Non-Reciprocal Supercurrents in a Field-Free Graphene Josephson Triode John Chiles1y Ethan G. Arnault1y Chun-Chia Chen1 Trevyn F.Q. Larson1 Lingfei Zhao1 Kenji Watanabe2 Takashi Taniguchi2

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Non-Reciprocal Supercurrents in a Field-Free Graphene Josephson Triode

John Chiles1†*, Ethan G. Arnault1†, Chun-Chia Chen1, Trevyn F.Q. Larson1,

Lingfei Zhao1, Kenji Watanabe2, Takashi Taniguchi2,

Fran¸cois Amet3, Gleb Finkelstein1

1Department of Physics, Duke University, Durham, NC 27701, USA

2National Institute for Materials Science, Tsukuba, 305-0044, Japan

3Department of Physics and Astonomy, Appalachian State University, Boone, NC 28607, USA

†These authors contributed to this work equally

∗To whom correspondence should be addressed; E-mail: john.chiles@duke.edu

(Dated: October 7, 2022)

Superconducting diodes are proposed non-reciprocal circuit elements that should exhibit non-

dissipative transport in one direction while being resistive in the opposite direction. Multiple exam-

ples of such devices have emerged in the past couple of years, however their eﬃciency is typically

limited, and most of them require magnetic ﬁeld to function. Here we present a device achieving

eﬃciencies upwards of 90% while operating at zero ﬁeld. Our samples consist of a network of three

graphene Josephson junctions linked by a common superconducting island, to which we refer as a

Josephson triode. The triode is tuned by applying a control current to one of the contacts, thereby

breaking the time-reversal symmetry of the current ﬂow. The triode’s utility is demonstrated by

rectifying a small (tens of nA amplitude) applied square wave. We speculate that devices of this

type could be realistically employed in the modern quantum circuits.

I. INTRODUCTION

Diodes form one of the most important building blocks

in electronic circuits, since they can be used in AC-

DC conversion, signal rectiﬁcation, and photodetection.

The utility of diodes resides in their ability to oﬀer non-

reciprocity – a low resistance to current ﬂowing in one

direction and a high resistance to current ﬂowing in the

opposite direction. While traditional diodes exploit P-N

interfaces in semiconducting materials, a ﬂurry of theo-

retical interest has focused on developing their supercon-

ducting analogues [1–8].

While these studies have followed a decade-long ex-

plorations of non-reciprocal supercurrents [9–19], the re-

cent interest is driven by the search of novel materials

which break both the inversion and time-reversal sym-

metry, thereby intrinsically enabling the superconduct-

ing diode eﬀect (SDE). Such materials have indeed been

experimentally identiﬁed and investigated, ranging from

metallic ﬁlms and proximitized semiconductors to van

der Waals heterostructures [20–30]. While this direction

oﬀers a probe into the symmetry properties of novel ma-

terials, the resulting devices typically have limited diode

eﬃciency, which is deﬁned as a ratio of supercurrent in

the forward and backward directions.

In the meanwhile, it has been realized that higher su-

perconducting diode eﬃciency can be achieved in prop-

erly designed nanostructures with an external magnetic

ﬁeld applied to break the time-reversal symmetry [31–

35]. Unfortunately, magnetic ﬁeld is often undesired for

integrating the diodes in superconducting circuits. In

this work, we rectify this problem by creating supercon-

ducting diodes which can operate at zero external mag-

netic ﬁeld and achieve eﬃciency approaching 100%. Our

devices are based on multiterminal Josephson junctions

made in graphene. In the past few years, the multitermi-

nal junctions have been realized in a variety of materials

[36–41] and have even found a foothold as a solution to

technological problems [42, 43].

We utilize the developments of multi-terminal Joseph-

son junction design to eliminate the necessity of an ap-

plied magnetic ﬁeld to achieve the SDE. The structure is

based on three graphene Josephson junctions tied at the

central superconducting island (Fig. 1a). Without ap-

plying a DC oﬀset bias, all junctions are superconduct-

ing and the I−Vcurves are symmetric. By applying

a dissipationless control current in one of the junctions,

we break the time-reversal symmetry and tune the I−V

curves of the other two junctions, achieving the SDE eﬃ-

ciencies exceeding 90%. Our devices are further tunable

by electrostatic gating [44], which allows us to adjust the

scale the supercurrent that can be rectiﬁed.

