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arXiv:1011.3011

Effect of weak magnetic field on quantum spin correlation in an s-wave superconductor

R. Afzali, A. T. Rezakhani, Hamidreza Alborznia

Published Nov 12, 2010• 1 citation
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Abstract

We study the effect of a weak magnetic field on the state of the spins of a pair of electrons forming a Cooper pair in an s-wave superconductor. By perturbatively solving time-dependent Bogoliubov equations up to first order, we obtain the two-particle Green function, and whence the two-electron spin-space density matrix. It appears that up to first order approximation, the spin state of a Cooper pair retains the form of a Werner state. This state is then examined in the sense of quantum correlations, i.e., quantum discord.

DOI
10.48550/arxiv.1011.3011

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We study the effect of a weak magnetic field on the state of the spins of a pair of electrons forming a Cooper pair in an s-wave superconductor. By perturbatively solving time-dependent Bogoliubov equations up to first order, we obtain the two-particle Green function, and whence the two-electron spin-space density matrix. It appears that up to first order approximation, the spin state of a Cooper pair retains the form of a Werner state. This state is then examined in the sense of quantum correlations, i.e., quantum discord.
We investigate entanglement of two electron spins forming Cooper pairs in an sss-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.
Bipartite quantum entanglement of electron spins of a Cooper pair in a dirty sss-wave superconductor is investigated at absolute zero temperature in terms of the exchange interaction and potential scattering as well as the relative distance between the two electrons. In the case of transition-metal impurities, we utilize the T-matrix approach to obtain the relevant Green's functions. We employ the two-electron spin-space density matrix, which is associated with the perturbed Green's functions. We show that a two-spin state can be described by the Werner state for dirty superconductors as well as for clean ones. We find that both the first and second quantum phase transitions (QPTs) are generated by the competition between potential scattering and other interactions. Meanwhile, it is not possible to determine the allowable value for each interaction individually. In the case of rare-earth impurities, concurrence, as a measure of bipartite entanglement, is discussed in terms of the relative distance and collision times for all finite and infinite Debye frequencies. The results confirm that quantum correlation and QPTs can be tuned by impurities.
A supercurrent is well recognized as being of prime importance within mean-field theory, but remains largely unexplored in strongly correlated electron systems (SCES) and the quantum critical region. To clarify the impact of the supercurrent on magnetism and superconductivity near an antiferromagnetic quantum critical point, we study the two-dimensional Hubbard model based on a fluctuation exchange approximation for a current-carrying superconducting state. We show a supercurrent-induced antiferromagnetism and emergence of spin-triplet Cooper pairs. The former results from Bogoliubov Fermi surfaces, suppression in the superconducting gap, and strong correlation effects beyond the mean-field theory. Our results suggest that the supercurrent can bring out rich phenomena of superconductivity in SCES.
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.
Abstract By considering transition-metal (Shiba-Rusinov model) and rare-earth metal impurities (Abrikosov-Gorkov theory) effect on a many-body system, i.e., a BCS s-wave superconductor, quantum bipartite entanglement of two electrons of the Cooper pairs in terms of the exchange interaction, J, the potential scattering, V(playing an important role, unexpectedly), and the distance of two electron spins of the Cooper pair is calculated at zero temperature by using two-electron spin-space density matrix (Werner state). In transition-metal case, we find new quantum phase transitions (QPTs). The changes of J, which causes to have localized excited state, V and the pairing interaction (via energy gap) lead to the displacement of the QPTs (interactions act in the same direction, however sometimes the pairing interaction causes the competition with other interactions), regardless of their effects on the value of concurrence. Determining the allowable values of all interactions by itself is not possible, due to the smallness of the perturbed Green’s functions (appearing in the density matrix). For non-magnetic and magnetic (rare-earth) impurity cases, concurrence versus the distance and collision times is discussed for all finite and infinite Debye frequency. The quantum correlation, instability of the system and what's more important QPT can be tuned by the impurity.
The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization β I in addition to the electron polarization β S have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β S ≈ β I and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.