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arXiv:cond-mat/0201512 · Physical review. B, Condensed matter

Spin ordering and quasiparticles in spin-triplet superconducting liquids

Fei Zhou

Published Jun 18, 2002• 2 citations
arXivHTMLPDF

Abstract

Spin ordering and its effect on low-energy quasiparticles in a p-wave superconducting liquid are investigated. We study the properties of a two-dimensional (2D) p-wave superconducting liquid where the ground state is spin rotation invariant. In quantum spin disordered liquids, the low-energy quasiparticles are bound states of the bare Bogolubov--De Gennes (BdeG) quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low-energy limit. Further more, spin collective excitations are fractionalized ones carrying a half-spin and obeying fermionic statistics. In thermally spin disordered limits, the quasiparticles are bound states of bare BdeG quasiparticles. The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.

DOI
10.1103/physrevb.65.220514

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Spin ordering and its effect on low-energy quasiparticles in a p-wave superconducting liquid are investigated. We study the properties of a two-dimensional (2D) p-wave superconducting liquid where the ground state is spin rotation invariant. In quantum spin disordered liquids, the low-energy quasiparticles are bound states of the bare Bogolubov--De Gennes (BdeG) quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low-energy limit. Further more, spin collective excitations are fractionalized ones carrying a half-spin and obeying fermionic statistics. In thermally spin disordered limits, the quasiparticles are bound states of bare BdeG quasiparticles. The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.
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We propose that the disordered state of a two-dimensional spin-1/2 Heisenberg antiferromagnet is physically equivalent to the incompressible liquid state of the fractional quantum Hall system. The fractional quantum Hall state for bosons is shown to be an exact spin singlet and to possess a low variational energy for the near-neighbor Heisenberg model on a triangular lattice. Variational wave functions for neutral spin-1/2 excitations are constructed and shown to form an exact spin doublet. Variational energies of these states are calculated, and their spin density profiles are determined. We find that a localized spin-1/2 quaisparticle has a size comparable to a lattice bond length and an excitation energy \ensuremath{\Delta}=1.3J. The energy-momentum dispersion of quasiparticles and spin-1 collective modes, obtained variationally, supports the hypothesis that the spin liquid state has a finite energy gap. The 1/2 fractional statistics exhibited by the quasiparticle excitations is explicitly demonstrated.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
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We study the electron spectral function of various zero-temperature spin-charge separated phases in two dimensions. In these phases, the electron is not a fundamental excitation of the system, but rather ``decays'' into a spin-1/2 chargeless fermion (the spinon) and a spinless charge e boson (the chargon). Using low-energy effective theories for the spinons (d-wave pairing plus possible N\'eel order) and the chargons (condensed or quantum-disordered bosons), we explore three phases of possible relevance to the cuprate superconductors: (1) AF∗,{\mathrm{AF}}^{*},AF∗, a fractionalized antiferromagnet where the spinons are paired into a state with long-ranged N\'eel order and the chargons are 1/2-filled and (Mott) insulating; (2) the nodal liquid, a fractionalized insulator where the spinons are d-wave paired and the chargons are uncondensed; and (3) the d-wave superconductor, where the chargons are condensed and the spinons retain a d-wave gap. Working within the Z2{Z}_{2}Z2​ gauge theory of such fractionalized phases, our results should be valid at scales below the energy gap of the vison---the basic vortex excitation in the theory. However, on a phenomenological level, our results should apply to any spin-charge separated system where the excitations have these low-energy effective forms. Comparison with angle-resolved photoemission spectroscopy data in the undoped, pseudogapped, and superconducting regions is made.