1. Pauli-limiting effects in the flux lattice of CeCoIn5
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

2. Superconductivity at high B – what determines Bc2?
and
=>
‘Heavy fermion’ materials have
low Tc (~ 1 K)
but high Bc2 (~ 10 T)
=>
Birmingham Condensed Matter Website Ted Forgan

3. 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?
=>
=>
Compare =>
Birmingham Condensed Matter Website Ted Forgan

4. Pairing controlled by spin energy
D ~ D0 exp (iqz)
with q = ( k + k ) Bz
i.e.
paired eF  k k
but
2mB
This was predicted by Fulde & Ferrell in 1964 k
Carries a supercurrent // B !
Maybe D ~ cos (qz) – Larkin & Ovchinnikov (same time)
Flux lines modulated along z
“LOFF / FFLO”
Birmingham Condensed Matter Website Ted Forgan

5. Speed of sound Phase Diagram
Maybe FFLO in CeCoIn5
proposed shape of flux lines
i.e. flux lines turn into “strings of sausages”
Birmingham Condensed Matter Website Ted Forgan

6. NMR on CeCoIn5 versus B and T
Kumagai et al. cond-mat/
Birmingham Condensed Matter Website Ted Forgan

7. Flux Lattice in CeCoIn5, B // c
Hexagonal =>
Rhombic =>
Square =>
Hexagonal
d-wave superconductivity +
paramagnetic effects??
Birmingham Condensed Matter Website Ted Forgan

8. 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

9. Results in niobium near Bc2
Diffracted Intensity vs. T at B = 0.2 T
log
scale
Note: intensity falls rapidly to zero near Bc2 in a conventional material
linear
scale
Birmingham Condensed Matter Website Ted Forgan

10. 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
Is there a sign of FFLO –for B // c ?? B
Birmingham Condensed Matter Website Ted Forgan

11. Birmingham Condensed Matter Website Ted Forgan