Time-reversal symmetry breaking in superconductors through loop Josephson-current orderh

T
h
e
U
K
’
s
E
u
r
o
p
e
a
n
u
n
i
v
e
r
s
it
y
Time-reversal symmetry breaking in
superconductors through Loop Josephson-
Current order / Jorge Quintanilla, Oxford
2018

blogs.kent.ac.uk/strongcorrelationsOxford 2018
Fountains of wealth and knowledge
Theory:

Kent: Sudeep K. Ghosh, Phil Whittlesea

Bristol: Gabor Csire, James F. Annett

Osaka: Kazumasa Miyake
Experiments:

RAL: Adrian Hillier (Re6Zr, LaNiC2, LaNiGa2)

Zhejiang/Dresden: Huiqiu Yuan, Michael Smidman, Frank Steglich, ZF Weng, JL Zhang, T
Shang, M Nicklas, GM Pang, L Jiao, WB Jiang, Y Chen (LaNiGa2)

Warwick: Ravi P Singh, Gheeta Balakrishnan, Martin Lees, Don Paul (Re6Zr)

RAL/Johannesburg/Dresden/Aoyama-Gakuin: Amitava Bhattacharyya, Devashibai Adroja, A M
Strydom, N Kase, J Akimitsu (Lu5Rh6Sn18)

Huddersfield: Bob Cywinski (LaNiC2, LaNiGa2)
Funding:

EPSRC (grants EP/P00749X/1 and EP/P007392/1).

University of Kent, STFC and SEPnet.
unconventionalsuperconductors.wordpress.com

Oxford 2018
Unconventional
superconductors

Oxford 2018
Photo:commons.wikimedia.org
Photo:KennethG.Libbrecht,snowflakes.com
Unconventional
superconductors
‘Unconventional’
superconductors:
Cuprates,
Sr2RuO4,
PrOs4Sb12, UPt3,
(UTh)Be13 , ...
Photo:EddieHui-Bon-Hoa,www.shiromi.com

Oxford 2018
==> no magnetic fields

Oxford 2018
Avatar (2009)
Director: James Cameron
Production: $300m Marketing: $150m
Box office: $2,800m
Unobtanium:
“a room-temperature
superconductor […] proved
to be the most baffling of
scientific discovery in the
area of superconductors as
it had an extremely strong
magnetic field, reversing
prior knowledge that all
superconductors repel
magnetic fields”
Source: Avatar Wiki,
accessed 26/Apr/2018
Avatar 2
18 Dec 2020
Avatar 3
17 Dec 2021

Oxford 2018
Detecting broken time-reversal
symmetry

blogs.kent.ac.uk/strongcorrelations
11
Oxford 2018
Time-reversal symmetry breaking

12
Oxford 2018
Detecting broken time-reversal symmetry:
Zero-field muSR
Field on:
measure χ
Field off:
measure m
Gives yes/no answer to the
question:
“Does this system respect
time-reversal symmetry?”
+

13
Oxford 2018
The “classics”

14
Oxford 2018
Confirmed by the Kerr effect

15
Oxford 2018
LaNiC2 and LaNiGa2

16
Oxford 2018
Two additions: LaNiC2 and LaNiGa2
AD Hillier, J Quintanilla, B Mazidian, JF Annett,
and R Cywinski, PRL 109, 097001 (2012)
AD Hillier, J Quintanilla, and R Cywinski,
PRL 102 , 117007 (2009)

Oxford 2018
Confirmed by bulk SQUID measurements on LaNiC2: [1,2]
Notes: Only the 3rd
superconductor where broken TRS confirmed indepedently
Effect had been predicted for LaNiC2/LaNiGa2 non-unitary triplet pairing state [3]
1st
superconductor where bulk spontaneous magnetisation measured at Tc
No such effect in scanning [4] and bulk [2] SQUID measurements on Sr2RuO4
[1] A Sumiyama et al.,
JPSJ 84, 13702
(2015).
[2] Sumiyama et al.,
JPS Conf. Proc.,
3, 015017 (2014).
[3] AD Hillier, JQ,
B Mazidian, JF Annett,
and R Cywinski,
PRL 109, 097001
(2012).
[4] Hicks et al.,
PRB 81, 214501 (2010).0

