Science - USA (2020-05-01)

Next,weturnedtoafeaturenotobservedin
the LP experiment. The curves ofDfnsuggest
that at lowT, it is possible to detect excited
states. Using high-resolution scans, we have
resolved weak excitation branches trailing from
the scalloped boundary (Fig. 3A). As shown by

the green dots in Fig. 3A, the branches fit well

to Eq. 1. The excitations are also directly visible

in individual traces ofdV/dIversusI(Fig. 3B).

The large peak traces out the arcs of the scal-

loped boundary (Fig. 3B, yellow curve). At the

cusp, a small peak (20× to 30× weaker in

strength) emerges and traces out an excitation

branch (Fig. 3B, blue curve). These excitations

arealsoseeninsampleS2(fig.S9).

Our scenario for the excitation branch is

sketched in Fig. 3, C and D. Whenfis fixed at

nf 0 (Fig. 3C, dashed line), the system lies at

536 1 MAY 2020•VOL 368 ISSUE 6490 sciencemag.org SCIENCE

Fig. 2. Area scaling, frequency chirp, and

scalloped profile.(A) Variation of the flux

penetration areaAf=h(B)Aphysin five samples

measured atT= 20 mK, whereh(B) is the fraction

of flux penetration in fieldB. In weakB, the data

(black symbols) fall on the line withh(B~ 0) = 0.35

(black dashed line). AsBincreases,h(B) in each

sample increases toward 1 (broad arrows). At

the red circles,Bequals 7.6, 1.1, 1.5, 3.6, and

0.6 mT in samples S1, S2, S3, S5, and S6,

respectively. (B) The increase inAfversusB

(in sample S1) saturates forB> 6 mT (Bc≈

10 mT). The red curve is a Gaussian fit. The

dashed line indicatesAphys.(C) Sketch of fluxoids

(black arrows) trapped in a superconducting

cylinder in the Little Parks experiment ( 21 ) (left)

and by the edge supercurrentJes(white arrows)

in MoTe 2 (right). The widthdeofJesis shown.

(D) Changes in the superfluid kinetic energy lead

to a set of branches of the free energyDfn,

each centered atf=nf 0. Jumps between

intersecting branches result in a sawtooth profile

forvsand oscillations in the edge condensate

amplitude squaredDY^2 e, observed as a

characteristic scalloped boundary in the critical

currentIc(B).

A B

C

D

Little Parks

Expt.

Present Experiment 012 3

e^2

vs

012 3

012 3

fn

-8 -6 -4 -2 0 2 4 6 8 10

4.0

4.5

5.0

5.5

6.0

6.5

A

(

m)

B (mT)

S1

0 10 20 30 40 50 60 70

0

10

20

30

40

50

60

70

S5

S6

S3

S2

A

m

2 )

Aphys(m^2 )

S1

B = B (c = 1)

B ~ 0 ( = 0.35)

Jes

w

d

e

Aphys

2

Fig. 3. Emergence of excitation branches.(A) High-

resolution color map ofdV/dIcurves showing weak

excitation branches trailing from each minimum in the

scalloped boundary. The data are obtained at 20 mK

in sample S6 withB< 0 andI> 0. Green dots represent

fits to Eq. 1. (B) Shown are 21 traces ofdV/dIversus

Iin the interval–0.29 <B<–0.35 mT (shifted vertically

for clarity). The scalloped boundary (yellow curve)

is traced by the large peak. At each cusp, a weak peak

emerges and branches off to the left to trace out an

excitation branch (blue curve). (C) Schematic plots

ofDfnandDfn– 1 (magenta parabolas) and the sawtooth

profile ofvs. The corresponding curves ofY^2 eare plotted

in (D) (green parabolas). Bold blue arcs represent

the scalloped boundary ofIc(B). Withffixed atnf 0

(dashed lines), the system occupies the lowest-energy

branch, withn= 3 fluxoids andvs= 0. WhenIis scanned

at fixedB, the excited state (with 2 fluxoids and a

largev′s) is encountered at a current smaller thanIc(B).

This is observed as the excitation branch.

78910

0

1

2

3

4

5

6

7

B=-0.35mT

dV/dI (

1

)

Ibias(+A)

-0.29 mT

B

C

n-1 n q/q

0

6 fn

v’

6 fn-1 D

^

2

e, Ic

ground state

exc. state

-0.4 -0.35 -0.3 -0.25

B (mT)

7

8

9

10

I (

A)

0

0.5

1

1.5

2

2.5

3

dV/dI (

1

)

A

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