The two-dimensional Wigner solid transition at finite magnetic field

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1993

OSTI ID:7071611

Price, R D

A two-dimensional system of electrons in a strong magnetic field will form a Wigner solid in two limits: first, as the magnetic field goes to infinity, the size of the cyclotron orbits of the electrons shrink to the vanishing point, and behaving like classical point charges, they form a Wigner solid; and second, as the density of the system is made very small, the kinetic energy becomes so small in comparison with the potential energy of the system that it is negligible, and again the electrons minimize the potential energy by forming a Wigner solid. In dimensionless parameters [nu] and r[sub s], these limits are, respectively [nu] [yields] 0 and r[sub s] [yields] [infinity]. At fractional magnetic filling factors [nu] = p/q (p,q integer) and small r[sub s], the electrons form a quantum liquid, the fractional quantum Hall effect (FQHE) liquid. This thesis is a study of the phase boundary between the FQHE liquid and the Wigner solid in r[sub s] and v, both at zero temperature and at finite temperature. In particular, the author examines the phase transition as [nu] is held fixed at [nu] = 1/3, 1/5, 1/7, and 1/9 and r[sub s] is allowed to vary. The author first discusses experimental evidence for a phase transition, the properties of the FQHE liquid and Wigner solid that affect the phase transition is reviewed, as well as presenting some estimates of the melting using characteristics of the solid phase alone. At zero temperature, it is found that the liquid freezes at r[sub s] [approximately] 22 and r[sub s] [approximately] 15 at [nu] = 1/3 and 1/5, respectively, and the solid phase exists at all r[sub s] for [nu] = 1/7 and 1/9. At finite temperature, an unusual reentrant melting behavior at [nu] = 1/3 and 1/5 is found. The system is liquid at low r[sub s], freezing into a solid at somewhat higher r[sub s], then melting again into the FQHE liquid at still higher r[sub s]. At [nu] = 1/7 and 1/9, melting from Wigner solid into FQHE liquid also occurs.

• Research Organization: California Univ., San Diego, La Jolla, CA (United States)
• OSTI ID: 7071611
• Country of Publication: United States
• Language: English

Related Subjects

665400* -- Quantum Physics Aspects of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FLUIDS
HALL EFFECT
MAGNETIC FIELDS
MAGNETO-OPTICAL EFFECTS
PHASE TRANSFORMATIONS
QUANTUM FLUIDS
SOLIDS
TEMPERATURE RANGE
TEMPERATURE RANGE 0000-0013 K
WIGNER THEORY