicinity of the merging transition of Dirac cones. The latter is described by the so-called universal hamiltonian. In this framework, the inter-band tunneling problem depends on two dimensionless parameters: one measures the proximity to the merging transition and the other the adiabaticity of the motion. Under the influence of a constant force, the probability for a particle to tunnel from the lower to the upper band is computed numerically in the whole range of these two parameters and analytically in different limits using (i) the Stueckelberg theory for two successive linear band crossings, (ii) diabatic perturbation theory, (iii) adiabatic perturbation theory and (iv) a modified Stueckelberg formula. We obtain a complete phase diagram and explain the presence of unexpected probability oscillations in terms of interferences between two poles in the complex time plane. We also compare our results to the above mentioned experiment.

14 pages, 19 figures, accepted in Phys. Rev. A

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• The electronic properties of graphene
• Merging of Dirac points in a two-dimensional crystal
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
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• Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry
• Artificial graphenes: Dirac matter beyond condensed matter
• Signatures of merging Dirac points in optics and transport
• Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices
• Zhu-Nakamura theory and the superparabolic level-glancing models
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• Analytical Results for the Dynamics of Parabolic Level-Crossing Model
• Semiclassical Lattice effects on interband tunneling of a two-state system
• Correspondence between a shaken honeycomb lattice and the Haldane model
• Nonadiabatic transition at a band-touching point