China/US Joint Winter School on Novel Superconductors Hong Kong January 2013

Transcription

1 China/US Joint Winter School on Novel Superconductors Hong Kong January 2013 The Search for New High T c Superconductors from an Applications Perspective or Physical Limits to the Utility and Transition Temperatures of Very High Temperature Superconductors M.R. Beasley Stanford University MRB in Special Issue of the MRS Bulletin on Superconductivity, MRS BULLETIN 36, (2011)

2 Objectives of the Talk Looking back What have we learned in recent decades about the fundamental physics (independent of the mechanism) of very high T c superconductivity? What does it tell us about the prospects of electric power applications of superconductivity at much higher temperatures? What does it tell us about the material characteristics necessary for very high T c? Looking ahead How might we proceed? Or at least what guidance might we offer?

3 In Search of the Holy Grail BCS Theory High Field/Current SC The Quest for a Room Temperature Superconductor Pr(O- F)FeAs Adapted from a DoE Report

4 In Nature the Transition Temperature Can Be Astronomically High Quark- Gluon Plasma Color- Flavor Locked Quark MaIer Alfred and Schmitt RMP 80 (2008)

5 With Some Experimental Evidence

6 But What About a Room Temperature Superconductor? It must: Operate in an earthly environment Be made from earthly forms of maier And from a praclcal point of view, exhibit good superconduclng properles* * In the past it has been an arlcle of faith that superconduclng properles improve as T c increases

7 But Higher T c Does Not Always Bring Higher J c Thermodynamic Critical Current Density of Various Superconductors The theoretical maximum current density Cri4cal Current Density MgB 2 ConvenLonal Low T c Transi4on Temperature

8 So What s Going On? Factors Governing the Thermodynamic Critical Current Density For any superconductor: The supercurrent density J s = n s * e * v s The kinelc energy density G K = 1 2 n * smv 2 s = 1 2 Λ K = m * n s * e * 2 = 4πλ2 c 2 m * n * s e * J 2 2 s = 1 2 Λ 2 KJ s = Kinetic inductivity CondensaLon Energy ΔG G n J c = 1 2 n h * se * m*ξ n * s m* T c where ξ = size of Cooper pair (ξ 1/ T c ) Large J c requires high T c and high pair density J c J s H c 2 / 8π

9 And How Good is YBCO for Electric Power Applications? YBCO DoE Report

10 The Practical Reality YBCO is the best cuprate superconductor for electric power applications (least anisotropic) If there are to be commercial electric power applications of superconductivity above 77K, an entirely new superconductor will be required We should be looking

11 A Primer on The Fundamentals of Very High Temperature Superconductivity What would the Cooper pairs be like? Are there generic (pairing mechanism independent) limits on T c? How do these insights square with experience?

12 Whatever Else, The Cooper Pairs Will Be Very Small Size Σιζε of Cooper οφ Χοοπερ Pair παιρσ ξ (Å) Room Temperature Room Temperature Room Temperature Superconductor BCS Theory (v F const.) Pairing Temperature T P (K) The physics of pairing will be local (i.e., real space pairing)

13 To Determine T c There are Two Characteristic Temperatures to Consider Superconductivity arises when electrons (or holes) form pairs and the quantum phases of these pairs order (lock) to form a coherent macroscopic quantum state with a single phase. e e Pairs form Pairing interaction e e ψ p = ψ p e iϕ ψ p ϕ e e e e e e e e SC arises Phase locking e e e e e e e e Macroscopic quantum state ψ pi Phase locking ϕ Ψ sc ϕ i ϕ = ϕ 1 = ϕ 2 = ϕ 3 i i i Each process has its own characteristic temperature

14 The Actual Superconducting Transition Temperature T c The Destruction of Superconductivity by Increasing Temperature Pairs dissociate T p Binding energy (InteracLon strength) 0 0 Phases unlock Temperature T ϕ Temperature T T Tendency of phase to fluctuate (Phase slffness 1/Λ Κ ) If T ϕ < T p T c = T ϕ If T p < T ϕ T c = T p (and T ϕ renormalizes down to T p as in BCS theory)

15 Thermodynamic Limit to the Transition Temperature Due to Thermal Phase Fluctuations Independent of the pairing interaction, phase ordering is lost when the RMS phase difference Δφ across a Cooper pair due thermal phase fluctuations is of order π! Δφ V p = Volume of a Cooper pair! Ψ sc (x) V p = ξ ab Ψ sc (x + ξ ab ) 2 ξ c ξ c 1/ ξ ab ξ ab Temperature at which thermal fluctualons produce phase unlocking Energy to twist phase by π Λ K ( φ) 2 V p = k B T φ π ξ ab T φ 1 2 1/Λ Κ = Phase stiffness 1 Λ K ξ ab γ = 1 2 h 2 n s * ξ ab m * γ n s * 1 m * γ T p γ = (M/m) 1/2 GL mass anisotropy

16 Is a Room Temperature Superconductor Possible? NoLonal High Temperature Superconductors RelaLve to YBCO (v F constant) Yes, but will require strong interactions, high pair density and low anisotropy

