# Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions

## Abstract

Unconventional superconductivity arising from the interplay between strong spin–orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the three-dimensional topological insulator Bi _{2}Se _{3}. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi _{2}Se _{3} and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov–Bohm flux.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1465880

- Alternate Identifier(s):
- OSTI ID: 1511469

- Grant/Contract Number:
- SC0012368

- Resource Type:
- Published Article

- Journal Name:
- Nature Communications

- Additional Journal Information:
- Journal Name: Nature Communications Journal Volume: 9 Journal Issue: 1; Journal ID: ISSN 2041-1723

- Publisher:
- Nature Publishing Group

- Country of Publication:
- United Kingdom

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Chen, Angela Q., Park, Moon Jip, Gill, Stephen T., Xiao, Yiran, Reig-i-Plessis, Dalmau, MacDougall, Gregory J., Gilbert, Matthew J., and Mason, Nadya. Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions. United Kingdom: N. p., 2018.
Web. doi:10.1038/s41467-018-05993-w.
```

```
Chen, Angela Q., Park, Moon Jip, Gill, Stephen T., Xiao, Yiran, Reig-i-Plessis, Dalmau, MacDougall, Gregory J., Gilbert, Matthew J., & Mason, Nadya. Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions. United Kingdom. doi:10.1038/s41467-018-05993-w.
```

```
Chen, Angela Q., Park, Moon Jip, Gill, Stephen T., Xiao, Yiran, Reig-i-Plessis, Dalmau, MacDougall, Gregory J., Gilbert, Matthew J., and Mason, Nadya. Tue .
"Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions". United Kingdom. doi:10.1038/s41467-018-05993-w.
```

