Fluctuations and topological transitions of quantum Hall stripes: Nematics as anisotropic hexatics

We study fluctuations and topological melting transitions of quantum Hall stripes near half filling of intermediate Landau levels. Taking the stripe state to be an anisotropic Wigner crystal (AWC) allows us to identify the quantum Hall nematic state conjectured in previous studies of the two-dimensional (2D) electron gas as an anisotropic hexatic. The transition temperature from the AWC to the quantum Hall nematic state is explicitly calculated, and a tentative phase diagram for the 2D electron gas near half filling is suggested.

Figure 1

Schematic view of (a) a smectic, (b) a smectic with an edge dislocation, and (c) an anisotropic Wigner crystal where the guiding centers of the electrons occupy the sites of an anisotropic triangular lattice.

Figure 2

(Color online) Finite parts ${\tilde{c}}_{ij}$, $i,j=1,2$, of the compression moduli for the anisotropic Wigner crystal as a function of the partial filling factor ${\nu }^{*}$ in Landau level $N=2$.

Figure 3

Critical temperature $T_{c1}$ for the dislocation-mediated melting of the anisotropic Wigner crystal into a nematiclike state near half filling of Landau level $N=2$.

Figure 4

Tentative phase diagram showing the various relevant regimes for the melting of quantum Hall stripes as a function of temperature $T$ and length scale $L$. ${\xi }_{disc}$ is the average spacing between disclinations. Below this length scale, above $T_{c2}$ the system retains the properties of an anisotropic hexatic. Note that $T_{c1}$ here can be extremely small, and may be driven to zero by quantum fluctuations.