General relation between the group delay and dwell time in multicomponent electron systems

Abstract

For multicomponent electron scattering states, we derive a general relation between the Wigner group delay and the Bohmian dwell time. It is found that the definition of group delay should account for the phase of the spinor wave functions of propagating modes. The difference between the group delay and dwell time comes from both the interference delay and the decaying modes. For barrier tunneling of helical electrons on a surface of topological insulators, our calculations including the trigonal-warping term show that the decaying modes can contribute greatly to the group delay. The derived relation between the group delay and the dwell time is helpful to unify the two definitions of tunneling time in a quite general situation.

Valley filtering and valley-polarized collective modes in bulk graphene monolayers

“…Under the scattering boundary condition and the continuity of wave function, the transmission probability T τ (E, k y ) can be calculated numerically by means of the scattering matrix method. [84,85] At a low temperature T K (in unit of E 0 /k B ) and Fermi energy E F , the valley-resolved ballistic conductance G τ (E F ) can be expressed in terms of the transmission probability T τ (E, k y ),…”

Tunneling time and transmission properties in strained graphene with a time-oscillating potential

“…The dwell time, t , d represents the time a particle spends in the barrier region, regardless of whether it is ultimately reflected or transmitted [35]. Recently, many studies were carried out on the group delay time and the dwell time in different structures [35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Zhai and Lu theoretically studied the relation between the dwell and the group delay time for helical electrons in the topological insulator barrier [40].…”

“…Recently, many studies were carried out on the group delay time and the dwell time in different structures [35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Zhai and Lu theoretically studied the relation between the dwell and the group delay time for helical electrons in the topological insulator barrier [40]. They showed that in this structure the difference between the dwell and the group delay time comes from the evanescent modes.…”