Husimi function for electrons moving in magnetic fields

Abstract

Husimi functions allow one to obtain sensible and useful phase space probability distributions from quantumechanical wavefunctions or classical wave fields, linking them to (semi-)classical methods and intuition. They have been used in several fields of physics, including electronic transport. We show that applying Husimi functions to ballistic electron dynamics in magnetic fields needs special consideration in order for them to obey gauge invariance and energy conservation. We therefore extend the Husimi function formalism to allow for magnetic fields making use of magnetic translation operators. We demonstrate the application in tight-binding magneto-transport calculations in graphene nanodevices, highlighting connections with Klein tunneling. In continuation of recent work, with this paper we further pave the way for using the Husimi function to unravel quantum transport phenomena in nanodevices.