1. New challenges and opportunities for high-Tc superconducting materials
Alex Gurevich
Department of Physics
Old Dominion University, Norfolk VA
78-th Annual Meeting of SESAP, Roanoke, VA, Oct , 2011

2. Superconductivity How to make superconducting materials useful?
Superconductors – frictionless conductors of electricity
Low temperature superconductors such as Nb compounds (LTS)
High temperature cuprate superconductors (HTS) – much more complex materials
New family of Fe-based superconductors
What makes them useful?
To save energy and reduce the dependence on oil
Electric utility applications
Power cables, fault current limiters, transformers, motors, generators
Superconducting magnets
Avoid 20 MW per user magnet
Particle accelerators (Large Hadron collider, Free electron lasers, etc)
To produce energy in fusion power reactors
ITER – International Tokomak Experimental Reactor
How to make superconducting materials useful?
Main parameters of merit for applications: high critical current density Jc(T,T) and the irreversibility field H*(T) require strong pinning of vortices and low anisotropy:
Reduce strong thermal fluctuation of vortices
Reduce current-blocking effect of grain boundaries in polycrystal conductors

3. Heike Kamerlingh-Onnes Gilles Holst
How did it start?
Electron liquid
In metals
Heike Kamerlingh-Onnes Gilles Holst Hg R T Tc
Liquifying helium by Onnes in 1908
led to the discovery of superconductivity in 1911
and superfluidity of He in 1935
Ideas at the beginning of the 20-th century:
electron liquid may crystallize at low temperatures
Metals would become insulators at low T

4. First proposal of superconducting magnets…. Onnes in Chicago 1913
“only” a 10 T
magnet

5. Phase diagram of a superconductor
Temperature
Magnetic
Field
Normal
Metal
Phase transition from the normal to
superconducting state below the
critical temperature Tc
Superconductivity is destroyed by magnetic fields
exceeding the upper critical magnetic field Hc2
Zero resistance disappears if the current
density exceeds the critical current density Jc
Search for higher-Tc superconductors
Tuning materials properties to
increase Hc2 > 10 Tesla and
Jc > 0.1 MA/cm2 at 5T

6. Lots of superconducting materials have been discovered
pnictides
Highest Tc = 164K (under 30 GPa)

7. Main players in applications
Tc = 9.2K
Tc = 40K
NbTi
MgB2
Qubic, or hexagonal
low-Tc superconductors
Highly anisotropic
layered high-Tc
superconductors
Tc seems to scale with
crystalline/chemical
complexities
Nb3Sn
Tc = 18K
YBa3Cu3O7
Tc = 92K
Bi2Sr2Ca2Cu3Ox
Tc = 108K

8. Vortices in type-II superconductors
Pancake vortices
in layered SC
Continuous vortex filaments
Meissner state for H below the lower critical field Hc1
Vortex state at Hc1 < H < Hc2
For magnets we need superconductors with high upper critical field Hc2:
Many materials have Hc2 > T, more than ten times
the Onnes 1913 dream

9. Main parameter in applications: the critical current density Jc(B)
field
Current produces the Lorentz force which moves vortices
Defects pin vortices
No dissipation below the critical current density: Jc(B)  A/cm2

10. Designer nanoparticle structures
J.L. McManus-Driscoll, Nature Materials 3, 439 (2004) (BZO); S.A. Harrington et al, SUST 22, (2009)
T. Haugan et at, Nature 430, 867 (2004) (Y2BaCuOx nanoparticles in PLD YBCO films)
Y. Yamada et al, APL 87, (2005); K. Matsumoto et al, JJAP, 44, L246 (2005).
J. Gutierrez et al, Nature Materials, (2007); X. Obradors et al, SUST 19, S1 (2006)
S. Solovyev et al, SUST, 20, L20 (2007).
M.W. Rupich et al, MRS Bull., 29, 572 (2004)
Self assembles BZO
nanpparticles
Combination of nanoparticles and columnar pins
S. Kang et al, Science 311, (2006)
B. Maiorov et al,
Nature Materials 8, 398 (2009)
weaker flux creep at high fields
weaker field dependence (reduced  in Jc  H- )

