Comparing two different descriptions of the I-V characteristic of graphene: theory and experiment

Anatolii Panferov,Narine Gevorgyan,David Blaschke,Stanislav Smolyansky,S Bondarenko,V Burov,A Malakhov

doi:10.1051/epjconf/201920406008

Abstract

The formalism of the nonperturbative description of transport phenomena in graphene in the framework of the quantum kinetic equation for the Schwinger-like process is compared with the description on the basis of Zener- Klein tunneling. The regime of ballistic conductivity in a constant electric field is considered.In the latter case the interaction of carriers with electric field is described in terms of the spatial dependence of their potential energy (x-representation). The presented kinetic formalism uses an alternative method of describing the interaction with a field through the introduction of a quasimomentumP=p– (e/c)A(t), whereA(t) is the vector potential (t-representation). Both approaches should lead to the same physical characteristics of the described process.The measurement of the current in experiments is realized in static conditions determined by the potential difference between the electrodes and the distance between them. These parameters are native for the x-representation. On the contrary, in the approach based on the t-representation it is necessary to consider the situation in dynamics and introduce the effective lifetime of the generated carriers. In the ballistic regime this time depends on the distance between the electrodes.We give a detailed comparison of these two descriptions of the current and demonstrate a good coincidence with the experimental data of the alternative approach based on the t-representation. It provides a reliable foundation for the application of nonperturbative methods adopted from strong field QED, that allows one to include in the consideration more general models of the field (arbitrary polarization and time dependence) and extend the scope of the theory.

Highlights

In recent years considerable interest in a nonperturbative, dynamical description of transport phenomena in condensed matter physics was inspired by the physics of strong electromagnetic fields
The aim of this work is a comparison of the results of the strong nonperturbative kinetic approach to graphene [11, 12] with the results of other works based on the WKB-type estimations and, in the end, with experiment
We want to show that in the case of a ballistic nondissipative regime, the nonperturbative kinetic approach leads to the same results in the case of a constant electric field as the methods developed in the works [13,14,15]

Summary

Introduction

In recent years considerable interest in a nonperturbative, dynamical description of transport phenomena in condensed matter physics was inspired by the physics of strong electromagnetic fields (for example, [1] and references there). In this case there is an obvious similarity with the creation of electron-positron pair from vacuum in strong electromagnetic fields (Schwinger effect [4,5,6]). We want to show that in the case of a ballistic nondissipative regime, the nonperturbative kinetic approach leads to the same results in the case of a constant electric field as the methods developed in the works [13,14,15] This latter approach is called commonly the Landauer approximation (or the Landauer-DattaLundstrom (LDL) [16,17,18]. The analogical problem arises at an exact solution the task with a constant electric field in the t-representation [23]

Kinetic equation approach

LDL approximation

Verification of two approaches

Conclusion