Implications of the Klein tunneling times on high frequency graphene devices using Bohmian trajectories

Abstract

Because of its large Fermi velocity, leading to a great mobility, graphene is expected to play an important role in (small signal) radio frequency electronics. Among other, graphene devices based on Klein tunneling phenomena are already envisioned. The connection between the Klein tunneling times of electrons and cut-off frequencies of graphene devices is not obvious. We argue in this paper that the trajectory-based Bohmian approach gives a very natural framework to quantify Klein tunneling times in linear band graphene devices because of its ability to distinguish, not only between transmitted and reflected electrons, but also between reflected electrons that spend time in the barrier and those that do not. Without such distinction, typical expressions found in the literature to compute dwell times can give unphysical results when applied to predict cut-off frequencies. In particular, we study Klein tunneling times for electrons in a two-terminal graphene device constituted by a potential barrier between two metallic contacts. We show that for a zero incident angle (and positive or negative kinetic energy), the transmission coefficient is equal to one, and the dwell time is roughly equal to the barrier distance divided by the Fermi velocity. For electrons incident with a non-zero angle smaller than the critical angle, the transmission coefficient decreases and dwell time can still be easily predicted in the Bohmian framework. The main conclusion of this work is that, contrary to tunneling devices with parabolic bands, the high graphene mobility is roughly independent of the presence of Klein tunneling phenomena in the active device region.

A corner reflector of graphene Dirac fermions as a phonon-scattering sensor

“…This observation is consistent with the above estimate and theoretical predictions in refs. 55,56 ; it shows that CRs are as fast as conventional graphene transistors (see e.g., refs. 57,58 ).

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Hallmarks of tunneling dynamics with broken reflective symmetry

“…4 V определяет яму, в которой будет локализовано состояние. В работе [19] локализация состояний продемонстрирована путем довольно сложной процедуры прямого интегрирования уравнения Шредингера с потенциалом ( ) V определяет яму, в которой будет локализовано состояние. В работе [19] локализация состояний продемонстрирована путем довольно сложной процедуры прямого интегрирования уравнения Шредингера с потенциалом ( )…”

“…It decisively matters in the localization of states of a Hamiltonian with two symmetric wells upon incorporating the interaction, which breaks the reflective symmetry. (19) for the ground and first excited level wave functions (see Table 2). Looking on them one may notify the essential contribution into the under-barrier wave function of the disturbed Hamiltonian comes from the states of the tunnel doublet of H. The contribution of more higher states of H is small, though their values are comparable to each other.…”

“…The first experimental evidence of these theoretical ideas comes from pioneering work on quantum tunneling of magnetization [16], [17]; the realization of Bose-Einstein condensates of cold atoms has simplified the observation of macroscopic quantum tunneling in all forms [18] (and Refs therein). Another feature of the tunneling effect worth to mention is that experiments in this branch put even foundations of Quantum Mechanics [20] on the test, since some of the tunneling properties in modern artificial materials like graphene [19] are naturally described within alternativethe Bohmian -interpretation of Quantum Mechanics.…”

Dirac fermion optics and plasmonics in graphene microwave devices

“…Due to the aforementioned issues with contact resistance, a more detailed analysis of cut-off frequency, power gain and other figures of merit of high speed transistors and the comparison with theoretical proposals [196], in particular concerning the dwell time [209], are beyond the scope of this thesis.…”