A scale for magnetic field resilience of a superconductor is set by the paramagnetic limit. Comparing the condensation energy of the Bardeen–Cooper–Schrieffer (BCS) singlet ground state with the paramagnetically polarized state suggests that for an applied field μ0H>1.8Tc (in SI), singlet pairing is not energetically favorable. Materials exceeding or approaching this limit are interesting from fundamental and technological perspectives. This may be a potential indicator of triplet superconductivity, Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing, and other mechanisms involving topological aspects of surface states and may also allow Cooper pair injection at high magnetic fields. We have analyzed the microscopic composition of such a material arising from an unexpected source. A microjet of an organo-metallic gas, W[(CO)6], can be decomposed by a gallium ion-beam, leaving behind a track of complex residue of gallium, tungsten, and carbon with remarkable superconducting properties, like an upper critical field, Hc2>10T, above its paramagnetic limit. We carried out atomic probe tomography to establish the formation of nano-crystalline tungsten carbide (WC) in the tracks and the absence of free tungsten. Supporting calculations show that for Ga distributed on the surface of WC, its s,p-orbitals enhance the density of states near the Fermi energy. The observed variation of Hc2(T) does not show features typical of enhancement of critical field due to granularity. Our observations may be significant in the context of some recent theoretical calculation of the band structure of WC and experimental observation of superconductivity in a WC-metal interface.

1.
G.-H.
Lee
,
K.-F.
Huang
,
D. K.
Efetov
,
D. S.
Wei
,
S.
Hart
,
T.
Taniguchi
,
K.
Watanabe
,
A.
Yacoby
, and
P.
Kim
,
Nat. Phys.
13
,
693
(
2017
).
2.
A.
Yacoby
,
APS March Meeting Abstracts
45
,
001
(
2017
).
3.
A. M.
Clogston
,
Phys. Rev. Lett.
9
,
266
(
1962
).
4.
B.
Chandrasekhar
,
Appl. Phys. Lett.
1
,
7
(
1962
).
5.
Y. S.
Hor
,
A. J.
Williams
,
J. G.
Checkelsky
,
P.
Roushan
,
J.
Seo
,
Q.
Xu
,
H. W.
Zandbergen
,
A.
Yazdani
,
N. P.
Ong
, and
R. J.
Cava
,
Phys. Rev. Lett.
104
,
057001
(
2010
).
6.
T.
Asaba
,
B.
Lawson
,
C.
Tinsman
,
L.
Chen
,
P.
Corbae
,
G.
Li
,
Y.
Qiu
,
Y. S.
Hor
,
L.
Fu
, and
L.
Li
,
Phys. Rev. X
7
,
011009
(
2017
).
7.
X-y.
Hou
,
Z.
Wang
,
Y.-D.
Gu
,
J.-B.
He
,
D.
Chen
,
W.-L.
Zhu
,
F.
Zhang
,
Y.-F.
Xu
,
S.
Zhang
,
H.-X.
Yang
 et al,
Phys. Rev. B
100
,
235109
(
2019
).
8.
L.
Aggarwal
,
A.
Gaurav
,
G. S.
Thakur
,
Z.
Haque
,
A. K.
Ganguli
, and
G.
Sheet
,
Nat. Mater.
15
,
32
(
2016
).
9.
X.-Y.
Hou
,
Y.-D.
Gu
,
S.-J.
Li
,
L.-X.
Zhao
,
W.-L.
Zhu
,
Z.
Wang
,
M.-D.
Zhang
,
F.
Zhang
,
L.
Zhang
,
H.
Zi
 et al,
Phys. Rev. B
101
,
134503
(
2020
).
10.
W.
Zhu
,
X.
Hou
,
J.
Li
,
Y.
Huang
,
S.
Zhang
,
J.
He
,
D.
Chen
,
Y.
Wang
,
Q.
Dong
,
M.
Zhang
 et al,
Adv. Mater.
32
,
1907970
(
2020
).
11.
A.
Kononov
,
M.
Endres
,
G.
Abulizi
,
K.
Qu
,
J.
Yan
,
D. G.
Mandrus
,
K.
Watanabe
,
T.
Taniguchi
, and
C.
Schönenberger
, arXiv:2007.04752 (
2020
).
12.
E.
Sadki
,
S.
Ooi
, and
K.
Hirata
,
Appl. Phys. Lett.
85
,
6206
(
2004
).
13.
O.
Dobrovolskiy
,
D. Y.
Vodolazov
,
F.
