Methods
Device fabrication
The multilayer of [Nb (1.0 nm)/V (1.0 nm)/Ta (1.0 nm)] 40 /SiO 2 (5.0 nm)
was deposited on a MgO (100) substrate using a d.c. magnetron
sputtering method^20. The deposition rates were 0.35 Å s−1, 0.21 Å s−1
and 0.44 Å s−1 for the Nb, V and Ta targets, respectively, and the MgO
substrate was heated at 973 K during the deposition of the [Nb/V/
Ta ]n superlattice. To prevent oxidation, a 5.0-nm-thick SiO 2 layer was
stacked onto the superlattice at room temperature (around 300 K).
Next, the deposited film was patterned onto a 50-μm-wide wire
using conventional photolithography and an Ar ion milling process.
Finally, for the current injection, a Ti (5.0 nm)/Au (100 nm) metal elec-
trode was deposited on the wire. To make an Ohmic contact, the SiO 2
capping layer was removed by weak Ar ion milling before the electrode
deposition.
Direct- and alternating-current transport measurements
A Yokogawa 7651 was used to inject a d.c. current into the wire and the
longitudinal d.c. voltage was measured with a Keithley 2182A Nanovolt-
meter. For the a.c. current injection, a Keithley 6221 AC and DC Current
Source was used and both the first- and second-harmonic signals were
measured with a LI 5640 (NF Corporation).
Details of band structure calculation
To identify the Rashba spin–orbit interaction in the artificial super-
lattice [Nb/V/Ta]n without a centre of inversion, we carried out den-
sity functional theory calculations for the slab [Nb/V/Ta]n using the
full-potential linearized augmented plane wave+local orbitals method
within the generalized gradient approximation in the WIEN2k pack-
age^31 ,^32. We created a slab [Nb/V/Ta] 5 containing 30 atoms, which
corresponds to stacking two layers of Nb, V and Ta of a body-centred
cubic structure five times. We used 31 × 31 × 1 k-point sampling for the
self-consistent calculation and the muffin-tin radius RMT of 2.50 atomic
units for all atoms. The plane-wave cutoff was given by RMTKmax = 8.0,
where Kmax is the maximum reciprocal lattice vector. Extended Data
Fig. 1 shows the band structure along the high-symmetry line. We
obtained the Rashba splitting at the Fermi level near the M points. The
magnitude of the Rashba splitting is around 10 meV, which may origi-
nate from the V atoms. We thus verified that the [Nb/V/Ta]n superlattice
is a Rashba superconductor.
Nonreciprocal component ΔIc of a Nb control sample
As a control experiment, we prepared a 120-nm-thick Nb film and car-
ried out the same d.c. measurement. The multilayer Nb (120 nm)/SiO 2
(5.0 nm) was deposited on a MgO (100) substrate at 973 K by d.c. mag-
netron sputtering and processed onto a 50-μm-wide wire structure. As
shown in the inset of Extended Data Fig. 2, the Tc of the Nb film is 9.2 K.
We then measured the R–I curves to obtain ΔIc plots at 8.0 K. Although
the field dependence of ΔIc was clearly observed in the temperature
range 3.0–4.3 K for the [Nb/V/Ta]n superlattice (Tc = 4.41 K), no differ-
ence in ΔIc was observed for the Nb control sample when changing the
field direction. Therefore, the superconducting diode effect can be
attributed to the asymmetric structure of the [Nb/V/Ta]n superlattice.
Coherence length of [Nb/V/Ta]n superlattice
We investigated the coherence length of the [Nb/V/Ta]n superlattice
to check whether the vortices exist or not when the superconducting
diode effect is observed. The coherence length ξ is equivalent to the
size of the vortex core around which the supercurrent circulates in
type-II superconductors. Through an emergence of the vortex and the
increase of the kinetic energy of the supercurrent, a magnetic field
destroys Cooper pairs in type-II superconductors. The orbital limiting
field Bc2orb, referring to the critical field at which vortex cores begin to
overlap, is given as Bc2orb = Φ 0 /2πξ^2 , where Φ 0 = 2.07 × 10−15 T m^2 is the flux
quantum. Here, Bc2orb is usually calculated from the initial slope of the
plot of Bc2 versus temperature around Tc by using the Werthamer–Helfand–Hohenberg formula as BTorc2b(0)=−0.6 (^9) cc(d/BT 2 d )T
c
in the
dirty limit^33. Therefore, we can estimate the coherence length ξ from
the temperature dependence of Bc2 at Tc. As shown in Extended Data
Fig. 3, we obtained the first-harmonic sheet resistances Rω as a function
of magnetic field at T = 4.0–4.35 K. The measurement setup and pro-
cedure were the same as those shown in the main text. Here, the middle
point of the Rω curve during the transition is defined as the Bc2, and the
temperature dependence of Bc2 is plotted in the inset of Extended Data
Fig. 3. As a result of linear fitting, the orbital limiting field and the coher-
ence length are estimated to be Bc2orb = 1.9 T and ξ = 13 nm. Thus, the
vortices probably penetrate into the [Nb/V/Ta]n superlattice along the
field direction because the coherence length is much shorter than the
thickness of the [Nb/V/Ta]n superlattice (120 nm).
Data availability
The data that support the findings of this study are available from the
corresponding author upon request.
- Blaha, P. et al. WIEN2k, An Augmented Plane Wave+Local Orbitals Program for Calculating
Crystal Properties (Karlheinz Schwarz, 2018). - Blaha, P. et al. WIEN2k: An APW+lo program for calculating the properties of solids.
J. Chem. Phys. 152 , 074101 (2020). - Werthamer, N. R., Helfand, E. & Hohenberg, P. C. Temperature and purity dependence of
the superconducting critical field, Hc2. III. Electron spin and spin-orbit effects. Phys. Rev.
147 , 295–302 (1966).
Acknowledgements We thank Y. Kasahara, Y. Matsuda and K. Ishida for discussions about the
superconducting properties of the [Nb/V/Ta]n superlattice. This work was supported partly by
JSPS KAKENHI grants (15H05702, 15H05884, 15H05745, 17H04924, 18K19021, 18H04225,
18H01178, 18H05227, 18H01815, 19K21972 and 26103002), by the Cooperative Research Project
Program of the Research Institute of Electrical Communication, Tohoku University, and by the
Collaborative Research Program of the Institute for Chemical Research, Kyoto University.Author contributions T.O. supervised the study. F.A. and Y.M. deposited the films and
fabricated them into the devices. F.A. designed the transport measurement setup with help
from T.L. and collected the data. T.A. reproduced the experimental results of the
superconducting diode effect in another cryogenic equipment. J.I. and Y.Y. calculated the
band structure and helped with the analysis of the experimental results. All authors
contributed to the interpretation of the results and to the writing of the manuscript.
Competing interests The authors declare no competing interests.Additional information
Correspondence and requests for materials should be addressed to T.O.
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