Chemistry Reference
In-Depth Information
(a).
β
=0.9 (close to critical value)
1.4
1.2
1
0.8
0.6
ε
/t
0.4
0.2
0
-0.2
2.5
2.75
3
k
y
Fig. 7. (a) The energy eigenvalues around the Dirac point plotted as function of
k
y
for
β
=0
.
9. The collapse can be clearly seen. (b) The modulus of the eigenvalues
|
n,k
y
|
for a value of
k
y
=2
.
785 computed from the tight binding model for system size
600
a×
600
a
, magnetic field
B
=27
.
3
Tesla
or
l
c
=20
a
, electric field given by parameter
β
=0
.
0
,
0
.
5
,
0
.
9, plotted as a function of
n
.
binding results shows a faster collapse. Figure 7(a) shows the collapse has
already occurred at
9, near one of the Dirac points.
We show below that one of the consequences of the Landau level con-
traction (15) and the
β
=0
.
dependent Gaussian shift (17) is the possibility
of a 'dielectric breakdown', which is different from the conventional ones.
The single particle spectrum and states we have obtained thus far (for a
given
n
) can be used to construct stable many-body quantum Hall
ground states. However, the external electric field not only modifies the
single particle wave function and spectrum, but can also destabilise the
ground state through spontaneous creation of particle-hole pairs; i.e., by
a dielectric breakdown. This problem is analogue of relativistic vacuum
break down through pair production.
We present a simple formula for dielectric breakdown, without giving
full details. It has an unusual dependence on the length scale over which the
potential fluctuates and on the Landau level index
E
and
B
n
. This peculiar feature
is absent in standard quantum 2
d
electron systems [31]. Specifically we find
