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arXiv:1007.0745

On the new superfluid state - II

George Kastrinakis

Published Jul 5, 2010• 0 citations
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Abstract

In a previous report (arxiv:0901.2487), we introduced a new fermionic variational wavefunction, suitable for interacting multi-species systems and sustaining superfluidity. This wavefunction contains a new quantum index of ghostly character, which does not appear in any observable quantity. Here we introduce a spin triplet version of this wavefunction, with parallel spin pairs only. Moreover, we present numerical solutions for the spin singlet superconducting state previously introduced.

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In a previous report (arxiv:0901.2487), we introduced a new fermionic variational wavefunction, suitable for interacting multi-species systems and sustaining superfluidity. This wavefunction contains a new quantum index of ghostly character, which does not appear in any observable quantity. Here we introduce a spin triplet version of this wavefunction, with parallel spin pairs only. Moreover, we present numerical solutions for the spin singlet superconducting state previously introduced.
We introduce a new fermionic variational wavefunction, generalizing the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from quark matter to the high temperature superconductors. A wide class of Hamiltonians, comprising interactions and hybridization of arbitrary momentum dependence between different fermion species, can be treated in a comprehensive manner. This is the case, as both the intra-species and the inter-species interactions are treated on equally rigorous footing, which is accomplished via the introduction of a new quantum index attached to the fermions. The index is consistent with known fermionic physics, and allows for heretofore unaccounted for fermion-fermion correlations. We have derived the finite temperature version of the theory, thus obtaining the renormalized quasiparticle dispersion relations, and we discuss the appearance of charge and spin density wave order. We present numerical solutions for two electron species in 2 dimensions. Based on these solutions, we show that, for equivalent spin up and down fermions, the Fermi occupation factor (per spin) equals 1/2 deep in the Fermi sea. This constitutes a unique experimental prediction of the theory, both for the normal and superfluid states. Interestingly, this result, obtained in the thermodynamic limit, is consistent with Fermi occupation factor (in-)equalities for finite systems of electrons, derived (in a different context) by Borland and Dennis, J. Phys. B {\bf 5}, 7 (1972) and by Altunbulak and Klyachko, Commun. Math. Phys. {\bf 282}, 287 (2008).
Although our discussion in this section will be largely phenomenological we must anticipate the major result of the microscopic theory which will be developed in Parts II and III; in particular we must make use of the fact that superfluidity in Fermi systems arises from the formation of a special kind of bound state in which electrons (or He quasiparticles) on (or near) the Fermi surface having oppositely directed momenta, + p and – p , form (collectively) bound pairs. For the vast majority of superfluid electron systems (metals), the pairs form in a state with no net orbital angular momentum, an l = 0 or s-wave state which we will refer to as conventional fermion superfluidity; by the Pauli principle the electrons must then be in a singlet spin state (s = 0). In the decade or so following the development of the BCS theory, and especially after the experimental discovery of the superfluid phases of liquid He, theorists explored various types of pairing in systems with a more complicated orbital and spin structure in which the gap can vary, in both magnitude and phase, with position on the Fermi surface. In the case of odd l pairing, the pairs form (again due to the Pauli principle) in a triplet s = 1 rather than a singlet spin state. The energy gap associated with such states may have zeros (i.e., vanish) at points or lines on the Fermi surface, and as a result the number of excitations at low temperatures varies as a power of the temperature, rather than exponentially.
Triplet character of 2D-fermion dimers arising from sss-wave attraction via spin-orbit coupling and Zeeman splitting
We theoretically study spin-1/2 fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting -- a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak s-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its p-wave character, provide observable signatures of unconventional pairing.