Amm. Pruisken et al., (Mis-)handling gauge invariance in the theory of the quantum Hall effect. III. The instanton vacuum and chiral-edge physics, PHYS REV B, 60(24), 1999, pp. 16838-16864
The concepts of an instanton vacuum and F invariance are used to derive a c
omplete effective theory of massless edge excitations in the quantum Hall,
effect. Our theory includes the effects of disorder and Coulomb interaction
s, as well as the coupling to electromagnetic fields and statistical gauge
fields. The results are obtained by studying the strong-coupling limit of a
Finkelstein action, previously introduced for the purpose of unifying both
integral and fractional quantum Hall regimes. We establish the fundamental
relation between the instanton vacuum approach and the completely equivale
nt theory of chiral edge bosons. In this paper we limit the analysis to the
integral regime. We show that our complete theory of edge dynamics can be
used as an important tool to investigate long-standing problems such as lon
g-range, smooth disorder, and Coulomb interaction effects. We introduce a t
wo-dimensional network of chiral-edge states and tunneling centers (saddle
points) as a model for smooth disorder. This network is then used to derive
a mean-field theory of the conductances, and we work out the characteristi
c temperature (T) scale at which the transport crosses over from mean-field
behavior at high T to the critical behavior plateau transitions at much lo
wer T. The results explain the apparent lack of scaling which is usually se
en in the transport data taken from arbitrary samples at finite T. Second,
we address the problem of electron tunneling into the quantum Hall edge. We
show that the tunneling density of states near the edge is affected by the
combined effects of the Coulomb interactions and the smooth disorder in th
e bulk. We express the problem in terms of an effective Luttinger liquid wi
th conductance parameter (g) equal to the filling fraction (nu) of the Land
au band. Hence, even in the integral regime, our results for tunneling are
completely non-Fermi-liquid-like, in sharp contrast to the predictions of s
ingle-edge theories. [S0163-1829(99)13739-1].