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