Oxford 2018
D Singh, Sajilesh KP, JAT Barker, D McK
Paul, AD Hillier, and RP Singh, PRB 97,
100505(R) (2018)
RP Singh, AD Hillier, B Mazidian, JQ,
JF Annett, DMcK Paul, G Balakrishnan, and
MR Lees, PRL 112, 107002 (2014)
Re6
Zr
Re6
Hf
D Singh, JAT Barker, A Thamizhavel,
DMcK Paul, AD Hillier, and RP Singh,
PRB 96, 180501(R) (2017)
Re6X family
(α-Mn structure)

Oxford 2018
A Bhattacharyya, DT Adroja, JQ, AD Hillier,
N Kase, AM Strydom, and J Akimitsu,
PRB 91, 060503(R) (2015)
R5Rh6Sn18 family
Lu5
Rh6
Sn18

Oxford 2018
La7Ir3
J.A.T. Barker, D. Singh, A. Thamizhavel, A.D. Hillier, M.R. Lees, G. Balakrishnan, D. McK. Paul, and R.P. Singh
Phys. Rev. Lett. 115, 267001 – Published 30 December 2015

Oxford 2018
Identifying the pairing state

22
Oxford 2018
What's the state? It's easy...
James F. Annett,
Symmetry of the Order Parameter for High-Temperature Superconductivity.
Adv. Phys. 39, 83-126 (1990)
Broken
TRS

23
Oxford 2018
In practice, states with broken time-reversal symmetry
are hard to pin down
E.g. Sr2
RuO4
(Gc
= D4h
): 10 irreps of Gc
(dc
= 1-2)

Weak SOC:
36 ground states (7 singlets, 29 triplets) of which
20 break time-reversal symmetry (1 singlet, 19 triplet) [1]

Strong SOC:
14 ground states (7 singlets, 7 triplets) of which
2 break time-reversal symmetry (1 singlet, 1 triplet) [1]

Believed to be triplet [2]

Lots of puzzles:
− Susceptibility anisotropy
− Local magnetisation (scanning SQUID) [3]
− Bulk magnetisation (SQUID) [4]
− Unitary or non-unitary? (Knight shift) [5]
[1] Annett, Adv. Phys. (1990)
[2] MacKenzie & Maeno RMP (2003)
[3] Hicks et al. PRB (2010)
[4] Sumiyama et al., JPS Conf. Proc.,
015017 (2014)
[5] Miyake JPSJ (2014)
[6] Veenstra et al. PRL (2014)

24
Oxford 2018
LaNiC2 and LaNiGa2
Crystal point group has 4 x 1D irreps
==> must have non-unitary (equal-spin)
triplet pairing [1,2,3]
==> prediction of a spontaneous magnetisa [3]tion [3]:
[1] AD Hillier, JQ, and
R Cywinski,
PRL 102, 117007 (2009).
[2] JQ, AD Hillier, JF Annett,
& R Cywinski,
PRB 82, 174511 (2010).
[3] AD Hillier, JQ,
B Mazidian, JF Annett,
and R Cywinski,
PRL 109, 097001 (2012).
[4] Sumiyama et al.,
JPS Conf. Proc.,
3, 015017 (2014).
as observed [4]

25
Oxford 2018
RP Singh, AD Hillier, B Mazidian, JQ,
JF Annett, DMcK Paul, G Balakrishnan, and
MR Lees, PRL 112, 107002 (2014)

26
Oxford 2018
PRB 91, 060503(R) (2015)
Point or line
nodes

Oxford 2018
Identity irrep: D = 1
Other irreps: D = 1 or > 1
Nodes are fundamental

Oxford 2018
Nodes are fundamental site
(or orbital)
unit cell
pairing
potential
A1

Oxford 2018
Nodes are fundamental site
(or orbital)
unit cell
pairing
potential
+
+
- -
Non-trivial irrepA1

Oxford 2018
Identity irrep: D = 1
Other irreps: D = 1 or > 1
Singlet irrep: D = 1
Triplet irrep: D = 3
Nodes are fundamental

blogs.kent.ac.uk/strongcorrelationsOxford 2018
Low-temperature thermodynamics & transport appear to be
well described as a fully-gapped, two-band superconductor
ZF Weng, JL Zhang, M Smidman, T Shang, JQ, JF
Annett, M Nicklas, GM Pang, L Jiao, WB Jiang, Y
Chen, F Steglich, and HQ Yuan, PRL (2016)
J Chen, L Jiao, J L Zhang, Y Chen, L Yang,
M Nicklas, F Steglich, and H Q Yuan,
New J. Phys. 15, 53005 (2013)
LaNiGa2
Appears to be a generic feature.
Consistent with - but WHY?

