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arXiv:1309.6673 · Acta Physica Polonica A

On the Imbalanced d-Wave Superfluids Within the Spin Polarized Extended Hubbard Model: Weak Coupling Limit

Agnieszka Cichy

Published Apr 1, 2012• 1 citation
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Abstract

We investigate the superuid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic eld.We analyze the temperature and magnetic eld dependencies of the order parameter.We nd that in the two-dimensional case, the spatially homogeneous spin polarized superuidity (SC (P ̸ = 0)) is stable in the weak coupling limit, at T = 0, as opposed to the s-wave pairing symmetry case in 2D.We construct the ground state phase diagrams both for xed chemical potential and electron concentration.Furthermore, we obtain the temperature vs. magnetic eld and temperature vs. spin polarization phase diagrams.

DOI
10.12693/aphyspola.121.824

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We investigate the superuid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic eld.We analyze the temperature and magnetic eld dependencies of the order parameter.We nd that in the two-dimensional case, the spatially homogeneous spin polarized superuidity (SC (P ̸ = 0)) is stable in the weak coupling limit, at T = 0, as opposed to the s-wave pairing symmetry case in 2D.We construct the ground state phase diagrams both for xed chemical potential and electron concentration.Furthermore, we obtain the temperature vs. magnetic eld and temperature vs. spin polarization phase diagrams.
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We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LPs) with increasing attraction, in the presence of the Zeeman magnetic field ( h ) for d =2, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation as well as the strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin-independent hopping integrals ( t ↑ = t ↓ ), we find no stable homogeneous polarized superfluid (SC M ) state in the ground state for the strong attraction and obtain that for a two-component Fermi system on a 2D lattice with population imbalance, phase separation (PS) is favoured for a fixed particle concentration, even on the LP (BEC) side. We also examine the influence of spin-dependent hopping integrals (mass imbalance) on the stability of the SC M phase. We find a topological quantum phase transition (Lifshitz type) from the unpolarized superfluid phase (SC 0 ) to SC M and tricritical points in the h -| U | and t ↑ / t ↓ -| U | ground-state phase diagrams. We also construct the finite temperature phase diagrams for both t ↑ = t ↓ and t ↑ ≠ t ↓ and analyze the possibility of occurrence of a spin-polarized KT superfluid.
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The influence of the Zeeman magnetic field (h) on the ground state evolution of superfluid properties from the weak coupling (BCS-like) to the strong coupling limit of tightly bound local pairs with increasing attraction has been studied.The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a d = 3 simple cubic lattice.The broken symmetry Hartree approximation was used.For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC M ) was found in the h-|U | and P -|U | diagrams.
The imbalanced superfluid state of spin- 1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally to the spin polarized normal state. The second case may be relevant to cold fermionic systems, where the number of fermions of each species is fixed as in a canonical ensemble. In this case, the ground state depends on the pairing strength. For weak pairing, the order parameter exhibits a periodic domain wall lattice pattern with a localized spin distribution at low spin imbalance, and a sinusoidally modulated pattern with extended spin distribution at high spin imbalance. For strong pairing, the phase separation between the superfluid state and polarized normal state is found to be preferable, while the increase of spin imbalance simply changes the ratio between them.