My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 5.
THE JELLIUM SLAB
-0.3
Surface energy (mHa bohr -2 )
-0.4
-0.5
ε bulk
= -7.865 mHa
ε bulk
= -7.532 mHa
ε bulk
= -7.109 mHa
10 15 20 25 30
Slab width
Figure 5.5: The surface energy as a function of slab width, calculated using different values of
the bulk energy. The middle curve uses the Perdew-Wang parameterisation [69] of Ceperley and
Alder’s early QMC results [12], which was the functional employed in the slab calculation. The
upper curve is from the Perdew-Zunger [70] paremeterisation of the same results; the lower curve
is from the Perdew-Zunger parameterisation of Ortiz and Ballone’s later QMC calculations [63].
slab and bulk calculations; figure 5.5 shows the effect of using the wrong bulk energy.
This figure, though simple, emphasises the important requirement that the bulk and
slab calculations must be carried out consistently. The error in the surface energy
induced by using an incorrect value of the bulk energy increases with the slab width.
If it is not possible to carry out consistent slab and bulk calculations, it is better to
use slab results only and to deduce the surface energy by fitting ɛ slab against 1/s.
Pitarke and Eguiluz [72] analysed the oscillations in the infinite-system curve
using the infinite barrier model, and showed that they should have a wavelength of
λ F /2, where the Fermi wavelength is
( ) 1/3 4
λ F = 2πr s . (5.7)
9π
When r s = 2.07, the Fermi wavelength is 6.78. The wavelength of the oscillations
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