Oxford 2018
At the Hartree-Fock level F0
a > 0 implies a net-attractive interaction
e.g. in a 3D continuum, [see e.g. Quintanilla & Schofield PRB (2006)]
A
B
Must involve
two different
orbitals A,B
Wilson ratio
RW = (1+F0
a
)-1
≈ 0.3
Wilson ratio
RW = (1+F0
a
)-1
≈ 0.3
Suggests a negative-U, equal-spin interaction (driven, for example,
by Hund on Ni):
[S. Katano et al.
JPSJ 86, 104704
(2017)]
[S. Katano et al.
JPSJ 86, 104704
(2017)]
The model turns out to be consistent with the
experiments
[PW Whittlesea, SK Ghosh et al., unpublished]
[G. Csire et al., unpublished]

Oxford 2018
Something’s going on...
DA Mayoh, JAT Barker,
RP Singh, G Balakrishnan,
DMcK Paul, and MR Lees,
PRB 96, 064521 (2017).
Re6ZrLu5Rh6Sn18
PRB 91, 060503(R) (2015).
La7Ir3
B Li, CQ Xu, W Zhou, WH
Jiao, R Sankar, et al.,
Sci. Rep. 8, 651 (2018).

Oxford 2018
The Loop Josephson Current
state

Oxford 2018
A common feature:
large unit cells, with many
symmetry-related atomic
sites within the same unit
cell
A Bhattacharyya et al.,
Sci. Rep. 5, 12926 (2015)
B Li, CQ Xu, W
Zhou, WH Jiao, R
Sankar, et al.,
Sci. Rep. 8, 651
(2018).
K Matano et al., PRB 94, 214513 (2016)

Oxford 2018
Back to the drawing board site
(or orbital)
unit cell
pairing
potential
Singlet,
intra-site,
intra-orbital
pairing
Sudeep Kumar Ghosh, James F. Annett, and JQ,
arXiv:1803.02618

Oxford 2018
Minimal model - Sudeep Kumar Ghosh, James F. Annett,
and JQ, arXiv:1803.02618

Oxford 2018
Symmorphic space group P4
Point group C4
Non-symmorphic space group P42
Factor group isomorphic to C4
Character table
4 x 1D irreps

Oxford 2018
Order
parameter
Free energy
Inverse pairing
susceptibility matrix
Must obey:
Rg
are point/factor group
operations e.g.

Oxford 2018
The matrix takes the form
Eigenvectors:

Oxford 2018
Josephson
current:
==> Prediction of magnetic moment upper bound:
Consistent with LaNiC2, LaNiGa2, Re6X, ...

Oxford 2018
Normal state must have time-reversal symmetry:
|L> and |R> become degenerate at the quadratic level:
Construct the symmetrised free energy to quartic level:

Oxford 2018
Application to Re6
X

Oxford 2018
Is Re6X compatible with this new scenario?
Sudeep Kumar Ghosh, James F. Annett, and JQ, arXiv:1803.02618

Space group I43m, point group Td

58 atoms in unit cell, incl. 48 Re atoms (12 x 2 + 12 x 2)

Choose group of 12 Re atoms as smaller set of symmetry-related atoms
that does not have higher symmetry than the crystal

Find LJC eigenvectors of the 12 x 12 alpha-matrix

Impose TRS and derive beta matrix

Find stabilisation of LJC states with spontaneously-broken TRS

Oxford 2018

Broken Time-reversal Symmetry is
observed using muSR in a growing number
of superconductors

For UPt3, Sr2RuO4, and LaNiC2 there is
evidence from another direct probe (Kerr or
SQUID)

In many instances broken TRS coexists
with a full gap – a deep puzzle

In LaNiC2 and LaNiGa2 there are two gaps

This is consistent with inter-orbital, non-
unitary triplet pairing
ZF Weng, JL Zhang, M Smidman, T Shang, JQ,
JF Annett, M Nicklas, GM Pang, L Jiao, WB
Jiang, Y Chen, F Steglich, and HQ Yuan,
PRL 117, 0127001 (2016)

Oxford 2018
Is the edge special … ?

Time-reversal symmetry breaking in superconductors through loop Josephson-current orderh

Recommended

Recommended

More Related Content

Similar to Time-reversal symmetry breaking in superconductors through loop Josephson-current orderh

Similar to Time-reversal symmetry breaking in superconductors through loop Josephson-current orderh (18)

More from Jorge Quintanilla

More from Jorge Quintanilla (18)

Recently uploaded

Recently uploaded (20)

Time-reversal symmetry breaking in superconductors through loop Josephson-current orderh