ABSTRACT

Graphene devices utilize quantum states in extensive nonequilib-

rium conditions caused with strong fields. Therefore, adequate un-

derstanding of the nonequilibrium quantum dynamics of nanoscale

devices nowadays is regarded as an important problem. Graphene

quantum well represents a new type of a device and can be

constructed using the graphene field-effect transistors. Such a

system functions in competitive situations while balancing the

thermal relaxation and the external driving which emerge under

extreme nonequilibrium conditions. The theoretical methods for

understanding such systems, however, are still under development.

Nonequilibrium effects in graphene and carbon nanotube devices

emerge in conditions when either an external field or a heat flow

are applied to the sample (Shafranjuk 2008, Shafranjuk 2009,

Shafranjuk 2011a, 2011b, Rinzan et al. 2012). If the energy supply

from outside the system exceeds the dissipation and the energy

escape from the system to outside, then the system state can

deviate from equilibrium. At first, when energy is supplied into

a system, it can be absorbed with a certain subsystem and only

later can be redistributed among the other subsystems of the same

system. In particular, if a graphene device is exposed to an external

electromagnetic field (EF), the field acts directly on the electrically

charged particles, which are the chiral fermions (Shafranjuk 2009,

Shafranjuk 2011a, 2011b). Therefore, at the initial stage, the

external field energy is absorbed by the chiral fermions. On the next

stage, owing to the inelastic electron-phonon collisions, part of the

absorbed energy is transferred from electrons to phonons, which

carry it far away from the active region. In principle, depending

on the system’s geometry and the average temperature, the whole

scenario might be more complicated due to secondary reabsorption

of the excessive phonon energy by the chiral fermions again. In

general, there are several most important micro-and macroscopic

parameters which characterize the energy exchange between the

system and the external environment. Some essential quantities

might be evaluated theoretically, while others can be extracted from

experiments. For instance, the electron density of states in pristine

graphene is computed as