11. Enhancement of Jc by “designer” nanoparticle structures
Self-assembled chains of BZO nanoparticles
8 nm YBa2CuO5 nanoparticles
AFOSR
 10
P. Mele, K. Matsumoto, T. Horide, A. Ichinose,
M. Mukaida, Y. Yoshida,S. Horii, R. Kita
SUST 21, (2008)
T. Haugan, et al. Nature 430, 867 (2004)

12. Superconducting cables years later: Avoid Joule losses at the expense of cryogenic refrigeration
Cooling by liquid helium at 4.2K
Cooling by liquid nitrogen at 77K (much cheaper)
The higher the temperature, the more efficient the superconducting systems
are: Search for high-Tc materials
Superconducting cable
Cryostat to keep T < Tc
Nb3Sn filaments in Cu
Bi-2212 in silver

13. Power magnet applications.
HTS motors & generators
Research magnets
Medical MRI
Fusion
Power transmission lines
MagLev

14. U.S. HTS Cable Installations
Albany, NY
Long Island, NY
Early tests have been done with silver-sheathed BSCCO wires, now being replaced by better and cheaper YBCO wires
New York, NY (DHS)
Columbus, OH
While there are four HTS cable installations in the US, the Long Island, Albany, and Columbus projects are currently being funded by DOE.
Carrollton, GA Installation
12.47 kV, 1250 Amps
- three single-phase coax cables
- energized Jan 2, 2000
- public commissioning Feb 18, 2000
- 1st HTS cable in world to provide power to live load
- provides power to Southwire manufacturing complex
- operated 7 years
- system has never dropped the load - been cause of outage
- system has survived many real-world transient events including fault currents and lightening strikes, including a direct lightening strike to pole inside the HTS switchyard
Carrollton, GA
New Orleans, LA
New Project

15. Superconducting LINAC
Power RF applications
Spallation neutron source (ORNL)
X-ray free electron laser
ILC: cavites, 500 tons of high purity Nb; 20 kW refrigeration at 2K
Tunable m light source at JLab
Superconducting LINAC

16. Large Hadron Collider-CERN – 2009 turn on
Mont Blanc
1500 tonnes of SC cables
1232 SC Dipoles
3286 HTS Leads
Lake Geneva
Switzerland
Large Hadron Collider
15000 MJ of magnetic energy
27 km Tunnel
France

17. Conventional LTS approach
Increase Hc2 by alloying the material with nonmagnetic impurities
The highest impurity concentration which does not produce significant Tc suppression
Dirty limit: Hc2(0)  0 /20  n
Produce appropriate defect structures to pin vortices
The more pinning defects the better
Make multifilamentary conductors to suppress thermo-magnetic instabilities and reduce ac losses in alternating electromagnetic fields
Not easy to implement in high-Tc cuprates and Fe-based superconductors

18. Figures of merit for magnet applications
Vortex pinning and critical current density Jc(T,H)
Irreversibility field H*(T) below which Jc(T,H) = 0
Thermal fluctuations of vortices
H/H*
pinned
vortex
solid
liquid
bad metal
LTS
HTS
It is neither Tc nor Hc2, but the high Jc and H*(T), which make superconductors useful

19. Strong suppression of H* in anisotropic HTS
Hc2
Strong anisotropy
can eliminate all benefits
of higher Tc and Hc2
YBCO (Tc = 92K) is
much better than
Bi (Tc = 110K)
MgB2 (Tc = 40K) or
oxypnictides (Tc < 52K)
can be as good as
Bi-2223 for 20K < T < 35K, and
B < 15T
Nd(F,O)FeAs

