''Hall crystal'' versus Wigner crystal

Journal Article · Sat Apr 15 00:00:00 EDT 1989 · Phys. Rev. B: Condens. Matter; (United States)

OSTI ID:6311240

Tes-hacekanovic, Z; Axel, F; Halperin, B I

We consider the possibility of coexistence of the quantized Hall effect (QHE) and a weak charge-density wave. For suitably chosen interactions between the fermions, there is a crystalline ordered state (''Hall crystal'') exhibiting QHE. Unlike the standard Wigner crystal, the energy of the Hall crystal does not have a cusp minimum when the fermion density is precisely an integer per unit cell of the structure. The density is locked onto a multiple of the magnetic flux density, while the period of the charge-density wave can vary continuously. The normal modes of the Hall crystal show separate transverse and longitudinal modes, with linear dispersion at long wavelengths. We propose a model for which the Hartree approximation is accurate and which exhibits a Wigner-crystal phase, a Hall-crystal phase, and a translationally invariant quantized--Hall-''liquid'' phase, as the coupling constant is varied. We study the one-particle band structure and its associated Diophantine equations, the Hall conductance, and the normal modes of this model, in its various regimes, exploiting the existence of two topological invariants (Chern numbers) which characterize the system. We also examine the transitions between different phases.

• Research Organization: Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138
• OSTI ID: 6311240
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 39:12
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ELECTRON GAS
HALL EFFECT
DISPERSION RELATIONS
ELECTRONIC STRUCTURE
FERMIONS
HARTREE-FOCK METHOD
INTERACTIONS
INVARIANCE PRINCIPLES
NORMAL-MODE ANALYSIS
PLASMA WAVES
QUANTUM MECHANICS
TOPOLOGY
FLUIDS
GASES
MATHEMATICS
MECHANICS
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)