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New challenges and opportunities for high-Tc superconducting materials

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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 state
Ek 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 symmetries
h 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


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