20. Thermal fluctuations in superconductors
Critical fluctuation region:
T = Tc – T < TcGi
Ginzburg parameter:
Anisotropy parameter in a uniaxial superconductor:
Tc  Tc5 2/n3
LTS: Gi  10-8, T  10-7 K
YBCO, higher-Tc Fe-pnictides: Gi  10-2, T  1K
BSCCO: Gi  0.1, T  10K
Tc reduction by phase fluctuations (Emery & Kivelson, 1995)
Low anisotropy and high superfluid density reduce thermal fluctuations

21. Thermal fluctuations of vortices
2  3 nm
λ  nm
Elastic energy of a distorted vortex line
Brandt, Rep. Prog. Phys. 58, 1465 (1995);
Blatter et al, RMP 66, 1125 (1994)
Dispersive line tension of a single vortex
 rigid rods
Anisotropy strongly reduces bending rigidity of the vortex:
ℓ  3 K/Å 0K)
ℓ  0.5 K/Å 77K)
ℓ  103 K/Å for LTS
 soft filaments
Mostly determined by superfluid density and mass anisotropy!

22. Melting of vortex lattice
G. Blatter et al, RMP 66, 1125 (1994)
Weak pinning: Jc = 0 in the vortex
liquid phase B > Bm
Lindemann criterion: <u2(T,Bm)> = cL20/Bm,
cL  0,1-0.3 (Nelson et al; Blatter et al, Brandt et al; …)
Upper branch of the melting field Bc1 << Bm << Bc2:
For YBCO, Bm(77K)  9T, Bc2(77K)  20T
Similar relation between Bm and Bc2 in Nd-1111,
but weaker reduction of the melting field in
lower-Tc FBS
Main material parameter:
Calorimetric measurements by
Schilling et al PRL, 78, 4833 (1997);
Nature, 382, 791 (1996)
YBCO

23. Magnetic granularity in HTS polycrystals
16O [001] tilt GB in YBCO  J
Magnetic granularity caused
by grain boundaries d
Only small currents can pass through GBs
despite strong pinning of vortices caged in
the grains
Fragmentation of uniform current flow
into decoupled current loops in the grains
AG and L. Cooley, PRB 50, (1994)
d = b/2sin(/2)

24. The grain boundary problem in cuprates and FBS
First measurement of Jc
on a Ba2(Fe1-xCox)2As2 bicrystal
S. Lee, et al. APL 95, (2009).
Dimos, Chaudhari and Mannhart, PRB 41, 4038 (1990)
Hilgenkamp and Mannhart, APL 73, 265 (1998); RMP 74, 485 (2002) d
Similar nearly exponential drop of Jc with the misorientation
angle both in the cuprates and Fe-based superconductors

25. Similarities of cuprates and Fe-based superconductors
1 nm
short coherence length,   1-2 nm
charging and strains effects of dislocation cores
competing orders: nonsuperconducting AF phase precipitates on GB
low carrier density  long Thomas Fermi screening length lTF  1-2 nm
AG and Pashitskii, PRB 57, (1998);

26. 15 years of R&D to overcome the current-limiting GBs: “YBCO single crystal by the mile”
Eliminate high-angle GBs by growing YBCO films of textured substrates
State of the art: complex, expensive, only a small fraction carries current, high ac losses
Jc of YBCO layer must be pushed to its limit
Industry produces km long second generation YBCO coated conductors

27. Iron-based superconductors
Fe-based superconductors: unconventional multiband superconductivity originated from magnetic Fe ions
Superconductivity competing with antiferromagnetic states in low-carrier density semi-metals
High Tc and huge upper critical magnetic fields. Interplay of orbital and paramagnetic pairbreaking in multiband SCs and their effect on Hc2(T)
Effective tuning of Hc2 by doping-induced small shifts of the Fermi energy,
Instead of the conventional way of introducing disorder.
Strong Pauli pairbreaking in FBS can lead to exotic effects at high magnetic fields, such as FFLO state.
Good prospects for magnet applications if grain boundary problem is resolved

28. Diverse family of Fe-based superconductors (FBS)

29. Phenomenology of pnictides
Tetragonal
Orthorhombic
Paramagnetic AF
La-1111
H. Luetkens et al, Nature Mat. 8, 305 (2009)
C. Lester et al, PRB 79, (2009)

