General(ized) Hartman effect

Abstract

In this letter we prove explicitly that if Hartman effect exists for an arbitrary `unit cell' potential, then it also exist for a periodic system constructed using the same `unit cell' potential repeatedly. We further show that if Hartman effect exists, the tunneling time in the limiting case of a sufficiently thick `unit cell' potential is same as that of its periodic system. This is true for any arbitrary value of the intervening gap between the consecutive `unit cell' of the periodic system. Thus generalized Hartman effect always occurs for a general potential constructed using multiple copies of single potential which shows Hartman effect.