Two-band model with attractive and repulsive interactions in one dimension: Ground state, excitations, and thermodynamics

Journal Article · Tue Mar 01 04:00:00 EST 1994 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.49.6132· OSTI ID:142595

Schlottmann, P ^[1]

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1. Department of Physics, Florida State University, Tallahassee, Florida 32306 (United States)

We present the exact solution via Bethe`s ansatz to an integrable model consisting of two parabolic bands of electrons of equal mass with a local {delta}-function exchange interaction. The interaction is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. The structure of the Bethe ansatz and the classification of states is similar to the one of the two-channel Kondo problem. The interest in two-band models arises from the possibility that both the 3{ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2} and 3{ital d}{sub {ital z}}{sup 2} orbitals may play a role in high-{ital T}{sub {ital c}} cuprates. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the (crystalline field) splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states, which exist at every temperature. There is no long-range order and no condensation of the Cooper pairs. A threshold magnetic field is required to overcome the binding energy of the Cooper pairs and there is no response to fields smaller than the critical one. The low-temperature specific heat is proportional to {ital T}, except at critical points (van Hove singularities of the bands) where {ital C}{proportional_to}{ital T}{sup 1/2}. The spectrum of elemental excitations is approximately parabolic.

• DOE Contract Number: FG05-91ER45443
• OSTI ID: 142595
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 9 Vol. 49; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BAND THEORY
COOPER PAIRS
CUPRATES
ELECTRONS
EXCHANGE INTERACTIONS
EXCITATION
GROUND STATES
SUPERCONDUCTIVITY
THERMODYNAMIC PROPERTIES