Loss and decoherence at the quantum Hall - superconductor interface Lingfei Zhao1Zubair Iftikhar1Trevyn F.Q. Larson1Ethan G. Arnault1 Kenji Watanabe2Takashi Taniguchi2Franc ois Amet3and Gleb Finkelstein1

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Loss and decoherence at the quantum Hall - superconductor interface

Lingfei Zhao,1, ∗Zubair Iftikhar,1Trevyn F.Q. Larson,1Ethan G. Arnault,1

Kenji Watanabe,2Takashi Taniguchi,2Franc¸ois Amet,3and Gleb Finkelstein1

1Department of Physics, Duke University, Durham, NC 27708, USA

2National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

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

(Dated: December 4, 2023)

We perform a systematic study of Andreev conversion at the interface between a superconductor and graphene

in the quantum Hall (QH) regime. We ﬁnd that the probability of Andreev conversion from electrons to holes

follows an unexpected but clear trend: the dependencies on temperature and magnetic ﬁeld are nearly decoupled.

We discuss these trends and the role of the superconducting vortices, whose normal cores could both absorb and

dephase the individual electrons in a QH edge. Our study may pave the road to engineering future generation of

hybrid devices for exploiting superconductivity proximity in chiral channels.

Combining superconductors and quantum Hall (QH) sys-

tems has been proposed as a particularly promising direction

for creating novel topological states and excitations [1]. Over

the past few years, signiﬁcant progress has been achieved in

developing such hybrid structures [2–14]. In particular, hy-

bridization of QH edge states across a narrow superconduct-

ing wire is expected to create a gapped topological super-

conductor [6, 15]. In the fractional QH systems, the strong

interactions potentially fractionalize Majorana fermions into

parafermions [13, 16], a key ingredient for universal topolog-

ical quantum computing [1] and exotic circuit elements such

as fractional charge transistors [15].

At the interface between a superconductor and a QH sys-

tem, the QH edge states are expected to be proximitized, turn-

ing into chiral Andreev edge states (CAES). These are dis-

persive states which hybridize the electron and the hole am-

plitudes [17]. An electron approaching the superconducting

region is converted to a linear combination of CAES, which

interfere as they propagate along the interface. The outgoing

particle can either stay as an electron or turn into a hole. We

have previously observed clear evidence of the electron-hole

conversion in the quantum Hall devices with superconducting

contacts [12]. However, the exact mechanism of this conver-

sion remains open: the role of the disorder, superconducting

vortices, and the exact nature of the CAES in this system have

been discussed. It is known that in order to observe a strong

Andreev conversion in an ideal system a precise matching be-

tween the superconductor and the QH edge state momenta is

required [18–21]. However, the presence of disorder is ex-

pected to relax this constraint [22, 23]. Vortices in the su-

perconductor and extra QH channels induced by doping could

also modify the signal [22–25]. In particular, the normal cores

of the vortices can absorb the electrons and holes, reducing the

amplitude of the measured signal [12, 23, 26].

To address the microscopic mechanisms affecting the An-

dreev conversion, here we perform a systematic study of the

conversion probability vs temperature, T, magnetic ﬁeld, B,

and interfacial length, L. We ﬁnd that the dependence of

the electron-hole conversion probability on magnetic ﬁeld

and temperature nearly factorizes. We suggest a simple phe-

FIG. 1. (a) Optical image (left) and 3D schematics (right) of the de-

vice. The black dashed lines label the boundaries of the graphite gate

underneath. The yellow electrodes are normal Cr/Au contacts and the

light gray is the superconducting MoRe, which forms 0.5 µm and 1

µm interfaces with graphene. (b) Sketch of the measurement setup.

The current is injected from the upstream contact into the grounded

superconductor, while measuring the voltage at the downstream con-

tact. (c) The maximum and minimum values of Rd(left) and Peh

(right) measured for the shorter interface. The statistical information

is collected in the VGrange corresponding to ν= 2, as outlined by

the green lines in Fig. 3a. The temperature is 40 mK.

nomenological expression involving exponential decays as a

function of B,Tand L, and a prefactor determined by the

conﬁguration of superconducting vortices. The expression

captures the observed dependencies very well, and can be in-

terpreted in terms of the CAES loss and decoherence. We ﬁ-

nally discuss the distribution of the Andreev conversion prob-

ability [23], which is unexpectedly found to have a roughly tri-

angular shape. We discuss the implications of our ﬁndings for

the future development of the more complex devices, which

will further explore the physics of superconducting correla-

tions in the chiral states.

The main device studied here is a hBN/graphene/hBN het-

erostructure in contact with both superconducting and nor-

mal electrodes (Fig. 1a). The superconducting electrode (light

gray) is made of sputtered Mo-Re alloy (50-50 in weight) with

a critical temperature Tc∼10 K and an upper critical ﬁeld

Hc2exceeding 12 T. The work function of the alloy ∼4.2

eV [27] is slightly lower than that of graphene ∼4.5 eV [28],

resulting in an n-doped graphene region nearby. The graphene

sheet is separated into two independent regions by the etching

arXiv:2210.04842v2 [cond-mat.mes-hall] 1 Dec 2023

step that deﬁnes the superconducting electrode. The widths of

the resulting superconductor-graphene interfaces are 0.5 and

1µm. The normal contacts (yellow) are thermally evaporated

Cr/Au. The electron density inside the graphene is controlled

by applying a voltage VGto the graphite gate which spans

the whole area underneath the heterostructure. While such

graphite gates are known to efﬁciently screen the disorder po-

tential, the results here are similar to our previous measure-

ments of samples without the graphite gate. This indicates that

the observed physics is not strongly inﬂuenced by the disorder

in the graphene layer.

