Optical field modulation on the group delay of chiral tunneling in graphene

Abstract

The influences of optical fields on the group delay of chiral tunneling in graphene are investigated in real time using the finite-difference time-domain method. The group delay of tunneling electrons irradiated by an optical field is significantly different from that observed in traditional quantum tunneling. We found that when the barrier width increases, the group delay becomes constant for the reflected wave packet, but increases linearly for the transmitted wave packet. This peculiar tunneling effect can be attributed to current leakage in a time-dependent barrier generated via the optical Stark effect.Quantum tunneling time has received much attention since MacColl pointed out that it takes no approximate time ([1]; [2, 3] and references therein). The question of how long it takes an electron to tunnel through a potential barrier is still replete with controversy. The debates center around the definition of tunneling time and its exact physical meaning. Hartman [4] calculated the group delay or phase time and found that the group delay τ g becomes constant, while the barrier length increases. Thus, with a wider barrier, superluminal group velocities can be observed. Recently, Winful [3,5,6] proposed that the group delay in tunneling represents a lifetime of stored energy escaping through both sides of the barrier and does not represent a transit time. However, a unlimited group velocity is not a meaningful concept in tunneling and does not imply superluminality.

Non-perturbative effects of laser illumination on the electrical properties of graphene nanoribbons

“…Further studies focused on the optical response [17,19] as well as other interesting issues [20,21,22,23]. Recently, the possibility of inducing topologically protected states by laser illumination in semiconductors [24] and both in monolayer [25,26] and bilayer [27] graphene has become a hot field [28,29] with an impact on other areas such as condensates [30] and photonic crystals, where experiments are already available [31].…”

Group delay of electromagnetic pulses through multilayer dielectric mirrors combined with gravitational wave

“…Liu et al recently studied the effect of the electromagnetic fields of the group delay of electrons and found that the group delay of the transmitted wave packet increases linearly with barrier length for the transmitted wave packet 16 . This peculiar tunneling effect is attributed to current leakage in a time-dependent barrier generated via the electromagnetic fields 13,16 . If the quantum fluctuation or the zero-point field is considered, all potential barriers are combined with electromagnetic fields.…”

“…This result can be explained by the variations of the photonic bandgap attributed to the GW. Similar to the electron tunnelling in a time-dependent barrier 13,16 , the variations of the photonic bandgap will result in an additional leak photon current. Given that the amplitude of the additional leakage current attributed GW is quite small, for the case of a small number of MDM periods, e.g., n M DM < 15, the tunneling current is significantly larger than the additional leakage current and is unaffected by the extrinsic GW [see Fig.…”

“…The behavior of Dirac particles is found to be the same as that in nonrelativistic quantum mechanics. Liu et al recently studied the effect of the electromagnetic fields of the group delay of electrons and found that the group delay of the transmitted wave packet increases linearly with barrier length for the transmitted wave packet 16 . This peculiar tunneling effect is attributed to current leakage in a time-dependent barrier generated via the electromagnetic fields 13,16 .…”

Ballistic collective group delay and its Goos–Hänchen component in graphene

“…They describe the tunneling speed through a barrier in different aspects, and are both of paramount importance for solid-state devices working at high frequencies [6]. Recently, as graphene rises as a star material in condensed matter physics, extensive efforts [7][8][9][10][11][12][13] have been devoted to the investigations of group delay and/or dwell time in it.…”