Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation

Journal Article · Mon Jan 01 00:00:00 EST 1990 · Physical Review, B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.41.327· OSTI ID:6939503

Randeria, M; Duan, J; Shieh, L ^[1]

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1. Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 (USA)

We study a two-dimensional continuum model of a dilute gas of fermions at {ital T}=0 interacting via a given two-body potential, with an aim to investigate superconductors with coherence length of the order of the interparticle spacing ({ital k}{sub {ital F}}{xi}{sub 0}{similar to}O(1)), a striking feature of the high-{ital T}{sub {ital c}} materials. We find that a two-body bound state in vacuum is a necessary and sufficient condition for an {ital s}-wave pairing instability. We also find that the existence of such a bound state in a higher-angular-momentum ({ital l}{gt}0) channel is not a necessary condition for an {ital l}-wave pairing instability. We further investigate using a variational {ital ansatz} the evolution from a state with large overlapping Cooper pairs ({ital k}{sub {ital F}}{xi}{sub 0}{much gt}1) to one with Bose condensation of composite bosons ({ital k}{sub {ital F}}{xi}{sub 0}{much lt}1). For the {ital s}-wave case an exact solution of the variational equations shows a smooth crossover from one regime to the other at {ital T}=0. The {ital p}-wave solution has a weak singularity when the chemical potential goes through zero, which is the bottom of the band. We show, quite generally, independent of the dimensionality and of model details, that the gap--to--single-particle excitations is nodeless, even if the anisotropic pair wave function has nodes, when the coupling is strong enough that the chemical potential is negative.

• OSTI ID: 6939503
• Journal Information: Physical Review, B: Condensed Matter; (USA), Vol. 41:1; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FERMI GAS
SUPERCONDUCTIVITY
ABSOLUTE ZERO TEMPERATURE
BOND LENGTHS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
BOUND STATE
COHERENCE LENGTH
COOPER PAIRS
COPPER OXIDES
GROUND STATES
S STATES
TWO-DIMENSIONAL CALCULATIONS
CHALCOGENIDES
COPPER COMPOUNDS
DIMENSIONS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY LEVELS
FLUIDS
GASES
LENGTH
OXIDES
OXYGEN COMPOUNDS
PHYSICAL PROPERTIES
TRANSITION ELEMENT COMPOUNDS
656100* - Condensed Matter Physics- Superconductivity