II. RESULTS

Our devices feature a trapezoidal superconducting is-

land and three superconducting contacts labeled left (L),

right (R) and bottom (B), Fig. 1a. (An additional side-

gate approaching the island from the top does not con-

tact the device and is not used in these measurements.)

The contacts are connected to the island through 500

nm graphene channels which are etched such that none

of the contacts are connected through graphene alone –

all transport must occur through the central island. We

have measured two devices which yielded very similar re-

sults. For consistency, we present the results for one of

them, shown at the bottom of Fig. 1a.

The contacts and the island are made of sput-

tered molybdenum-rhenium (MoRe), which oﬀers high-

arXiv:2210.02644v1 [cond-mat.mes-hall] 6 Oct 2022

5 μm

Gate

Island

a) d)

5 μm

FIG. 1. a) An SEM image of the device and a schematic of the relevant Josephson network (inset). We measure the bottom

one of the two similar devices, which is comprized of a superconducting island connected to three superconducting leads (L, R,

B) via graphene junctions (not visible). The gate electrode approaching the island from the top is not used here. b) Map of

dVLB

dILwith a central diamond corresponding to junctions L and B both superconducting. The dashed lines mark the locations

of the I−Vcuts further analyzed in Fig. 2. c) A similar map of dVRB

dIRwith a central diamond corresponding to junctions R

and B both superconducting. d) Grayscale enhanced-contrast map averaging the maps in (b) and (c). The black central region

denotes the overlap of the central diamonds in (b) and (c) – a roughly hexagonal region where all transport through the device

is dissipationless.

transparency Ohmic contact to graphene [45, 46]. The

devices are cooled to a base temperature of 60 mK in

a Leiden Cryogenics dilution refrigerator. A signiﬁcant

hysteresis is observed between the switching and retrap-

ping currents, indicating either underdamping, or more

likely electron overheating [47]. To avoid this hysteresis,

the sample is heated to 1.75−1.9 K for the measurements

in Figs. 1-3. We have veriﬁed that all the features mea-

sured at this temperature range exhibit negligible hys-

teresis and can be measured by sweeping the current in

any direction. DC currents ILand IRare applied to

the left and right contacts with respect to the grounded

bottom contact, and a small AC excitation is used for

extracting diﬀerential resistances. To maximize the crit-

ical current, a back gate voltage of 20 V is applied in

Figs. 1, 2, and 4. The Dirac point in this sample is at

2.5 V. Importantly, all measurements take place at zero

magnetic ﬁeld.

Fig. 1b and Fig. 1c correspond to the diﬀerential re-

sistant maps measured between the left and bottom (1b)

and right and bottom (1c) contacts. Correspondingly,

the prominent horizontal (1b) and vertical (1c) features

correspond to the regimes where respectively the left and

right junctions are superconducting. The diagonal fea-

ture common to both maps corresponds to the bottom

junction being superconducting. The device’s collective

behavior can be gleaned from Fig. 1d where dVLB /dIL

and dVRB /dIRare averaged. The distinct black region

in the center of this map occurs where all three junctions

are superconducting and the transport across the entire

device is dissipationless.

The boundaries of the dissipationless region (an un-

even hexagon) correspond to points where at least one

junction on the device switches to normal. The non-

reciprocity we exploit here appears in the regions of the

hexagon deﬁned by the switching currents of two junc-

+IC

a) b) c)

-IC

FIG. 2. I−Vcurves of the left junction measured at 3 values of IR: a) −0.3µA, b) 0µA, and c) 0.3µA. In all cases, the control

current IRis well within the dissipationless range of the right junction. In all panels, ILis swept back and forth, showing

negligible hysteresis. In panel (b), the I−Vcurves are reciprocal, as expected. In (a) and (c), either I−

cor I+

care approaching

zero, resulting in a nearly ideal superconducting diode eﬀect.

tions. An example is the left dashed line in Fig. 1b, which

cuts through the hexagonal region away from its center.

As a result, the system stays dissipationless only for pos-

itive ILand becomes dissipative at negative IL(Fig. 2a).

Note that all three junctions play a role in this this pro-

cess: the bottom junction switches at IL=I−

c≈0 while

the left junction is responsible for the upper limit of the

dissipationless range, I+

c; ﬁnally, it is the biasing of the

right junction which establishes the required asymme-

try. For zero IR, one recovers a symmetric cross-section

along the ILdirection (central white line in Fig. 1b and

Fig. 2b). Finally, at the opposite value of the control

current IR(right dash line in Fig. 1b and Fig. 2c) the

system stays dissipationless only at negative IL≤0 and

the curves are reversed compared to Fig. 2a. Note that

the right junction is biased below its critical current in

all three cases.

