# Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations

## Abstract

A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed quantum Hall liquid crystals. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in {sup 4}He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering nematic, tetratic, and hexatic generalizations of Laughlin's trial wave function having twofold, fourfold, and sixfold broken rotational symmetry, respectively. In the limit of zero wave vector q the dispersion of these modes is singular, with a gap that is dependent on the direction along which q=0 is approached for nematic and tetratic liquid crystalline states, but remains regular in the hexatic state, as permitted by the fourth order wave-vector dependence of the (projected) oscillator strength and static structure factor.

- Authors:

- Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)

- Publication Date:

- OSTI Identifier:
- 20787938

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevB.73.085314; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; APPROXIMATIONS; COLLECTIVE EXCITATIONS; HALL EFFECT; HELIUM 4; LIQUID CRYSTALS; OSCILLATOR STRENGTHS; PHONONS; STRUCTURE FACTORS; SYMMETRY; TEMPERATURE DEPENDENCE; VECTORS; WAVE FUNCTIONS

### Citation Formats

```
Lapilli, Cintia M., and Wexler, Carlos.
```*Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVB.73.0.

```
Lapilli, Cintia M., & Wexler, Carlos.
```*Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations*. United States. doi:10.1103/PHYSREVB.73.0.

```
Lapilli, Cintia M., and Wexler, Carlos. Wed .
"Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations". United States.
doi:10.1103/PHYSREVB.73.0.
```

```
@article{osti_20787938,
```

title = {Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations},

author = {Lapilli, Cintia M. and Wexler, Carlos},

abstractNote = {A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed quantum Hall liquid crystals. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in {sup 4}He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering nematic, tetratic, and hexatic generalizations of Laughlin's trial wave function having twofold, fourfold, and sixfold broken rotational symmetry, respectively. In the limit of zero wave vector q the dispersion of these modes is singular, with a gap that is dependent on the direction along which q=0 is approached for nematic and tetratic liquid crystalline states, but remains regular in the hexatic state, as permitted by the fourth order wave-vector dependence of the (projected) oscillator strength and static structure factor.},

doi = {10.1103/PHYSREVB.73.0},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 8,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}