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Soviet Journal of Low Temperature Physics

Conditions for the formation of a moving bound state of a pair of quasiparticles

Yu. E. Kuzovlev, A. I. Lomtev

Published Apr 1, 1986• 0 citations
Publisher

Abstract

The spectra and the necessary criteria for the existence of a bound state of a pair of activation or Goldstone quasiparticles, whose energy depends on the momentum according to a power law with index n ≤ 2, are derived. In a space of dimensions d ≥ 2 a bound state forms with an arbitrarily weak attraction independently of the magnitude of the total momentum of the pair 2Q, while in a space of dimension > 2 the bound state forms only it 2Q is less than a critical value 2Qc. For Q > Qc the bound state is destroyed by a kinetic mechanism.

DOI
10.1063/10.0031485

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The spectra and the necessary criteria for the existence of a bound state of a pair of activation or Goldstone quasiparticles, whose energy depends on the momentum according to a power law with index n ≤ 2, are derived. In a space of dimensions d ≥ 2 a bound state forms with an arbitrarily weak attraction independently of the magnitude of the total momentum of the pair 2Q, while in a space of dimension > 2 the bound state forms only it 2Q is less than a critical value 2Qc. For Q > Qc the bound state is destroyed by a kinetic mechanism.
We consider a single Cooper pair with the spin dependent quasiparticle masses, with and without applied magnetic field.Such situation takes place for the strongly correlated electron systems, where a relatively strong Hubbard interaction differentiates the quasiparticle states in the majorityand the minority-spin subbands.In that situation, the two spin subbands in an applied magnetic field are not only shifted one with respect to the other, but also distorted differently, which results from the electronic correlations.Under these circumstances, the fermionic particles composing the Cooper pair, are quantum mechanically distinguishable.In result, the Cooper pair has a nonzero momentum (i.e.produces a stationary current in a similar manner as electron in the Bloch state), and there exists a critical value of the attractive interaction, below which the bound Cooper-pair state is not formed.The presence of the applied field (included via the Zeeman term) does not alter the picture qualitatively.Importance of these results for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov phase in strongly correlated systems is mentioned.
We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.
The ground state of two holes with opposite spins in the t-J model is discussed using a variational method in a restricted Hilbert space. It is assumed that the holes can move independently and scatter when they are close to each other. Various processes which lead to a scattering of the holes are all treated on the same footing. It is found that the two holes form a bound state with a binding energy which is smaller than 0.4J for any value t/J. A possible extension to the case of finite concentrations is discussed.
A partially filled shell (Landau level) of Laughlin quasiparticles (QP's) gives rise to an incompressible daughter state if the QP's themselves are Laughlin correlated. This occurs only if the pseudopotential V QP (L′) describing the interaction energy of a QP pair as a function of the total pair angular momentum L′ satisfies special conditions. V QP (L′) can be obtained quite accurately from numerical studies of small systems. It does not always satisfy these conditions (e.g. for quasielectrons of the Laughlin ν=1/3 state at their ν QE =1/3 filling). In such cases, formation of pairs or larger clusters may explain the recently observed incompressible states (like ν=4/11).