We measure the nonlocal resistance downstream of a

grounded superconducting contact, Rd=dVd/dI, as

sketched in Fig. 1b and demonstrated in the supplemen-

tary [29]. The CAES formed by the superconductor travel

along the interface and recombine into either an electron or

hole (or their linear combination) at the end of the inter-

face. Sweeping the gate voltage VGon top of the QH plateau

tunes the momentum difference between the interfering CAES

and produces an oscillating pattern of Rd(VG)(Fig. S1 in

[29]) [12]. Due to the disordered nature of the interface, these

interference patterns are highly irregular and resemble the uni-

versal conductance ﬂuctuations [22, 23]. Throughout the pa-

per we analyze the statistical properties of these patterns.

We further convert Rdinto the difference between the prob-

abilities of normal and Andreev reﬂections, Peh ≡Pe−Ph,

where Pe(Ph) is the probability of an electron (or a hole) to

be emitted downstream of the superconductor. It is straight-

forward to show that Peh =Rd/(Rd+RH), where RHis the

Hall resistance [12]. Note that the extreme values of Rdare

reached either for the pure electron reﬂection (Pe= 1,Ph= 0

and Rd=∞, the interface is effectively fully opaque), or for

perfect Andreev conversion (Pe= 0,Ph= 1,Rd=−RH/2,

a Cooper pair is transferred across the interface per incom-

ing electron). We therefore expect that the distribution of Rd

should be skewed toward positive resistances.

Indeed, this skewness can be observed by studying an im-

balance between the maximum and minimum values of the

downstream resistance Rd(VG). We extract these quantities

in the VGrange corresponding to the ν= 2 plateau for a

given ﬁeld and then plot Rmax and Rmin as a function of B

in Fig. 1c. The ﬁeld changes the vortex conﬁguration every

few mT [12], thereby allowing us to sample multiple different

patterns of Rd(VG). The data clearly shows that Rmax is on

average larger than |Rmin|. The apparent imbalance between

electrons and holes is eliminated by converting Rdto Peh in

Fig. 1c. (See Fig. S3 in [29] for the similar result measured

in another device.) We conclude that the probabilities of an

electron or a hole being emitted downstream (Peand Ph) are

very similar. From now on, we present Peh in lieu of Rd.

Depending on the length of the interface, the highest

electron-hole conversion efﬁciency we observe is about 0.2

– 0.3. While being very high, this value is still far from reach-

ing unity. Thermal smearing, decoherence and tunneling into

the normal vortex cores can all contribute to this suppression.

Since at zero temperature only the effect of the vortices re-

FIG. 2. (a) Peh measured for the 0.5 µm interface as a function of

VGon top of the ν=2 plateau at B=2.2 T. The temperature is

varied from the base temperature of 40 mK to about 670 mK. (b)

The standard deviation of Peh of the 0.5 µm (ﬁlled triangle) and 1

µm (open circle) interfaces as a function of temperature at various

magnetic ﬁelds. The inset plots the decay constant T0obtained from

exponential ﬁts vs. the magnetic ﬁeld. The lines represent the aver-

ages of the dots.

mains, we ﬁrst look into the dependence of Peh on tempera-

ture. Fig. 2a plots Peh of the shorter interface (0.5 µm) mea-

sured over the ν=2 plateau at B=2.2 T from 40 mK to

670 mK. As the temperature Tincreases, Peh gradually de-

cays towards zero, except around 400 mK where the traces

brieﬂy jump to a completely different oscillation pattern. We

attribute this jump to a temporary change of the conﬁguration

of superconducting vortices during the measurement.

To get a quantitative understanding of the thermal effects,

we plot the standard deviation of the traces, σ, as a function

of temperature in Fig. 2b for both interfaces at various mag-

netic ﬁelds. The ﬁlled triangles (open circles) represent L=

0.5 µm (1 µm). The green triangles correspond to the data in

Fig. 2a. We ﬁnd an exponential decay of σas a function of

temperature, i.e. σ∝exp(−T/T0), where T0is the decay

constant. Remarkably, σfollows roughly the same decay rate

for a given interface length. Even the curves of Fig. 2a which

experienced a random jump follow the same slope. (Note the

few green symbols nearly overlapping with the purple ones

around 0.4 K.) This means that the conﬁguration of supercon-

ducting vortices does not have a strong inﬂuence on the tem-

perature dependence, even if it dramatically affects the ampli-

tude and the pattern of ﬂuctuations!

The exponential decay is observed regardless of the length

of the interface and the magnetic ﬁeld. For the longer in-

terface, the decay rate becomes less steep at higher temper-

atures, but only as the signals approach the noise ﬂoor of a

few ×10−3, so we extract the slope from the low-temperature

range. In the inset of Fig. 2b, we plot the resulting T0vs. B

for L=0.5 and 1 µm. It is clear that T0does not show any

strong dependence on Band scales inversely with L.

In principle, the exponential temperature dependence could

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LossanddecoherenceatthequantumHall-superconductorinterfaceLingfeiZhao,1,∗ZubairIftikhar,1TrevynF.Q.Larson,1EthanG.Arnault,1KenjiWatanabe,2TakashiTaniguchi,2Franc¸oisAmet,3andGlebFinkelstein11DepartmentofPhysics,DukeUniversity,Durham,NC27708,USA2NationalInstituteforMaterialsScience,1-1Namiki,Tsukuba3...

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Loss and decoherence at the quantum Hall - superconductor interface Lingfei Zhao1Zubair Iftikhar1Trevyn F.Q. Larson1Ethan G. Arnault1 Kenji Watanabe2Takashi Taniguchi2Franc ois Amet3and Gleb Finkelstein1

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