Low Temperature Thermal Transport Across the Cuprate Phase Diagram Mike Sutherland

1. Low Temperature Thermal Transport Across the Cuprate Phase DiagramMike Sutherland Louis Taillefer Rob Hill Cyril Proust Filip Ronning Makariy Tanatar Christian Lupien Etienne Boaknin Dave Hawthorn J. Paglione M. Chiao R.Gagnon, H.Zhang D.Bonn, R.Liang, W.Hardy P.Fournier, R.Greene A.P.Mackenzie, D. Peets, S. Wakimoto Department of Physics University of Toronto

2. m a g n e t i s m Temperature pseudogap metal superconductor Carrier concentration What questions can we address by studying low temperature thermal conductivity as a function of doping in the cuprates ? How well does d-wave BCS theory describe the superconducting state ? Is the superconducting order parameter pure d-wave throughout the phase diagram? How does the pseudogap influence the behaviour of low-energy quasiparticles?

3. The density of states in a d-wave superconductor density of states presence of nodes  quasiparticles at low T g impurity bandwidth impurity effects clean limit Finite density of delocalised states at zero energy Linear density of states at low energy - governs all low temperature properties

4. E The quasiparticle excitation spectrum near the nodes takes the form of a ‘Dirac cone’ : With: Fermi Liquid Theory of d-wave Nodal Quasiparticles d-wave gap: D = D0cos(2f)

5. l A Q DT phonons ~ T3 electrons ~ T Thermal Conductivity Primer k= kelectrons + kphonons Kinetic theory formulation:

6. d-wave BCS theory of thermal conductivity Cooper pairs carry no heat Δo from κ0/T Electronic heat transport provided solely by quasiparticles ( T0, T<<g ) This result is universal with respect to impurity concentration A. Durst and P. A. Lee, Phys. Rev. B 62, 1270 (2000). M. J. Graf et al., Phys. Rev. B 53,15147 (1996).

7. Nodal quasiparticles in optimally doped Cuprates Optimally Doped Bi-2212 D0 =30 meV  Weak Coupling BCS: D0 =2.14kBTc= 17 meV Increase Coupling: ARPES: D0 4kBTc M.Chiao et al. PRB 62 3554 (2000) Ding et al. PRB 54 (1996) R9678 Mesot et al. PRL 83 (1999) 840

8. (0,p) (p,p) (p,0) G doping dependence: vF LSCO(x) essentially doping independent X.J. Zhou et. al. Nature 423 398 ( 2003 )

9. Nodal quasiparticles in overdoped Cuprates Tc = 15K overdoped Tl 2201 Doping Tc = 27K D0 =4kBTc Tc = 89K Tc = 85K How do we estimate hole concentration [p]? Tc=15 K sample: Proust et al., PRL 89 147003 (2002). Other samples: Hawthorn et. al. to be published

10. decrease decrease decrease decrease 0/T as doping vF/v2 as doping Nodal quasiparticles in underdoped Cuprates underdoped YBCO simple BCS theory violated: Δo does not follow ΔBCS ! Sutherland et al. PRB (2003)

11. (0,p) (p,p) (p,0) G The pseudogap in underdoped Cuprates T = 15 K pseudogap is : (i) quasiparticle gap (ii) must have nodes (iii) must have linear dispersion Campuzano et. al. PRL 83 (1999) 3709 Norman et. al. Nature 392, 157 (1998) White et. al. Phys. Rev. B. 54, R15669 (1996) Loeser et. al. Phys. Rev. B. 56, 14185 (1996)

12. Underdoped La2-xSrxCuO4 Presence of static SDW order? Large intrinsic crystalline disorder?

13. Summary and Outlook doping dependence of superconducting gap maximum : overdoped – optimal doped: D0scales with Tc (BCS theory) optimal doped – underdoped: D0increases while Tcdecreases (Failure BCS theory) existence of nodes throughout the phase diagram: no evidence for quantum phase transition to d+ix in the bulk Question: What happens near the AF – SC boundary?

14. (0,p) (p,p) (p,0) G doping dependence: vF LSCO(x) ARPES data Z.X.Shen essentially doping independent

15. Specular Reflection of Phonons V3Si s-wave SC (thermal insulator, el =0)  = 1.7 Sapphire Specular reflection lph = f(T) Fit data to /T = o/T + BT o/T = 0 ph/T~ T,  <2 R. O. Pohl* and B. Stritzker, PRB 25, 3608 (1982).