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Birmingham Condensed Matter Physics Group
Pauli-limiting effects in the flux
lattice of CeCoIn5
Ted Forgan
School of Physics and Astronomy, University of Birmingham, U.K.
Birmingham Condensed Matter Website
Ted Forgan
Superconductivity at high B –
what determines Bc2?
0
Bc 2 
2
2 
and
v F
0 
 (0)
 ( 0)
 eBc 2 (0) 
=> 
   c 0 
F
 m* 
2
c
T ( m*)
=> Bc 2 (0) 
2
kF
2
Birmingham Condensed Matter Website
2
‘Heavy fermion’
materials have
low Tc (~ 1 K)
but high Bc2 (~ 10 T)
Ted Forgan
Superconductivity and magnetic
fields – effect of electron spin
Pauli paramagnetism
favours normal state
- because paired antiparallel
electrons cannot line up with B
What energy balance decides if
paramagnetism is important?
=>
 B BPauli  (0)
Compare =>
Birmingham Condensed Matter Website
 B
F
2
B
=>
2
Pauli

 ( 0)
2
F
BPauli  Tc
2
c
T ( m*)
Bc 2 (0) 
2
kF
Ted Forgan
2
Pairing controlled by spin energy

 ~ 0 exp (iqz)
paired
Bz
F
2B
k
Maybe
k
i.e.
with q = ( k + k )
2 B B
q
v F

1
q
~
~


B
~

but B
 v
// B
F
This was predicted by
Fulde & Ferrell in 1964
k
Carries a supercurrent // B !
 ~ cos (qz) – Larkin & Ovchinnikov (same time)
Flux lines modulated along z
Birmingham Condensed Matter Website
“LOFF / FFLO”
Ted Forgan
Speed of sound Phase Diagram
Maybe
FFLO in
CeCoIn5
proposed
shape of
flux lines
Birmingham Condensed Matter Website
i.e. flux
lines turn
into “strings
of sausages”
Ted Forgan
NMR on CeCoIn5 versus B and T
Kumagai et al. cond-mat/0605394
Birmingham Condensed Matter Website
Ted Forgan
Flux Lattice in CeCoIn5, B // c
Hexagonal =>
Rhombic =>
Square =>
Rhombic =>
Hexagonal
d-wave
superconductivity +
paramagnetic
effects??
Birmingham Condensed Matter Website
Ted Forgan
d-wave heavy-fermion CeCoIn5
Note that we
could go very
close to Hc2 –
just 50 mT
below !
B – T Phase Diagram
Birmingham Condensed Matter Website
Ted Forgan
Results in niobium near Bc2
Diffracted Intensity vs. T at B = 0.2 T
log
scale
linear
scale
Note:
intensity
falls rapidly
to zero near
Bc2 in a
conventional
material
Birmingham Condensed Matter Website
Ted Forgan
d-wave heavy-fermion CeCoIn5
flux lines show stronger
field contrast at high field
– even up to Bc2 !
|F|2
Electron spins lining up
parallel in the de-paired
flux line cores...
Published in ‘Science’
(Bianchi et al) Jan ‘08
B
Is there a sign of FFLO –
for B // c ??
Birmingham Condensed Matter Website
Ted Forgan
Birmingham Condensed Matter Website
Ted Forgan