Method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state

Abstract

In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave functions in the magnetic unit cell. An exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper's equation. The cyclic-tridiagonal matrix associated with the Harper's equation is then tridiagonalized by another unitary transformation. The obtained eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which showing the merit of our method in studying the large-sized system. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor.

8 pages; 3 figures

References in corpus (3)

• Quasiparticle States at a d-Wave Vortex Core in High-Tc Superconductors: Induction of Local Spin Density Wave Order
• Vortex Charges in High Temperature Superconductors
• Vortex State in Na_xCoO_2.yH_2O: p_x\pm ip_y-wave versus d_{x^2-y^2}\pm id_{xy}-wave Pairing

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• Vortex core order and field-driven phase coexistence in the attractive Hubbard model
• Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors