Parity effect and tunnel magnetoresistance of ferromagnet/superconductor/ferromagnet single-electron tunneling transistors

Abstract

We theoretically study the tunnel magnetoresistance(TMR) of ferromagnet / superconductor / ferromagnet single-electron tunneling transistors with a special attention to the parity effect. It is shown that in the plateau region, there is no spin accumulation in the island even at finite bias voltage. However, the information of the injected spin is carried by the excess electron and thus the TMR exists. The spin relaxation rate of the excess electron can be estimated from the TMR. We also show that the TMR increases with decreasing the size of the superconducting island.

Spectral properties of the Wilson-Dirac operator and random matrix theory

“…generates the terms ðtrA þ trBÞ 2 and ðtrA À trBÞ 2 which correspond to the squares of traces in the chiral Lagrangian [24][25][26][27]. In the microscopic domain the corresponding partition function for N f fermionic flavors is then given by…”

“…Although these RMTs are more complicated than the chiral random matrix theory formulated in [17,18], in the case of Wilson fermions a complete analytical solution of the RMT has been achieved [9][10][11]13,[20][21][22][23]. Since the Wilson RMT shares the global symmetries of the Wilson-Dirac operator it will be equivalent to the corresponding (partially quenched) chiral Lagrangian in the microscopic domain (also known as the domain) [24][25][26][27][28][29].…”