Physics – Condensed Matter
Scientific paper
1999-02-08
Phys.Rev. B60 (1999) 8290
Physics
Condensed Matter
16 pages, 19 figures
Scientific paper
10.1103/PhysRevB.60.8290
We study the consequences of random mass, random scalar potential and random vector potential on the line of clean fixed points between integer/fractional quantum Hall states and an insulator. This line of fixed points was first identified in a clean Dirac fermion system with both Chern-Simon coupling and Coulomb interaction in Phys. Rev. Lett. {\bf 80}, 5409 (1998). By performing a Renormalization Group analysis in 1/N (N is the No. of species of Dirac fermions) and the variances of three disorders $\Delta_{M}, \Delta_{V}, \Delta_{A}$, we find that $\Delta_{M}$ is irrelevant along this line, both $\Delta_{A}$ and $\Delta_{V}$ are marginal. With the presence of all the three disorders, the pure fixed line is unstable. Setting Chern-Simon interaction to zero, we find one non-trivial line of fixed points in $(\Delta_{A}, w)$ plane with dynamic exponent z=1 and continuously changing $\nu$, it is stable against small $(\Delta_{M},\Delta_{V})$ in a small range of the line $1< w < 1.31$, therefore it may be relevant to integer quantum Hall transition. Setting $\Delta_{M} =0$, we find a fixed plane with z=1, the part of this plane with $\nu > 1$ is stable against small $\Delta_{M}$, therefore it may be relevant to fractional quantum Hall transition.
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