Proximity-induced pseudogap in mesoscopic superconductor/normal-metal bilayers

Abstract

Recent scanning tunneling microscopy ͑STM͒ measurements of the proximity effect in Au/ La 2−x Sr x CuO 4 and La 1.55 Sr 0.45 CuO 4 / La 2−x Sr x CuO 4 bilayers showed a proximity-induced pseudogap ͓O. Yuli, I. Asulin, Y. Kalcheim, G. Koren, and O. Millo, Phys. Rev. Lett. 103, 197003 ͑2009͔͒. We describe the proximity effect in mesoscopic superconductor/normal-metal bilayers by using the Bogoliubov-de Gennes equations for a tightbinding Hamiltonian with competing antiferromagnetic and d-wave superconductivity orders. The temperaturedependent local density of states is calculated as a function of the distance from the interface. Bound state due to both d-wave and spin-density wave gaps are formed in the normal metal for energies less than the respective gaps. If there is a mismatch between the Fermi velocities in the two layers we observe that these states will shift in energy when spin-density wave order is present, thus inducing a minigap at finite energy. We conclude that the STM measurement in the proximity structures is able to distinguish between the two scenarios proposed for the pseudogap ͑competing or precursor to superconductivity͒.

Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density

“…The next example is the proximity effects in an SNS Josephson junction, in which the gap symmetry of the superconducting electrodes is assumed to be s-wave. Josephson junctions and superconducting weak links have attracted great attention in various research fields such as superconducting device engineering 24) including Josephson qubits, 25) superconducting transport studies in superconducting wires, 26) fundamental studies on unconventional nano-superconductors, 7,[27][28][29] and so on. Numerical simulations for the BdG equations has been often carried out to study Josephson effects.…”

“…Very recently, a few groups [6][7][8] have proposed a highly efficient numerical method to solve the BdG equations by using the kernel polynomial expansion. 9) In these papers, the key idea is to expand Green's function with a set of the Chebyshev polynomials.…”

Numerical solution of large scale Hartree–Fock–Bogoliubov equations

“…The first study of HFB from the perspective of numerical analysis only appeared a few years ago by Lewin and Paul [34], which focused on the self-consistent field iterations in HFB calculations. Besides diagonalization methods, Fermi operator expansion methods (based on the Chebyshev expansion) have also been used to accelerate the solution of HFB equations [11,44,56].…”

Numerical Construction of a Low-Energy Effective Hamiltonian in a Self-Consistent Bogoliubov–de Gennes Approach of Superconductivity

“…[4][5][6][7] However, this approach requires a lot of computational memories and a long computational time. In contrast, the polynomial expansion method [8][9][10][11][12] allows efficient self-consistent calculations in superconductivity, without any diagonalization. This approach drastically reduces a computational cost and has an excellent parallel efficiency, but does not lead to direct calculations of eigen-pairs (eigenvalues and eigenvectors) of the BdG Hamiltonian.…”