We revisit the critical penetration of Pearl vortices in narrow superconducting flat rings cooled in magnetic fields. Scanning superconducting quantum interference device microscopy measurements showed how a magnetic field penetrates and vortices are trapped in flat rings made of amorphous MoGe thin films. Counting the number of trapped vortices for each image, we found that the vortices are completely excluded from the ring annulus when the applied field H is below a threshold field Hp: Above this field, the vortices increase linearly with the field. The obtained values of Hp depend on the annulus width wring and follow the relation μ0Hp=(1.9±0.1)Φ0/wring2 with the superconducting flux quantum Φ0. This relationship provides an insight into the effect of the net-current circulating in the annular region and also leads to a precise control to trap or eliminate vortices in flat rings.

1.
J.
Pearl
,
Appl. Phys. Lett.
5
,
65
(
1964
).
2.
E. H.
Brandt
,
Phys. Rev. B
72
,
024529
(
2005
).
3.
A. I.
Buzdin
,
Phys. Rev. B
47
,
11416
(
1993
).
4.
J. J.
Palacios
,
Phys. Rev. Lett.
84
,
1796
(
2000
).
5.
B. J.
Baelus
,
L. R. E.
Cabral
, and
F. M.
Peeters
,
Phys. Rev. B
69
,
064506
(
2004
).
6.
V. V.
Moshchalkov
,
L.
Gielen
,
C.
Strunk
,
R.
Jonckheere
,
X.
Qiu
,
C. V.
Haesendonck
, and
V.
Bruynseraede
,
Nature
373
,
319
(
1995
).
7.
R.
Benoiset
and
W.
Zwerger
,
Z. Phys. B
103
,
377
(
1997
).
8.
V. A.
Schweigert
and
F. M.
Peeters
,
Phys. Rev. B
57
,
13817
(
1998
).
9.
L. F.
Chibotaru
,
G.
Teniers
,
A.
Ceulemans
, and
V. V.
Moshchalkov
,
Phys. Rev. B
70
,
094505
(
2004
).
10.
I. V.
Grigorieva
,
W.
Escoffier
,
J.
Richardson
,
L. Y.
Vinnikov
,
S.
Dubonos
, and
V.
Oboznov
,
Phys. Rev. Lett.
96
,
077005
(
2006
).
11.
N.
Kokubo
,
S.
Okayasu
,
A.
Kanda
, and
B.
Shinozaki
,
Phys. Rev. B
82
,
014501
(
2010
).
12.
V. R.
Misko
,
H. J.
Zhao
,
F. M.
Peeters
,
V.
Oboznov
,
S. V.
Dubonos
, and
I. V.
Grigorieva
,
Supercond. Sci. Technol.
22
,
034001
(
2009
).
13.
N.
Kokubo
,
S.
Okayasu
,
T.
Nojima
,
H.
Tamochi
, and
B.
Shinozaki
,
J. Phys. Soc. Jpn.
83
,
083704
(
2014
).
14.
H. J.
Zhao
,
V. R.
Misko
,
F. M.
Peeters
,
S.
Dubonos
,
V.
Oboznov
, and
I. V.
Grigorieva
,
Europhys. Lett.
83
,
17008
(
2008
).
15.
N.
Kokubo
,
H.
Miyahara
,
S.
Okayasu
, and
T.
Nojima
,
J. Phys. Soc. Jpn.
84
,
043704
(
2015
).
16.
H. T.
Huy
,
M.
Kato
, and
T.
Ishida
,
Supercond. Sci. Technol.
26
,
06500
(
2013
).
17.
T.
Cren
,
D.
Fokin
,
F.
Debontridder
,
V.
Dubost
, and
D.
Roditchev
,
Phys. Rev. Lett.
102
,
127005
(
2009
).
18.
T.
Tominaga
,
T.
Sakamoto
,
H.
Kim
,
T.
Nishio
,
T.
Eguchi
, and
Y.
Hasegawa
,
Phys. Rev. B
87
,
195434
(
2013
).
19.
T. D.
Vu
,
H. T.
Huy
,
A.
Ito
,
M.
Toji
,
H.
Shishido
,
M.
Kato
,
M.
Hayashi
, and
T.
Ishida
,
Supercond. Sci. Technol.
31
,
125009
(
2018
).
20.
I.
Nsanzineza
and
B. L. T.
Plourde
,
Phys. Rev. Lett.
113
,
117002
(
2014
).
21.
C.
Wang
,
Y. Y.
Gao
,
I. M.
Pop
,
U.
Vool
,
C.
Axline
,
T.
Brecht
,
R. W.
Heeres
,
L.