30. Dirty limit can hardly be reached
Huge Hc2 in pnictides
High slopes Hc2/ = T/K at Tc
Hc2(0) for 1111 and 122 FBS,
extrapolate to > 100T
Short GL coherence lengths
𝜉 0 = 𝜙 0 2𝜋 𝑇 𝑐 𝐻 𝑐2 ′ 1/2 =1−2 𝑛𝑚
result from high Tc and low
carrier density in semi-metallic FBS
𝜉 0 = ℏ 𝑣 𝐹 2𝜋 𝑇 𝑐
Dirty limit can hardly be reached
AG, Nature Mat. 10, 255 (2011)

31. Does increasing Hc2 by disorder work in FBS?
Effect of the elastic mean free path ℓ on the orbitally-limited
(Werhamer-Helfand-Hohenberg, 1966)
Clean limit: ℓ >> 0 ⟹ ξ = 0= vF/ and
Dirty limit : ℓ << 0 ⟹ ξ = (ℓ0 )1/2
Works in conventional superconductors: 10 –fold increase of Hc2 in MgB2
Does not work in FBS because ℓ <0  1-2 nm implies the Joffe-Regel limit and
ℓkF < 1 for which the conventional dirty limit BCS theories fail
Hc2 in semi-metallic FBS can be effectively tuned by doping

32. Orbital or Pauli-limited Hc2?
FFLO
Orbitally limited
Mostly Pauli limited
Sarma, Maki,
Gruenberg and Gunther, 1966
Werthamer-Helfand-Hohenberg,

33. Chandrasekhar – Klogston limit First order phase transition
Pauli pairbreaking
Chandrasekhar – Klogston limit k -k
magnetic
energy
condensation
First order phase transition
Using BCS
yields a useful relation

34. Relation between orbital and Pauli pairbreaking
Maki parameter M = 21/2Hc2orb/Hp :
In ordinary metallic BCS superconductors with mab  m0 and  << EF ,
paramagnetic pairbreaking is negligible , M << 1
Pauli-limited superconductors with M > 1
Heavy fermions with mab/m0  103
Highly anisotropic materials with mc/m0  106 : layered organic SC, high-Tc
cuprates (BSCCO), etc for H||ab
Semi-metalic, strongly correlated FBS with EF < eV, and mab/m0  10

35. Orbital and Pauli coupling: FFLO stateEk k
kF - q
-kF - q
FFLO
Cooper pairing with nonzero momentum Q = 2q:
modulation of the order parameter along H
(z) = 0 cos(Qz) (Larkin-Ovchinnikov)
(z) = 0 exp(iQz) (Fulde-Ferrel) Q
FS nesting facilitates
the FFLO state

36. FFLO in heavy fermions and organics
CeCoIn5
B. Lortz et al, PRL 99, (2007)
Layered organic SC
Bianchi et al, PRL 91, (2003)
Heavy fermions

37. Equation for Hc2 and Q (single band)
 = 2
FFLO transition for  > 1
Spontaneous FFLO vector Q(T) appears at low T
The FFLO period (T) = 2/Q(T) diverges at the spinodal: T = TFFLO
At zero T: (0)  0 . First order transition line between two spinodals.

38. Electron spectrum from ab-initio calculations and ARPES
LaFeP(O,F)
multiple bands crossing the Fermi level
two hole pockets at  and two electron pockets at M
FeSe0.42Te0.58

39. New features of FBS revealed by ARPES
Small Fermi energies: EF  eV
Large effective mass renormalization:
m*  (2-16)me
Several shadow bands near the FS:
Lifshitz transition upon doping
Strongly correlated semimetals
Good candidates for the FFLO state:  > 1
Example of a Pauli-limited SC: FeSe0.5Te0.5 :
Tc = 16K, EF = 25 meV, mab = 10me
 = even for H||c
In-plane coherence lengths   1-2 nm