```
@article{osti_1465880,
```

title = {Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions},

author = {Chen, Angela Q. and Park, Moon Jip and Gill, Stephen T. and Xiao, Yiran and Reig-i-Plessis, Dalmau and MacDougall, Gregory J. and Gilbert, Matthew J. and Mason, Nadya},

abstractNote = {Unconventional superconductivity arising from the interplay between strong spin–orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the three-dimensional topological insulator Bi2Se3. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi2Se3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov–Bohm flux.},

doi = {10.1038/s41467-018-05993-w},

journal = {Nature Communications},

number = 1,

volume = 9,

place = {United Kingdom},

year = {2018},

month = {8}

}

DOI: 10.1038/s41467-018-05993-w

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Magnetic interference pattern in planar SNS Josephson junctions

journal, January 2008

- Mohammadkhani, G.; Zareyan, M.; Blanter, Ya. M.
- Physical Review B, Vol. 77, Issue 1

##
Josephson supercurrent through a topological insulator surface state

journal, February 2012

- Veldhorst, M.; Snelder, M.; Hoek, M.
- Nature Materials, Vol. 11, Issue 5

##
Probing unconventional superconductivity in inversion-symmetric doped Weyl semimetal

journal, June 2016

- Kim, Youngseok; Park, Moon Jip; Gilbert, Matthew J.
- Physical Review B, Vol. 93, Issue 21

##
Dynamical gate-tunable supercurrents in topological Josephson junctions

journal, July 2014

- Kurter, C.; Finck, A. D. K.; Ghaemi, P.
- Physical Review B, Vol. 90, Issue 1

##
Anomalous Fraunhofer interference in epitaxial superconductor-semiconductor Josephson junctions

journal, January 2017

- Suominen, H. J.; Danon, J.; Kjaergaard, M.
- Physical Review B, Vol. 95, Issue 3

##
Model Hamiltonian for topological insulators

journal, July 2010

- Liu, Chao-Xing; Qi, Xiao-Liang; Zhang, HaiJun
- Physical Review B, Vol. 82, Issue 4

##
Emerging evidence for FFLO states in layered organic superconductors (Review Article)

journal, March 2013

- Beyer, R.; Wosnitza, J.
- Low Temperature Physics, Vol. 39, Issue 3

##
Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells

journal, September 2016

- Hart, Sean; Ren, Hechen; Kosowsky, Michael
- Nature Physics, Vol. 13, Issue 1

##
Theory of Superconductivity

journal, December 1957

- Bardeen, J.; Cooper, L. N.; Schrieffer, J. R.
- Physical Review, Vol. 108, Issue 5

##
Coupled Superconducting and Magnetic Order in CeCoIn5

journal, September 2008

- Kenzelmann, M.; Strassle, Th.; Niedermayer, C.
- Science, Vol. 321, Issue 5896

##
$g$ -factors of conduction electrons and holes in $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ three-dimensional topological insulator

journal, April 2016

- Wolos, A.; Szyszko, S.; Drabinska, A.
- Physical Review B, Vol. 93, Issue 15

##
Influence of topological edge states on the properties of $\mathrm{Al}/{Bi}_{2}{\mathrm{Se}}_{3}/\mathrm{Al}$ hybrid Josephson devices

journal, April 2014

- Galletti, L.; Charpentier, S.; Iavarone, M.
- Physical Review B, Vol. 89, Issue 13

##
Significance of Electromagnetic Potentials in the Quantum Theory

journal, August 1959

- Aharonov, Y.; Bohm, D.
- Physical Review, Vol. 115, Issue 3

##
Pair-density wave states through spin-orbit coupling in multilayer superconductors

journal, October 2012

- Yoshida, Tomohiro; Sigrist, Manfred; Yanase, Youichi
- Physical Review B, Vol. 86, Issue 13

##
Surface Collective Modes in the Topological Insulators ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and ${\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{1.5}{\mathrm{Te}}_{3-x}{\mathrm{Se}}_{x}$

journal, December 2015

- Kogar, A.; Vig, S.; Thaler, A.
- Physical Review Letters, Vol. 115, Issue 25

##
Topological insulators in Bi_{2}Se_{3}, Bi_{2}Te_{3} and Sb_{2}Te_{3} with a single Dirac cone on the surface

journal, May 2009

- Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang
- Nature Physics, Vol. 5, Issue 6, p. 438-442

##
Possible Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_{5}$

journal, October 2003

- Bianchi, A.; Movshovich, R.; Capan, C.
- Physical Review Letters, Vol. 91, Issue 18

##
Superconductivity in a Strong Spin-Exchange Field

journal, August 1964

- Fulde, Peter; Ferrell, Richard A.
- Physical Review, Vol. 135, Issue 3A

##
Observation of the Fulde-Ferrell-Larkin-Ovchinnikov state in the quasi-two-dimensional organic superconductor κ-(BEDT-TTF) _{2} Cu(NCS) _{2} (BEDT-TTF=bis(ethylene-dithio)tetrathiafulvalene)

journal, September 2000

- Singleton, J.; Symington, J. A.; Nam, M-S
- Journal of Physics: Condensed Matter, Vol. 12, Issue 40

##
Josephson Effect in Fulde-Ferrell-Larkin-Ovchinnikov Superconductors

journal, May 2000

- Yang, Kun; Agterberg, D. F.
- Physical Review Letters, Vol. 84, Issue 21

##
Calorimetric Evidence for a Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in the Layered Organic Superconductor $\kappa \mathrm{\text{\u2212}}(\mathrm{BEDT}\mathrm{\text{\u2212}}\mathrm{TTF}{)}_{2}\mathrm{Cu}(\mathrm{NCS}{)}_{2}$

journal, October 2007

- Lortz, R.; Wang, Y.; Demuer, A.
- Physical Review Letters, Vol. 99, Issue 18

##
Fulde–Ferrell–Larkin–Ovchinnikov State in Heavy Fermion Superconductors

journal, May 2007

- Matsuda, Yuji; Shimahara, Hiroshi
- Journal of the Physical Society of Japan, Vol. 76, Issue 5

##
Evidence of Andreev bound states as a hallmark of the FFLO phase in κ-(BEDT-TTF)2Cu(NCS)2

journal, October 2014

- Mayaffre, H.; Krämer, S.; Horvatić, M.
- Nature Physics, Vol. 10, Issue 12

##
Magnetic enhancement of superconductivity from electron spin domains

journal, September 2003

- Radovan, H. A.; Fortune, N. A.; Murphy, T. P.
- Nature, Vol. 425, Issue 6953

##
Theory of a two-dimensional superconductor with broken inversion symmetry

journal, July 2007

- Dimitrova, Ol’ga; Feigel’man, M. V.
- Physical Review B, Vol. 76, Issue 1

##
Local and Nonlocal Fraunhofer-like Pattern from an Edge-Stepped Topological Surface Josephson Current Distribution

journal, August 2014

- Lee, Jae Hyeong; Lee, Gil-Ho; Park, Joonbum
- Nano Letters, Vol. 14, Issue 9

##
Fulde-Ferrell states in inverse proximity-coupled magnetically doped topological heterostructures

journal, August 2017

- Park, Moon Jip; Yang, Junyoung; Kim, Youngseok
- Physical Review B, Vol. 96, Issue 6

##
Microscopic Evidence for Field-Induced Magnetism in ${\mathrm{CeCoIn}}_{5}$

journal, January 2007

- Young, B. -L.; Urbano, R. R.; Curro, N. J.
- Physical Review Letters, Vol. 98, Issue 3

##
FFLO Superfluids in 2D Spin-Orbit Coupled Fermi Gases

journal, October 2014

- Zheng, Zhen; Gong, Ming; Zhang, Yichao
- Scientific Reports, Vol. 4, Issue 1

##
Symmetry protected Josephson supercurrents in three-dimensional topological insulators

journal, April 2013

- Cho, Sungjae; Dellabetta, Brian; Yang, Alina
- Nature Communications, Vol. 4, Issue 1

Works referencing / citing this record:

##
Top-down causation and quantum physics

journal, October 2018

- Ellis, George F. R.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 46