Scaling of the magnetoconductivity of silicon MOSFET's: evidence for a quantum phase transition in two dimensions

For a broad range of electron densities $n$ and temperatures $T$, the in-plane magnetoconductivity of the two-dimensional system of electrons in silicon MOSFET’s can be scaled onto a universal curve with a single parameter $H_{\sigma }(n,T)$, where $H_{\sigma }$ obeys the empirical relation $H_{\sigma }=A(n)[\mathrm{\Delta }(n{)}^2+T^2{]}^{1\mathrm{/}2}$. The characteristic energy $k_B \Delta$ associated with the magnetic field dependence of the conductivity decreases with decreasing density, and extrapolates to 0 at a critical density $n_0$, signaling the approach to a zero-temperature quantum phase transition. We show that $H_{\sigma }=AT$ for densities near $n_0$.