Nonadiabatic transition at a band-touching point

TL;DR

This paper investigates how quadratic and higher-order terms in low-energy Hamiltonians near band-touching points influence nonadiabatic transition probabilities, challenging the common linear approximation used in Dirac Hamiltonians.

Contribution

It demonstrates that quadratic terms cannot be neglected near band-touching points as they significantly impact transition probabilities, unlike higher-order terms which only matter away from the touching point.

Findings

Quadratic terms affect transition probabilities at the band-touching point.

Higher-order terms influence transition probabilities away from the touching point.

Conditions for oscillations in transition probability profiles are discussed.

Abstract

Low-energy Hamiltonians with a linear crossing in their energy dispersion (dubbed Dirac Hamiltonians) have recently been the subject of intense investigations. The linear dispersion is often the result of an approximation in the energy dispersion at the band-touching point in which higher order terms are discarded. In this paper, we show that, in terms of nonadiabatic transitions, by passing through a touching point, certain types of quadratic terms could not be omitted, even in the arbitrary vicinity of it, ie, quadratic terms could significantly affect the transition probability, hence the Hamiltonian is not reducible to a linear one. We further show that the presence of terms with exponents larger than two only affects the transition probability away from the touching point. In the end, we discuss conditions that may lead to the appearance of oscillations in the transition probability profile.