My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 5.
THE JELLIUM SLAB
The jellium slab is an electron gas with finite extent in one of the three spatial
dimensions. There are different ways to constrain the electrons to a slab: two will
be described here.
5.1.1 Constraining the electrons
The first and more usual way to define the slab is to set up the following background
charge density:
⎧
⎪⎨ 3/(4πrs)
3 0 < z < s
ρ b (z) =
(5.2)
⎪⎩ 0 otherwise.
This fixes the slab width s. In a QMC simulation, a finite number of electrons must
be used. The number of electrons then determines the size of the simulation cell in
the xy-direction; the cell extends from −∞ to ∞ in the z-direction. The integral of
the electron density over z is equal to that of the positive background density; this
is another way of saying that the system is charge-neutral.
The electrons are constrained by the attractive potential of the positive background,
and pushed apart by their own mutual repulsion and kinetic energy. A
typical electron density profile for this form of the jellium slab is shown in figure
5.1. Some electrons spill out of the slab into the vacuum region; standing wave
oscillations caused by reflection of electron waves from the confining potential are
evident, decaying from the edge of the slab towards the centre [47]. The oscillations
are more pronounced when a small number of electrons is used.
It is also possible to constrain the electrons further, by imposing infinite barriers
at z = 0 and at z = s. Electrons are no longer allowed to spill out into the vacuum
region; the resultant density is shown in figure 5.2. This is the infinite barrier
model; the term jellium slab is usually reserved for the unbounded system, and this
convention will be applied here.
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