3 74 | Nature | Vol 584 | 20 August 2020
Article
engineered three-dimensional superlattice. The nonreciprocal critical
current presented here can be considered to be a consequence of the
magnetochiral anisotropy in the Rashba superconductor.
The superlattice [Nb (1.0 nm)/V (1.0 nm)/Ta (1.0 nm)] 40 , which was
epitaxially grown on the MgO (100) substrate with well defined peri-
odic interfaces^20 , was fabricated into a wire structure for four-terminal
measurements (see Methods and Fig. 1b). An external magnetic field
was applied by a superconducting magnet in a Physical Property
Measurement Systems (PPMS-3) chamber, whose direction was in the
plane of the film and perpendicular to the flowing current I. Here, the
current and magnetic field directions are defined as the x and y axes,
respectively.
First, we measured the temperature dependence of the sheet resist-
ance with a small d.c. current I = +0.1 mA to determine the critical tem-
perature Tc. As shown in Fig. 1c, we found that the Tc is 4.41 K and the
normal resistance is around 3.75 Ω at low temperature. The alternating
switching between the superconducting and normal conducting states
(Fig. 1c) was demonstrated as follows: after setting the magnetic field
at +0.02 T (or −0.02 T) in the +y direction, the sheet resistance was con-
tinuously measured with the positive d.c. current I = +6.6 mA at 4.2 K,
slightly below Tc. Then, whereas zero resistance (about 0.0017 Ω) was
obtained with the positive magnetic field, normal resistance (3.76 Ω)
was obtained when the magnetic field reversed. When we applied a
negative d.c. current I = −6.6 mA, the switching behaviour reversed.
This result strongly indicates that the superconducting and normal con-
ducting states are fully switched depending on the sign of the magnetic
field and the current. Two important features are: a rectification ratio
over 2,000, comparable to those of typical semiconductor diodes, and
nonreciprocity that can be easily controlled by a small magnetic field.
To investigate the superconducting diode effect in detail, we meas-
ured the d.c. current dependence of the sheet resistance under various
magnetic fields and temperatures (Fig. 2 ). In the typical measurement
results at 4.2 K (Fig. 2a), we notice that the R–I curves show a jump at
different currents depending on whether the applied d.c. currents are
positive (+I) or negative (−I). The sharpness of the phase transition, per-
haps owing to the three-dimensionality of the [Nb/V/Ta]n superlattice
compared to other low-dimensional superconductors, allows switching
between the superconducting and normal conducting states (Fig. 1c).
Here, the midpoint of the R–I curve is defined as the critical current
Ic, and the Ic values under the various magnetic fields are plotted for
both positive (+I) and negative (−I) currents (Fig. 2b). The upper criti-
cal field Bc2 is estimated to be 0.2 T from the Ic curves, which means
the diode effect demonstrated in Fig. 1c can be controlled by a tenth
or less of the Bc2. These two curves clearly suggest that the sign of the
nonreciprocal components in Ic is uniquely determined by the rela-
tive angle between the current and magnetic field directions, where
Ic increases when the magnetic field is directed left of the current and
decreases when directed right of the current. Next, we investigated
the temperature dependence of the nonreciprocal critical current to
characterize its behaviour. Here, the nonreciprocal component ΔIc is
defined as in equation ( 2 ).Δ=IIcc(+II)−c(−I) (2)The magnetic field dependence of the ΔIc was investigated in the range
2.0–4.35 K (Fig. 2c). For each temperature, the results where the magnetic
field was swept forward (+y) and backward (−y) along the y axis exhibit an
antisymmetric behaviour with regard to the magnetic field; this confirms
that the ΔIc is intrinsically determined by the magnetic field. We find that
as the temperature increases towards the Tc, the ΔIc clearly appears and
subsequently shrinks, which resembles the behaviour of the nonrecipro-
cal charge transport in MoS 2 (ref.^10 ), WS 2 (ref.^11 ) and Bi 2 Te 3 /FeTe (ref.^12 ).
To understand the temperature dependence of the diode effect, it will
be desirable to develop a microscopic theory of the critical current.
We performed an alternating current (a.c.) harmonic measurement
to discover the mechanism of the nonreciprocal critical current by
comparing with the nonlinear resistance in equation ( 1 ). Once again,
the nonreciprocal nature induced by Rashba spin–orbit interaction
appears in the form of current-dependent resistance under the mag-
netic field B. To distinguish the linear and nonlinear resistances, the
first- and second-harmonic sheet resistances (Rω and R 2 ω) were meas-
ured using a lock-in amplifier under the application of an a.c. currentacMagnetic eldNormalSuperconductingb
Nb
Ta
V
Nb
Ta
V
Nb
Ta x
Magnetic eldy
100 μm2460123450204060012345Resistance (Ω)Temperature (K)+0.1 mA +6.6 mA
–6.6 mA–0.02 TMeasurement counts+0.02 T +0.02 T–0.02 T +0.02 T––0.02 T +0.02 T 0.02 TFig. 1 | Demonstration of the magnetically controllable superconducting
diode. a, Schematic images of the superconducting diode controlled by an
external magnetic field and the artificial [Nb/V/Ta]n superlattice, in which the
global inversion symmetry is broken along the direction of stacking. When the
directions of the current, the magnetic field and inversion symmetry breaking
are orthogonal to one other, the Cooper pairs can f low in only one direction.
b, Photomicrograph of the processed device and the measurement setup
with the definitions of electric current and magnetic field. c, Temperature
dependence of the sheet resistance of the [Nb(1.0 nm)/V(1.0 nm)/Ta(1.0 nm)] 40
film and alternating switching between the superconducting and normal
conducting states by changing the sign of the applied current or magnetic field
at 4.2 K.