Frunzio
,
M. H.
Devoret
,
G.
Catelani
,
L. I.
Glazman
, and
R. J.
Schoelkopf
,
Nature Comm.
5
,
5836
(
2014
).
22.
M.
Taupin
,
I. M.
Khaymovich
,
M.
Meschke
,
A. S.
Mel’nikov
, and
J. P.
Pekola
,
Nature Comm.
7
,
109777
(
2016
).
23.
K. K.
Likharev
,
Radiophys. Quantum Electron.
14
,
722
(
1971
).
24.
G. M.
Maksimova
,
Phys. Solid State
40
,
1607
(
1998
).
25.
G.
Stan
,
S. B.
Field
, and
J. M.
Martinis
,
Phys. Rev. Lett.
92
,
097003
(
2004
).
26.
K. H.
Kuit
,
J. R.
Kirtley
,
W. v. d.
Veur
,
C. G.
Molenaar
,
F. J. G.
Roesthuis
,
A. G. P.
Troeman
,
J. R.
Clem
,
H.
Hilgenkamp
,
H.
Rogalla
, and
J.
Flokstra
,
Phys. Rev. B
77
,
134504
(
2008
).
27.
V. G.
Kogan
,
J. R.
Clem
, and
R. G.
Mints
,
Phys. Rev. B
69
,
064516
(
2004
).
28.
T.
Nishio
,
A.
Toshu
,
A.
Nomura
,
K.
Miyachi
,
T.
Eguchi
,
H.
Sakata
,
S.
Lin
,
N.
Hayashi
,
N.
Nakai
,
M.
Machida
, and
Y.
Hasegawa
,
Phys. Rev. Lett.
101
,
167001
(
2008
).
29.
K.
Suzuki
,
Y.
Li
,
U.
Utagawa
, and
K.
Tanabe
,
Appl. Phys. Lett.
76
,
3615
(
2000
).
30.
E. H.
Brandt
and
J. R.
Clem
,
Phys. Rev. B
69
,
184509
(
2004
).
31.
R.
Wördenweber
and
P.
Selders
,
Physica C
366
,
135
(
2002
).
32.
S. A.
Mills
,
C.
Shen
,
Z.
Xu
, and
Y.
Liu
,
Phys. Rev. B
92
,
144502
(
2015
).
33.
M.
Mitsuishi
,
N.
Kokubo
,
K.
Kitano
,
S.
Okayasu
,
T.
Nojima
, and
T.
Sasaki
,
J. Phys. Conf. Ser.
969
,
012074
(
2018
).
34.
P. H.
Kes
and
C. C.
Tsuei
,
Phys. Rev. B
28
,
5126
(
1983
).
35.
See
J. R.
Kirtley
,
C. C.
Tsuei
,
V. G.
Kogan
,
J. R.
Clem
,
H.
Raffy
, and
Z. Z.
Li
,
Phys. Rev. B
68
,
214505
(
2003
) for details in the difference between the magnetic signal at the ring center and that outside the annular ring.
36.
For the subtraction, a careful adjustment was made with respect to a sample position in the scale of a lateral step size of 4 μm.
37.
T.
Nishio
,
S.
Okayasu
,
J.
Suzuki
,
N.
Kokubo
, and
K.
Kadowaki
,
Phys. Rev. B
77
,
052503
(
2008
).
38.
J. C.
Wynn
,
D. A.
Bonn
,
B. W.
Gardner
,
Y. J.
Lin
,
R.
Liang
,
W. N.
Hardy
,
J. R.
Kirtley
, and
K. A.
Moler
,
Phys. Rev. Lett.
87
,
197002
(
2001
).
39.
T.
Nishio
,
Q.
Chen
,
W.
Gillijns
,
K. D.
Keyser
,
K.
Vervaeke
, and
V. V.
Moshchalkov
,
Phys. Rev. B
77
,
012502
(
2008
).
40.
J.
Ge
,
J.
Gutierrez
,
J.
Cuppens
, and
V. V.
Moshchalkov
,
Phys. Rev. B
88
,
174503
(
2013
).
41.
A. A. B.
Brojeny
and
J. R.
Clem
,
Phys. Rev. B
68
,
174514
(
2003
).
42.
We used the fluxoid number N=3 and the effective area Aeff 1.8 × 1010 m2 of the centered hole at the penetration field for the MoGe-A square loop with the side length l=26μm and the centered hole with the radius a=3.5μm.33 The effective area was determined from the numerical result given in Fig. 7 of Ref. 2 by using the conditions of Λ(T)/l0.1 and the effective side spacing l1=πa of the hole.
You do not currently have access to this content.