Journal of Experimental and Theoretical Physics Letters

Scaling function near a transition to an insulator state

Valerii T. Dolgopolov

Published Dec 1, 1998• 0 citations

Abstract

Analysis of experimental results yields a scaling function of the form β( g )=121/ g near the metal-insulator transition in three-dimensional systems. In two-dimensional electronic systems demonstrating a transition to an insulator state, the same relation holds for the function νβ, where ν is the critical exponent characterizing the divergence of the correlation length.

DOI: 10.1134/1.567804

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Journal of Experimental and Theoretical Physics Letters

Scaling function near a transition to an insulator state

Valerii T. Dolgopolov

Published Dec 1, 1998• 0 citations

Publisher

Abstract

DOI: 10.1134/1.567804

Related papers

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{\mathbb{Z}}_{2}

insulator supporting a quantum spin Hall effect). This is not true of the boundary multifractal scaling exponents, which we show (numerically) to depend on whether the insulating state is topologically trivial or not.

κ\propto |μ- μ_c|^{-0.58\pm0.08}

where

μ_c

is the critical chemical potential. In the insulating phase, the localization length follows

ξ_l \propto |μ- μ_c|^{-ν_l}

with

ν_l = 0.26 \pm 0.05

. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent

ν_κ= 0.21 \pm 0.04

. Our results show that the exponents

ν_κ

and

ν_l

agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent

ν= 1/4

and dynamical exponent

z = 4

. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents

ν= 1/2

and

z = 2

{\mathit{h}}_{\mathit{r}}

{)}^{2}

being close to one this gives further support for a two-exponent scaling scenario implying \ensuremath{\eta}\ifmmode\bar\else\textasciimacron\fi{}=2\ensuremath{\eta}. The magnetization behaves discontinuously at the transition, i.e., \ensuremath{\beta}=0. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multipeak structure that would be characteristic for the phase-coexistence at first-order phase-transition points.