Ⅲ-1. Atomic & Solid State Physics (Ion)

RIKEN Accel. Prog. Rep. 53

Superconducting proximity eﬀect in epitaxial
Nb(110)/Au(111)/Nb(110) trilayers
H. Yamazaki,∗1 N. Shannon,∗2 and H. Takagi∗3
Superconducting electronics, in which currents are carried by superconducting pairs of electrons, have great
potential for future application in quantum computing. An essential element of superconducting circuits
is the π junction, in which the phase of a superconducting wave function is inverted. One promising approach to building such a junction is to exploit the interplay between superconductivity and magnetism in superconductor (SC)/ferromagnet (FM)/SC heterostructures. Such multilayer structures are widely believedto achieve a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
state, in which the superconducting proximity eﬀect
drives a superconducting order with oscillating phasewithin the FM layer.1) However, this approach suﬀers
from a serious drawback that the ferromagnetic elements
tend to suppress superconductivity, forcing devices tooperate at lower temperatures and with lower criticalcurrent densities.
In this study, we show that, in epitaxial Nb(110)/Au(111)/Nb(110) trilayers, the equilibrium superconducting state presents strong evidence of 0-π state transitions as a function of the Au-layer thickness (tAu ).
Through the analysis of experimental data, we makea reasonable argument that a form of order-parameter
oscillation, similar to the FFLO-like state in FM for
SC/FM/SC junctions, is intrinsic to the proximityinduced Cooper pairs in the Au(111) layer. We tentatively ascribe this eﬀect to the spin-orbit coupling (SOC)
within the Au layer. Where SOC lifts the degeneracy between “up” and “down” spin electrons, electron pairs canform with a non-zero momentum. This leads to FFLOlike oscillations of the superconducting order parameterin real space. In the fcc lattice of Au, inversion symmetry is broken in the direction perpendicular to the (111)plane because of the ABCABC. . . stacking sequence of
atomic planes, and the lack of inversion symmetry leads
to the emergence of SOC.
We prepared a series of Nb(110)/Au(111)/Nb(110)Fig. 1. Schematic diagram of a vertical section of the sample
and the reversal images of RHEED patterns obtained in
the growth process (right).
∗1∗2∗3RIKEN Nishina Center
Okinawa Institute of Science and Technology Graduate University
Max-Planck-Institute for solid state research

Fig. 2. Critical current density Jc of the Nb/Au[tAu ]/Nb trilayers at 4.2 K and 6.0 K (ML: atomic monolayer).

trilayers on single crystals of Al2 O3 (1120) using MBE
method. The sample structure is shown in Fig. 1. We
will focus on single-domain samples (0 < tAu ≤ 2.10 nm),the superconducting properties of which are uniquely determined by tAu . The superconducting critical current
density Jc in zero magnetic ﬁeld was estimated from thewidth of the M-H hysteresis curve for H// sample planeby using a Bean model.2) The data in Fig. 2 appear exactly like those for FM/SC multilayers, which have been
conﬁrmed to exhibit the 0-π state transitions as a function of tFM .3) Following previous articles,3,4) we used theequation:
Jc = Jc0 | sin y|/y,whereeﬀ
y = 2πEex
tAu /hVfAu .

(1)

The solid and dashed lines in Fig. 2 show theoretical ﬁtsto the data for 6.0 K and 4.2 K, respectively. Fits areeﬀ(= 84.6 meV) for νfAu =obtained as a function of Eex
1.39 × 106 m/s and the ratio Jc0 (4.2 K)/Jc0 (6.0 K) =eﬀ
is an eﬀective parameter characterizing
5.0, where Eex
the order-parameter oscillations in the Au layer, νfAu theFermi velocity of Au, and Jc0 the overall scale for Jc .
eﬀ(=84.6 meV) is consistent with theThe value of Eex
SOC strength (120 meV) of conduction electrons in Au.
A pairing state should occur between two electrons on
the SOC-induced split parts of the Fermi surface. Onemight refute this argument on the grounds that a diﬀerence of 84.6 meV in energy between the spin-split bands
is too large for the electrons to form a pair since thesuperconducting gap is no more than 1.40 meV in Nb.
However, this is not the case with regard to the proximity eﬀects.5) Clearly, a theory is needed that treats theSOC eﬀect on the proximity-induced Cooper pairs in aSC/normal metal/SC system.
References1) A. I. Buzdin et al., JETP Lett. 35, 178 (1982).
2) E. M. Gyorgy et al., Appl. Phys. Lett. 55, 283 (1989).
3) Y. Blum et al., Phys. Rev. Lett. 89, 187004 (2002).
4) A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).
5) T. Kontos et al., Phys. Rev. Lett. 86, 304 (2001).

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