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NEOCLASSICAL THEORY OF INTERACTION 97

In section 2.2.6 of this chapter, we shortly discuss the drift of electrons inside the conductive
medium under the influence of external E-field. When E-field is not strong enough to cause the
nonlinear effects, the average electron drift velocity according to (2.28) is proportional to E-
field strength and can be written as = , where the parameter is called the electron
26

2
mobility and measured in [(m/s)/(V/m) = m /(V∙s)]. It was found that the electrons travel along
graphene sheet extremely fast, about 20 kilometers (!) per second while the applied E-field
intensity is 10 V/m only (µ = 2000 [m /
2
(V·s)] at room temperature and
increases to 10000 at low
temperature). If so, it takes only 43 ns
for average electron pass the distance
1 mm that opens way for ultra-fast and
ultra-broadband connections between
circuit elements and thereby ultra-fast
Microwave Band computer chips and transistors. For
comparison, in average = 13.5 in
Figure 2.9.2 Graphene complex conductivity over silicon, = 39 in germanium, = 60
frequency in GaAs, =100 in InP, = 95 in
silver, the best metal conductor, =
57.7 in copper, and = 26 in aluminum. Figure 2.9.2 illustrates the real (solid lines) and
27
imaginary (dotted lines) part of the conductivity of single-layer graphene over the frequency at
room temperature. The Fermi energy [eV] has been selected as a parameter. Recall that

the Fermi energy is a concept in quantum mechanics usually referring to the energy difference
between the highest and lowest occupied single-particle states.
Applying a positive gate voltage to the graphene will shift the Fermi level into the conduction
band. A negative gate voltage will lower the Fermi level making holes the dominant carriers.
Thereby, the gate, aka bias, voltage allows the dynamic control of both real and imaginary part
of the conductivity According to Figure 2.9.2, graphene in the microwave range behaves like a
moderate conductor.
Though graphene is the best
electrical conductor known,
=0.15 eV it is mono-atomic and thus
the surface resistance =
□
1/ ∙ is relatively high
compared to metals at micro
and mm-waves frequencies
(see Figure 2.9.2), even
with the possibility of
doping and electric field
biasing. Nevertheless, it
preserves the outstanding
property of tunability.
Figure 2.9.3 Graphene relative dielectric constant

26 Do not mix up this parameter with material permittivity. Such notification is customary in physics and
we decided to keep it.
27 All plots are derived using Kubo formula.