Porrati
,
R.
Sachser
,
V.
Bevz
,
M. Y.
Mikhailov
,
A.
Chumak
, and
M.
Huth
,
Nat. Commun.
11
(
1
),
3291
(
2020
).
14.
R.
Córdoba
,
P.
Orus
,
Ž. L.
Jelić
,
J.
Sesé
,
M. R.
Ibarra
,
I.
Guillamón
,
S.
Vieira
,
J. J.
Palacios
,
H.
Suderow
,
M. V.
Milosević
 et al,
Sci. Rep.
9
(
1
),
12386
(
2019
).
15.
F.
Porrati
,
S.
Barth
,
R.
Sachser
,
O. V.
Dobrovolskiy
,
A.
Seybert
,
A. S.
Frangakis
, and
M.
Huth
,
ACS Nano
13
,
6287
(
2019
).
16.
F.
Porrati
,
L.
Keller
,
C.
Gspan
,
H.
Plank
, and
M.
Huth
,
J. Phys. D
50
,
215301
(
2017
).
17.
I.
Guillamón
,
H.
Suderow
,
S.
Vieira
,
A.
Fernández-Pacheco
,
J.
Sesé
,
R.
Córdoba
,
D.
Teresa
, and
M.
Ibarra
,
New J. Phys.
10
,
093005
(
2008
).
18.
Y.
Sun
,
J.
Wang
,
W.
Zhao
,
M.
Tian
,
M.
Singh
, and
M. H.
Chan
,
Sci. Rep.
3
,
2307
(
2013
).
19.
R.
Córdoba
,
T.
Baturina
,
J.
Sesé
,
A. Y.
Mironov
,
J.
De Teresa
,
M.
Ibarra
,
D.
Nasimov
,
A.
Gutakovskii
,
A.
Latyshev
,
I.
Guillamón
 et al,
Nat. Commun.
4
,
1437
(
2013
).
20.
S.
Sengupta
,
C.
Li
,
C.
Baumier
,
A.
Kasumov
,
S.
Guéron
,
H.
Bouchiat
, and
F.
Fortuna
,
Appl. Phys. Lett.
106
,
042601
(
2015
).
21.
H.
Chakraborti
,
S.
Deb
,
R.
Schott
,
V.
Thakur
,
A.
Chatterjee
,
S.
Yadav
,
R. K.
Saroj
,
A.
Wieck
,
S.
Shivaprasad
,
D.
Gupta
 et al,
Supercond. Sci. Technol.
31
,
085007
(
2018
).
22.
D.
Blavette
,
A.
Bostel
,
J.-M.
Sarrau
,
B.
Deconihout
, and
A.
Menand
,
Nature
363
,
432
(
1993
).
23.
P.
Bas
,
A.
Bostel
,
B.
Deconihout
, and
D.
Blavette
,
Appl. Surf. Sci.
87–88
,
298
(
1995
).
24.
B.
Yang
,
X.
Wang
,
H.
Zhang
,
Z.
Wang
, and
P.
Feng
,
Mater. Lett.
62
,
1547
(
2008
).
25.
F.
Porrati
,
R.
Sachser
,
M.
Strauss
,
I.
Andrusenko
,
T.
Gorelik
,
U.
Kolb
,
L.
Bayarjargal
,
B.
Winkler
, and
M.
Huth
,
Nanotechnology
21
,
375302
(
2010
).
26.
D.
Haviland
,
Y.
Liu
, and
A. M.
Goldman
,
Phys. Rev. Lett.
62
,
2180
(
1989
).
27.
K. D.
Gupta
,
G.
Sambandamurthy
,
S. S.
Soman
, and
N.
Chandrasekhar
,
Phys. Rev. B
63
,
104502
(
2001
).
28.
K. D.
Gupta
,
S. S.
Soman
,
G.
Sambandamurthy
, and
N.
Chandrasekhar
,
Phys. Rev. B
66
,
144512
(
2002
).
29.
A. E.
Lita
,
D.
Rosenberg
,
S.
Nam
,
A. J.
Miller
,
D.
Balzar
,
L.
Kaatz
, and
R.
Schwall
,
IEEE Trans. Appl. Supercond.
15
,
3528
(
2005
).
30.
G.
Sambandamurthy
,
D.
Gupta
, and
N.
Chandrasekhar
,
Phys. Rev. B
64
,
014506
(
2001
).
31.
S.
Witanachchi
,
S.
Patel
,
D.
Shaw
, and
H. S.
Kwok
,
Appl. Phys. Lett.
