Nature | Vol 584 | 20 August 2020 | 375with an amplitude of 2.0 mA and a frequency of 503 Hz. The other
measurement configurations, such as the wire structure and the mag-
netic field, are the same as those of the d.c. measurement (Fig. 2b).
Here, Rω corresponds to the linear resistance R 0 , which is independent
of the current magnitude. In contrast, R 2 ω represents the second-order
resistance, which is proportional to the current and the magnetic field
(Rγ 2 ω=R 20 BI). Both Rω and R 2 ω were measured while sweeping the mag-
netic field at 4.2 K (Fig. 3a). R 2 ω is greatly enhanced during the transitions
and antisymmetric with respect to the magnetic field when the mag-
netic field is orthogonal to the current (±y direction), whereas it is
negligibly small when the magnetic field is set parallel to the current
(+x direction). This direction-dependent R 2 ω is characteristic of the
Rashba superconductors. To our knowledge, this is the first direct
evidence of the Rashba superconductivity in a three-dimensional super-
lattice. We next measured the temperature dependence of the R 2 ω
signals, to compare with that of the ΔIc (Fig. 3b). The R 2 ω signals observed
at each temperature are enhanced around the critical field, perhaps
because the nonreciprocal charge transport may be caused by super-
conducting fluctuations^10 ,^13 ,^21.
The temperature dependence of the γ values, which are calculated
as γ=RB^2 Rω^2 ωI (see equation ( 1 )), is plotted in Fig. 4. Here, we adopted the
maximum R 2 ω for each temperature and the corresponding Rω and
magnetic field. The notable observations are that the γ value increases
in the vicinity of Tc and reaches γ ≈ 550 T−1 A−1 at its maximum. These
trends are entirely consistent with those in other low-dimensional
systems. The magnetochiral anisotropy of the [Nb/V/Ta]n superlattice
naturally leads to nonreciprocal critical current; this was also clearly
observed in the vicinity of Tc.
Finally, we discuss the possible origin of the magnetochiral ani-
sotropy in the [Nb/V/Ta]n superlattice from a theoretical point of
view. A first-principles calculation was performed to identify the
band structure of a [Nb/V/Ta]n superlattice, where two-atomic-layer
slabs of body-centred cubic Nb, V, and Ta were repeatedly stacked
five times (see Methods). Indeed, we noticed the Rashba spin–orbit
interaction-induced energy splitting near EF (Extended Data Fig. 1), which
was estimated to be ER = 10 meV at maximum (about 1% of EF). The Rashba
splitting is induced by the artificially engineered superlattice structure of
intrinsically centrosymmetric metals. Thus, the Rashba splitting, which
causes nonreciprocal charge transport in the [Nb/V/Ta]n superlattice
(Fig. 3 ), is also verified theoretically, and can be controlled by the super-
lattice structures. Our first-principles calculation reveals that electronic
states near EF are composed of strongly hybridized orbitals of Ta, Nb and
V atoms. Such orbitals are affected by asymmetric heterostructures, and
a combination with a large atomic spin–orbit interaction of Nb and Ta
atoms generates a sizeable Rashba spin–orbit interaction. Here, an essen-
tial feature of the Rashba superconductor is the mixing state of the spin
singlet and triplet pairings^22 –^25. According to the predictions from Wakat-
suki and Nagaosa^21 , one of the mechanisms of magnetochiral anisotropy
in Rashba superconductors could be the superconducting fluctuation
with the mixed spin-singlet and spin-triplet pairings. If we adopt thisacb–0.2 –0.1 0.0 0.1 0.202468ΔIc(mA)I (mA)cΔIc(mA)Magnetic
eld (T)+I- I
4.2 K
6.6 mA2 4681001234- I
0.02 T
0.06 T
0.10 T
0.14 T
0.18 T
Resistance (Ω)|I| (mA)4.2 K+I–0.4–0.20.00.20.4–0.4–0.20.00.20.4–1.0 –0.5 0.00.5 1.0+y- y
2.0 K 3.0 K 4.0 K4.2 K 4.3 K
Magnetic
eld (T)–1.0 –0.5 0.00.5 1.0
Magnetic
eld (T)–1.0 –0.5 0.0 0.5 1.0
Magnetic
eld (T)4.35 K+y- y
+y- y
+y- y
+y- y
+y- y
Fig. 2 | Asymmetric R–I curves and the nonreciprocal critical currents in the
[ N b/ V/ Ta]n superlattice. a, Current dependences of the sheet resistance
under various magnetic fields for both positive and negative currents at 4.2 K.
b, Nonreciprocal critical current Ic as a function of the magnetic field. The red
dashed line indicates a current of 6.6 mA, corresponding to the current
amplitude, demonstrating the superconducting diode effect shown in Fig. 1.
c, The nonreciprocal component of the critical current ΔIc plotted as a function
of the magnetic field at various temperatures. As the temperature increases
towards the Tc, the ΔIc clearly appears and subsequently shrinks.–0.6–0.4–0.2 0.00.2 0.40.6–0.2–0.10.00.10.2Magnetic eld (T)3.5 K4.0 K
4.1 K
4.2 K4.3 K
4.35 KabAmplitude 2.0 mA
–0.4 –0.2 0.0 0.2 0.401234R 2 Z
RZ
+y+y
+x- y
Magnetic eld (T)RZ(Ω) (^2) ZR
(Ω
) R^2
(Z
Ω)
–0.10
–0.05
0.00
0.05
0.10
Amplitude 2.0 mA4.2 K +y–y Fig. 3 | Nonreciprocal charge transport during the
superconducting transition in the [Nb/V/Ta]n
superlattice. a, Magnetic field dependence of first-
(Rω) and second-harmonic (R 2 ω) sheet resistances at
4.2 K. The white and blue shadings indicate the
superconducting and normal conducting regions,
respectively. R 2 ω values are clearly enhanced when
the directions of the current and magnetic field are
orthogonal. b, Temperature dependence of the
antisymmetric second-harmonic sheet resistances.