Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

Abstract

The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal / insulator / diffusive ferromagnet / insulator / s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the DF is calculated in various regimes for different magnitudes of the resistance, Thouless energy and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect (large resistance of the DF/S interface) and strong proximity effect (small resistance of the DF/S interface).In ferromagnet/superconductor (F/S) junctions Cooper pairs penetrating into the F layer from the S layer have a nonzero momentum due to the influence of exchange field 1,2,3 . This results in oscillating behavior of the pair amplitude or a π-phase shift of the order parameter in the ferromagnet. A negative sign of the real part of the order parameter may occur when the thickness of the F layer is larger than the coherence length of the F layer. The occurrence of the π-phase shift makes it possible to realize the SFS π -junctions 1 , as was confirmed experimentally 4,5,6,7,8 . The order parameter oscillations also lead to nonmonotonous dependence of T c in SF bilayers on the F-layer thickness 9,10,11,12,13 . Effects of resonant transmission in conductivity of SF structures were discussed in Ref 14,15,16 .Another interesting consequence of the oscillations of the pair amplitude is the spatially damped oscillating behavior of the density of states (DOS) in a ferromagnet predicted theoretically 17,18,19,20 in various regimes. The energy dependent DOS calculated in the clean 18 and the dirty 21 limits exhibits rich structures. Experimentally DOS in F/S bilayers was measured by Kontos et al. who found a broad DOS peak around zero energy when the π-phase shift occurs 22 . In diffusive ferromagnet/superconductor (DF/S) junctions the zeroenergy DOS may have a sharp peak 21 . However the conditions for the appearance of such anomaly have not been studied systematically so far.The purpose of the present paper is to calculate DOS in N/DF/S junctions and to formulate the conditions for the zero-energy DOS peak in two regimes corresponding to the weak proximity effect (large DF/S interface resistance) and strong proximity effect (small DF/S interface resistance). We will show that in the former case the condition is equivalent to the one of Ref. 21 , while in the latter case the new condition is found. The calculation will be performed in the zero-temperature regime by varying the interface resistances as well as the resistance, the exchange field and the Thouless energy of the DF layer.We consider a junction consisting of normal and superconducting reservoirs connected by a quasi-onedimensional diffusive ferromagnet conductor (DF) with a resistance R d and a length L much larger than the mean free path. The DF/N interface located at x = 0 has the resistance R ′ b , while the DF/S interface...

Current-voltage characteristics of tunnel Josephson junctions with a ferromagnetic interlayer

“…52. A similar effect was also discussed in N/F/S structures, where it was shown that a zero energy peak appears in DOS if E T h = h. 53 We also show in Fig. 2 the analytical approximation, Eq.…”

Spin-polarized proximity effect in superconducting junctions

“…The resonant proximity effect was discussed in [80] and can be characterized as follows. When the proximity effect is weak (R d /R b 1), the resonant condition is given by R d /R b ∼ 2h/E Th due to the exchange splitting of DOS in different spin sub-bands.…”

“…The DOS has been studied extensively [74,[77][78][79] but the condition for the appearance of the DOS peak was not studied systematically. We studied the conditions for the appearance of such anomaly, i.e., strong enhancement of the proximity effect and found two conditions corresponding to weak proximity effect and strong one [80]. Since DOS is a fundamental quantity, this resonant proximity effect can influence various transport phenomena.…”

Charge transport in 2DEG/s-wave superconductor junction with Dresselhaus-type spin–orbit coupling

“…For example, interesting spin-dependent phenomena are predicted in ferromagnet/superconductor junctions [2][3][4][5]. Another important subject is an effect of spin-orbit coupling (SOC) on transport properties of two-dimensional electron gas (2DEG) [6][7][8][9][10].…”