Collectively, the boundaries of the hexagon enable tun-

ing of the transport non-reciprocity between any pair of

contacts by adjusting the current applied to the third

contact. This leads to a diode eﬃciency,

η=I+

c+I−

I+

c−I−

,(1)

that in practice can be tuned to exceed 90%, as will be

seen in Fig. 2, where we plot the I−Vcurves corre-

sponding to the three cross-sections in Fig. 1b. Each set

of curves is measured in both directions, showing negligi-

ble hysteresis. When IR= 0 (Fig. 2b) the curves are ex-

pectedly symmetric, so I+

c=−I−

cand η= 0. However,

as IRis tuned away from zero, the non-reciprocity grows

and |η|increases until it reaches ±94% at IR=±0.3µA.

Further increase of ηis possible by applying higher IR.

In fact, formally ηcan exceed unity when I−

cbecomes

positive (same sign as I+

c). However, this regime should

be avoided if we are interested in rectifying small cur-

rents. Hence we stop increasing |IR|at the point where

the high slope “knee” of the I−Vcurve approaches the

point IL= 0. We then deﬁne I−

cconservatively as a point

at half the slope of the knee (see arrow in Fig. 2a), re-

sulting in the η≈94%. Finally, either positive (Fig. 2a)

or negative (Fig. 2c) currents can be rectiﬁed depending

on the desired operation.

To demonstrate the potential utility of the device in

quantum circuits, we decrease the gate voltage to zero

and apply a square wave of amplitude ±60 nA to the

left contact (Fig. 3a). IRcan then be set to produce

desirable device responses: namely, at IR= 50 and −50

nA, the negative and positive portions of the square wave

are respectively rectiﬁed. Further, when IR= 0, the de-

vice is fully superconducting for the entire square wave,

as its amplitude is smaller than the critical current of

the device. As a result, the entire square wave passes

through the device without dissipation. Interestingly, we

can change the biasing scheme to further utilize the tri-

ode’s three-terminal nature. In Fig. 3b, we continue

measuring VLB but now use ILas a control parameter,

while applying a square wave to IR. As a result, the volt-

age at the left contact, VLB , switches depending on the

sign of the square wave applied to the right contact.

Fig. 4 explores the behavior of the sample as a func-

tion of temperature. The top row demonstrates the ef-

fect of temperature on the map of RLB vs IL,R, ﬁrst

shown in Fig. 1. At the base temperature of 60 mK

(Fig. 4a), the hysteresis is evident as the central super-

conducting pocket is shifted upward in the sweep direc-

tion. This hysteresis is still evident but much reduced at

1.3K (Fig. 4b), and ﬁnally it is clearly absent at 1.9 K

(Fig. 4c). This is important, as hysteresis would prevent

the diode from properly rectifying small currents. The

bottom row presents the IL−VLB curves, measured at

the same three temperatures with the IRadjusted to op-

timally tune the diode eﬃciency. (The values of IRare

indicated as white lines across the corresponding maps.)

Again, pronounced hysteresis is observed at the lowest

temperature, but it is almost gone at 1.3 K, while the up-

per switching current, I+

c≈1µA, is not much suppressed

compared to the lowest temperature. Further optimisa-

tion may result in suppressing the hysteresis at the base

temperature. However, even the present device could be

placed at the still plate of the dilution refrigerator to eﬃ-

ciently rectify a range of currents in the 0.1−1µA range.

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Non-ReciprocalSupercurrentsinaField-FreeGrapheneJosephsonTriodeJohnChiles1y*,EthanG.Arnault1y,Chun-ChiaChen1,TrevynF.Q.Larson1,LingfeiZhao1,KenjiWatanabe2,TakashiTaniguchi2,FrancoisAmet3,GlebFinkelstein11DepartmentofPhysics,DukeUniversity,Durham,NC27701,USA2NationalInstituteforMaterialsScience,Tsuk...

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Non-Reciprocal Supercurrents in a Field-Free Graphene Josephson Triode John Chiles1y Ethan G. Arnault1y Chun-Chia Chen1 Trevyn F.Q. Larson1 Lingfei Zhao1 Kenji Watanabe2 Takashi Taniguchi2

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