40. Multiband pairing gap symmetriesh Q + - e h Q
Pairing coupling constants
Impurity scattering rates
s pairing: gaps with opposite signs
Mazin, Singh, Johannes, Du, PRL 101, (2008);
Kuroki et al, PRL 101, (2008)
Extended s-wave or d-wave gaps
Kuroki et al, PRL 101, (2008);
Graser, Maier, Hirshfeld, Scalapino, NJP 11, (2009)
Strong interband repulsion: 1221 > 1122
Phonons are not sufficient to explain high Tc

41. Multiband superconductivity on repulsion
BCS gap equations for two bands:
where E = (2 + 2)1/2
s pairing for repulsive interaction 12 < 0 and opposite signs of 1 and 2
Pairing glue due to AF spin fluctuations, w = 1122 - 1221 < 0

42. Upward curvature of Hc2(T) in two-band models
Bilayer model of two-band SC
Interaction of two bands with
conventional Hc2(T) can produce
unconventional Hc2(T) with upward
curvature
Model independent mechanism

43. Hc2 for two coupled bands (clean limit) H||c
AG, PRB 82, (2010)
Rep. Prog. Phys. 74, (2011)
Band coupling parameters:
a1 = (0 + -)/2w, a2 = (0 - -)/2w, - = 11 - 22, 0 = (-2 + 41221)1/2, w = 1122 - 1221
Band asymmetry parameters:

44. Band competition: hidden FFLO
Due to the significant differences in the band parameters,
one band can be FFLO unstable (1 > c) but another
one is not (2 < c).
Passive band reduces manifestations
of the FFLO in the WHH-like shape of Hc2(T), but
FFLO is still there
“Hidden” FFLO: no apparent signs in Hc2(T) but
can be revealed as the first order PT by
magnetic torque and specific heat or NMR

45. N. Kurita et al. J. Phys. Soc. Jpn. 80, 013706 (2011)
Experiment-I: LiFeAs
FFLO
Undoped composition corresponds to
the maximum Tc
No suppression of FFLO by doping -
induced disorder
Good candidate to search for FFLO,
mean free path >> 
K. Cho, H. Kim, M. A. Tanatar, Y. J. Song, Y. S. Kwon,
W. A. Coniglio, C. C. Agosta, AG, R. Prozorov,
PRB, 83, (R) (2011)
Small jump in magnetic torque develops
below 8K
N. Kurita et al. J. Phys. Soc. Jpn. 80, (2011)

46. Suppression of orbital pairbreaking in srained FeSe0. 5Te0. 5 films C
Suppression of orbital pairbreaking in srained FeSe0.5Te0.5 films C. Tarantini et al. cond-mat. arXiv:
FFLO

47. Experiment-III: tuning Hc2 by doping in Ba1-xKxAs2Fe2
C. Tarantini et al. cond-mat. arXiv:
Tuning the shapes of Hc2(T) due
to expansion and contraction of
FS pockets
Highest so far Hc2 in the optimally
doped Ba-122
Change from upward to downward
curvature of Hc2(T) upon doping
x = 0.4 (1); x = 0.25 (2); x = 0.15 (3)

48. FFLO triggered by the Lifshitz transition
Hc2 equation in effective 2-band form:
 = (1221 + 2332 )1/2
reduction of the FFLO instability threshold

49. Summary
The higher Tc, the less relevant for high-temperature applications it becomes
The key parameters to be optimized irrespective to pairing mechanisms:
Carrier density (the higher the better)
Electron mass anisotropy (the smaller the better)
Thomas Fermi screening length (the smaller the better)
The higher Tc the less parameter space we have to satisfy the constrains on
the carrier density and mass anisotropy
The symmetry of the order parameter and competing orders:
non-s-wave pairing and competing orders greatly complicate applications
Reduce current-blocking effect of grain boundaries
Designer pinning nanostructures would be required to minimize
vortex fluctuations and produce high critical currents
Fe-based superconductors: huge Hc2 and good prospects for applications