55
,
295
(
1989
).
32.
J.
Gibson
and
R.
Hein
,
Phys. Rev. Lett.
12
,
688
(
1964
).
33.
S.
Basavaiah
and
S.
Pollack
,
J. Appl. Phys.
39
,
5548
(
1968
).
34.
R.
Johnson
,
O.
Vilches
,
J.
Wheatley
, and
S.
Gygax
,
Phys. Rev. Lett.
16
,
101
(
1966
).
35.
Y.-C.
Lau
,
R.
Akiyama
,
H. T.
Hirose
,
R.
Nakanishi
,
T.
Terashima
,
S.
Uji
,
S.
Hasegawa
, and
M.
Hayashi
,
J. Phys.
3
,
034001
(
2020
).
36.
K.
Maki
and
T.
Tsuneto
,
Prog. Theor. Phys.
31
,
945
(
1964
).
37.
N.
Werthamer
,
E.
Helfand
, and
P.
Hohenberg
,
Phys. Rev.
147
,
295
(
1966
).
38.
E.
Helfand
and
N.
Werthamer
,
Phys. Rev.
147
,
288
(
1966
).
39.
S.
Poon
,
S.
Hasanain
, and
K.
Wong
,
Phys. Lett. A
93
,
495
(
1983
).
40.
W.
Carter
,
S.
Poon
,
G.
Hull
, Jr.
, and
T.
Geballe
,
Solid State Commun.
39
,
41
(
1981
).
41.
J.
Hofer
and
N.
Haberkorn
,
Thin Solid Films
685
,
117
(
2019
).
42.
V.
Gantmakher
,
L.
Klinkova
,
N.
Barkovskii
,
G.
Tsydynzhapov
,
S.
Wiegers
, and
A.
Geim
,
Phys. Rev. B
54
,
6133
(
1996
).
43.
J.
Lu
,
O.
Zheliuk
,
I.
Leermakers
,
N. F.
Yuan
,
U.
Zeitler
,
K. T.
Law
, and
J.
Ye
,
Science
350
,
1353
(
2015
).
44.
Y.
Matsuda
and
H.
Shimahara
,
J. Phys. Soc. Jpn.
76
,
051005
(
2007
).
45.
F.
Gamble
,
F.
DiSalvo
,
R.
Klemm
, and
T.
Geballe
,
Science
168
,
568
(
1970
).
46.
R. A.
Klemm
,
A.
Luther
, and
M.
Beasley
,
Phys. Rev. B
12
,
877
(
1975
).
47.
W.
McMillan
,
Phys. Rev.
167
,
331
(
1968
).
48.
S. W.
Liu
,
C. Q.
Xu
, and
J. Y.
Zhang
,
J. Supercond. Novel Magn.
33
,
1317
(
2020
).
49.
S.
Foner
and
B. B.
Schwartz
,
Superconductor Materials Science
(
Plenum
,
1981
).
50.
N.
Toyota
,
A.
Inoue
,
T.
Fukase
, and
T.
Masumoto
,
J. Low Temp. Phys.
55
,
393
(
1984
).
51.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
52.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
53.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
(
1993
).
54.
J.-Z.
Ma
,
J.-B.
He
,
Y.-F.
Xu
,
B.
Lv
,
D.
Chen
,
W.-L.
Zhu
,
S.
Zhang
,
L.-Y.
Kong
,
X.
Gao
,
L.-Y.
Rong
 et al,
Nat. Phys.
14
,
349
(
2018
).
55.
G.
Deutscher
,
O.
Entin-Wohlman
, and
Y.
Shapira
,
Phys. Rev. B
22
,
4264
(
1980
).
56.
M.
Tian
,
J.
Wang
,
N.
Kumar
,
T.
Han
,
Y.
Kobayashi
,
Y.
Liu
,
T. E.
Mallouk
, and
M. H. W.
Chan
,
Nano Lett.
6
,
2773
(
2006
).
57.
K.
Ma
,
K.
Gornicka
,
R.
Lefevre
,
Y.
Yang
,
H. M.
Ronnow
,
H. O.
Jeschke
,
T.
Klimczuk
, and
F. O.
von Rohr
,
ACS Mater. Au
1
,
55–61
(
2021
).
58.
G.
Sim
,
M. J.
Park
, and
S.
Lee
, arXiv:1909.04015 (
2019
).
59.
Y.-P.
Lin
,
Phys. Rev. Res.
2
,
043209
(
2020
).
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