Broken rotation symmetry in the fractional quantum Hall system

Abstract

We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells whose thickness exceeds a critical value which depends on the electron density. The order parameter at 1/3 reduced density resembles that of a nematic liquid crystal, in that a residual two-fold rotation axis is present in the low symmetry phase. At filling factors 1/5 and 1/7, there are states with four-and six-fold axes, as well. We discuss the experimental detection of these phases.

Pair-Distribution Functions of Laughlin Quasielectrons in Partially Filled Composite Fermion Levels

“…Similar form of g(r) was found [13] for broken-symmetry Laughlin states, in which the shoulder results from angular averaging of an anisotropic function g(r, φ) ∼ r 2 or r 6 , depending on φ. However, the present case of QE's is different, because g(r) is isotropic (nondegenerate ground state wave functions have L = 0) and the shoulders result from radial averaging of inter-and intra-cluster correlations (beginning as ∼ r 2 and a higher power of r at short range, respectively).…”

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

“…The linearity we have found supports the proposal to use a single-parameter to construct unimodularly deformed wave functions to describe the effect of interaction anisotropy in the disk geometry. 5 In fact, the family of deformed wave functions contain the same anisotropic Jastrow factor in their relative coordinate part, 10 which explicitly splits the order-3 zeros in the Laughlin liquid. Therefore, the emergence of the Hall smectic phase, as analyzed in the effective field theories, 11,12 at larger anisotropy is also a support of the geometrical description of FQH states.…”

“…[10][11][12][19][20][21] The rise of the smectic phase softens the magnetoroton mode and appears to be responsible for the reduction of the excitation gap for 2.0 < A c < 8.0 as shown in Fig. 1.…”

“…This Hamiltonian is a truncated summation over anisotropic pair interactions: (10) for two particles with the relative angular momentum of mh in the guiding-center coordinates. In the above expression, L m (x) are mth Laguerre polynomials and…”

“…Motivated by the anisotropic transport properties experimentally reported at the partially filled higher Landau level (LL), trial wave functions [10][11][12][13] have been proposed to describe the anisotropic FQH states. These variational wave functions modify the original isotropic Laughlin wave function by splitting the multiple-order zeros in the wave function.…”