17 General Considerations vs Experience Relevant for the Search for a Room Temperature Superconductor Commonly Stated Empirical Guidance* Increase interactions Low carrier density Two dimensional General Physical Considerations Increase interactions High carrier density Three dimensional There is an apparent conflict here In addition, very small pair size Local pairing on near atomic level Must learn to think and calculate in real space more like the chemists do

18 Fundamental Questions The general physical consideralons presented above are derived from thermodynamic reasoning and therefore carry great power This clearly raises some very fundamental queslons: Can strong interactions and high pair density be achieved under the same conditions? Or are they incompatible? (If the electron density is very high, one may just get a simple metal with weak interactions) Is reduced dimensionality beneficial (or possibly necessary) for high T c? For example, to weaken a competing ordered phase (e.g.,an anti-ferromagnetic parent phase) through increased fluctuations to allow superconductivity to emerge upon doping

19 Now Let s Focus on the Possible Specific Interac4ons Seemingly Favorable for Very High Temperature Superconductors What do we know empirically? What can we say theoretically? What guidance do theory and experiment provide us?

20 So What Can We Learn From the Present High Tc Superconductors? Pr(O- F)FeAs

21 Empirical Guidance on Specific Interactions Material Archetype Bismuthates (i.e., doped BaBiO 3 ) T c InteracLon Guidance 30K Charge + Lattice Cs 3 C 60 40K Lattice + Correlation (charge) Doped Negative U Insulator El-Ph Covalent Bonds MgB 2 40K Lattice El-Ph Covalent Bonds Prediction Fe-Based 50K Spin Antiferromagnetism Multiple orbitals Cuprates 130K Spin Doped Antiferromagnetic Positive U Mott Insulator Trace High T c Anomalies > Room Temperature? Shouldn t Ignore Electronic (charge and spin) interactions look good

22 A Case Study The Bismuthates Superconductivity in a doped charge-ordered oxide insulator Pr(O- F)FeAs

23 Crystal Structure of BaBiO 3 Distorted Perovskite Note three dimensional structure

24 Charge-Disproportionated (Negative U) Superconductors (e.g., BaBiO 3 ) A Failure of LDA Theory A new class of correlated insulator Oxygen Metal Bi 4+ Bi 4+ Bi 4+ Bi 4+ Bi 4+ e e e e e 2Bi 4 + (4s 1 ) Bi 3+ (4s 2 ) + Bi 5+ (4s 0 ) and Oxygen atoms move to screen charge (Breathing mode) NegaLve U - - Involves both charge and la`ce Insulator Bi 3+ Bi 5+ Bi 3+ Bi 5+ Bi 3+ U ee ee ee Superconductivity arises upon doping (Ba 1-x K x BO 3 and BaPb 1-x Bi x O 3 )

25 Phase Diagrams of the Superconducting Bismuthates BaPb 1- x Bi x O 3 BaPb 1- x K 1- x x BiO x3 O 3 12K Nega4ve- U CDW Pb Doping BaBiO 3 12K 30K SUPER- C SEMICONDUCTING Nega4ve- U CDW K Doping BaBiO 3 Ba Note similarity to the phase diagrams of the cuprate superconductors but where the ordered insulating state is in the charge sector

26 Optical Properties -- Puchkov et al Only 3 x carriers in Drude Peak and lible change with x. Strong MIR peak

27 Illustrative Theoretical Phase Diagram Illustrative Phase Diagram (Numerical SoluLon to the NegaLve- U Hubbard Model) (2D Negative-U Hubbard Model) Weak Interactions Itinerant BCS limit Seeking the Maximum T c S Strong Interac4ons Localized Phase fluctua4on limit Max T c occurs at crossover between weak and T c maximal at crossover from localized (e.g., AF, CDW) to itinerant strong coupling carriers; U and Seems bandwidth \Ma to be of a same generic order; feature optimal of carrier density strong interactions (including the el-ph interaction)

28 A New Theoretical Concept High T c and High Pair Density Superconductor Using a Normal Metal/Negative-U Insulator Proximity Effect Normal Band Metal Free electrons e T c max 0.08U T c Local pairing centers NegaLve- U Insulator Electrons coherently hop on and off the pairing centers to induce superconduclvity in the normal metal A key element here is the role of two distinct sets of electrons that are separated in space t Berg, Orgad and Kivelson PRB 78, (2008)

29 So Where Do We Stand in our Quest for a Useful Room Temperature Superconductor? There are generic limits to T c But they do not preclude a room temperature superconductor, if the anisotropy is low and the carrier density high The challenge will be to achieve strong interaclons under these condilons; there are some new ideas how to do this And we must learn how to deal with very small Cooper pairs The condilons necessary for room temperature superconduclvity are consistent with those needed for good praclcal performance

30 We offer three specific guidelines that seem essential: The interaction must be local (i.e., a real space phenomenon) because the size of the Cooper pairs will necessarily be small enlist the solid state chemists The structural units out of which the superconductor is built (e.g., the unit cell, or some molecular cluster) must be small in order to produce the necessary high pair density Three dimensional structures are advantageous and maybe necessary depending on the magnitude of the pair density.

31 Wish Good Luck to Those Willing to Try (and those that fund them)