Hartman effect in presence of Aharanov–Bohm flux

Abstract

The Hartman effect for the tunneling particle implies the independence of group delay time on the opaque barrier width, with superluminal velocities as a consequence. This effect is further examined on a quantum ring geometry in the presence of Aharonov-Bohm flux. We show that while tunneling through an opaque barrier the group delay time for given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux. The Hartman effect is thereby extended beyond one dimension and in the presence of Aharonov-Bohm flux.

Hartman effect and nonlocality in quantum networks

“…Since the stored energy in the evanescent field decreases exponentially within the barrier after a certain decay distances it becomes independent of the width of the barrier. The Hartman effect has been found in one dimensional barrier tunneling [18] as well as for cases beyond one dimension as in tunneling through mesoscopic rings in presence of Aharonov-Bohm flux [22]. In the current note we extend the study of phase times for branched networks of quantum wires.…”

Group delay time and Hartman effect in strained Weyl semimetals

“…Two important quantities in the dynamics of the tunneling process are the group delay time τ g , the length of time during which the wave packet peak occurs within the barrier region [3], and the dwell time, which measures the average time interval during which a particle interacts with the barrier, regardless of whether it is transmitted or reflected eventually. During the last two decades, the group delay time has been extensively studied, since this quantity is theoretically related to the density of states [4], and has practical applications in quantum networks [5] and even microelectronics [6]. The theoretical investigation on the tunneling time could be interesting for both the basic physics and the potential application of electronic devices based on topological materials such as graphene and Weyl semimetals (WSMs).…”

“…The Hartman effect can also be interpreted through the lens of quantum measurement theory in which it is argued that the the effect constitutes a case of a good precision 'weak' measurement [15]. Systems in which the Hartman effect have been theoretically studied include quantum clocks [16], the two-dimensional (2D) electron gas [17], relativistic systems [18], quantum rings with Aharonov-Bohm flux [5], symmetric double-barrier point potentials [19], and systems with multiple barriers [20][21][22][23][24][25].…”

Hartman effect in a Kane-type semiconductor quantum ring

“…A simple semi-classical derivation of the Hartman effect valid for the potential of a barrier of general shape in one dimension is presented in [13]. Bandopadhyay et al [14] verified the Hartman effect beyond one dimension and in the presence of Aharonov-Bohm flux. In another study, Bandopadhyay and Jayannavar [15] studied the phase delay time for tunnelling in the reflection mode.…”

“…The transmission across such systems has been studied in detail [20,21]. Analyses of the phase delay time in the present study are made following the method described by Bandopadhyay et al [14].…”