Stability of the Smectic Quantum Hall State: A Quantitative Study

We present an effective elastic theory which {\em quantitatively} describes the stripe phase of the two-dimensional electron gas in high Landau levels ($N\ge 2$). The dynamical matrix is obtained with remarkably high precision from the density-density correlation function in the time-dependent Hartree-Fock approximation. A renormalization group analysis shows that at T=0, as the partial filling factor $\mathrm{\Delta }\nu \equiv \nu -\lfloor \nu \rfloor$ moves away from 1/2, the anisotropic conducting state may undergo quantum phase transitions: stripes may get pinned along their conducting direction by disorder, or may lock into one another to form a two-dimensional crystal. The model predicts values of $\mathrm{\Delta }\nu$ for each transition. The transitions should be reflected in the temperature dependence of the dissipative conductivity.