Dirac Fermions in Graphene and Graphite—a view from angle ...

where ɛ is infinitely small. According to Equation(2.14), the spectral function A 0 (k, E)is a delta function
A 0 (k, E)=δ(E-E 0 k
) for a noninteracting system. In an interaction system, the electron-electron correlation
is expressed in terms of the electron self energy Σ(k, E)=Σ ′ (k, E)+iΣ ′′ (k, E). The real part contains information
about the energy renormalization and the imaginary part gives information about the lifetime of an
electron with energy Ek 0 and momentum k propagating in the many body systems. In this case the Green’s
function and the spectral function are
G(k, E) =
1
E − E 0 k − Σ(k, E) (2.16)
A(k, E) = − 1 π
Σ ′′ (k, E)
(E − E 0 k − Σ′ (k, E)) 2 + (Σ ′′ (k, E)) 2 (2.17)
2.1.4 Energy distribution curves (EDCs) and momentum distribution curves
(MDCs)
Figure 2.3. Typical two dimensional ARPES data and the analysis of EDCs and MDCs.
In ARPES, a typical scan shows two dimensional intensity as a function of binding energy and crystal
momentum, see Fig. 2.3. There are two ways to analyse the data. One way is to fix momentum at a particular
value, and study intensity as a function of energy - energy distribution curves (EDCs). Another way is to
fix energy at a particular value, and study intensity as a function of momentum - momentum distribution
curves (MDCs). Each of these two methods has its own advantages and disadvantages, and the analysis of
these two is complimentary to each other.
EDC gives a global overview of the spectral function and the line shape. It provides information about
whether a well-defined quasiparticle peak is present or not, whether the spectral function can be interpreted
in the Fermi liquid theory or not 21 . Moreover, subtle features such as small peaks at low binding energy,
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