The High T c Superconductors: BCS or Not BCS?

Transcription

1 The University of Illinois at Chicago The High T c Superconductors: BCS or Not BCS? Does BCS theory work for the high temperature superconductors? We take a look at the electronic excitations using angle resolved photoemission spectroscopy (ARPES).

2 The University of Illinois at Chicago Outline Brief introduction to ARPES. The phase diagram: the underdoped and overdoped regions. Difference in behavior between these two regions.

3 The University of Illinois at Chicago Collaborators A. Kanigel, U. Chatterjee, M. Shi, & J. C. C. University of Illinois at Chicago & Argonne National Laboratory M. R. Norman, S. Rosenkranz, D. Hinks Argonne National Laboratory M. Randeria Ohio State University T. Takahashi Tohoku University K. Kadowaki Tsukuba University Helené Raffy, Z.Z. Li Université Paris-Sud

4 The high temperature superconductors Schematic phase diagram Temperature (10 2 K) 4 2 T* Pseudo Gap Strange metal (no qp) d-wave superconductor Normal Metal AFM Mott 0 Insulator Doping (e - /Cu) How do we know all this? In large part from angle resolved photoemission T c

5 Angle resolved photoemission Photons in - electrons out z θ φ analyzer detector a or b k f // = 2mE k// i = sinθ 2 Why is ARPES important in the HTSC problem? Strong k-dependences in quantities of interest: SC gap; pseudogap; self-energy High temperature (Tc ~ 100K) & energy ( ~ 10 s mev) scales High resolution k ~ 0.01 (2π/a) δω ~ 5 15 mev Reviews: A. Damascelli, Z. Hussain and Z. X. Shen, Rev. Mod. Phys. 75, 473 (2003). J. C. Campuzano, M. R. Norman and M. Randeria; in "Physics of Conventional and Unconventional Superconductors", edited by K. H. Bennemann and J. B. Ketterson, (Springer Verlag, 2004); cond-mat/

6 # of electrons The ARPES spectra It provides a fairly complete view of the excitations E Slope: Velocity k v = de dk Width: 1/Lifetime Position: Energy Each spectrum Energy (ev) corresponds to a particular k

7 ARPES measures the spectral function A(k,ω) = 1 π ImG R probability of adding or removing a particle from a many-body system Randeria, et al., PRL 74 (95) 4951 Impulse approximation r r 2A(k,ω I ψ A p ψ ) f (ω ) f i Depends on Depends on k k polarization ω hν T * selection rules * sum rules

8 Eliminating the Fermi Function I(k,ω) A(k,ω)f (ω) adivided Arc region by f(ω) When all extraneous effects are removed, we are left with the single state crossing the Fermi energy PRB 52 (1995) 615 (0,π) k y Binding energy (ev) Fermi surface Campuzano, et al., PRL 64 (90) 2308 (0,0) k x

9 HTSCs: The Phase transition in the OD region 4 Temperature x 10 2 K 2 A F M Intensity (arb. units) 95K 90K 85K 80K 75K 70K 65K 58K 50K 40K SC 0.2 Doping 30K 13K Binding energy (ev)

10 HTSCs: The Phase transition in the OD region Temperature x 10 2 K 4 2 Δ (mev) BCS A F M SC Temperature ( K) Doping

11 How do we know we are looking at? Particle-hole mixing Γ (!,0) E BCS (0,!) (!,!) (b) T=95K T=13K ε k 2 Δ k k k x =2.30 ky= k x =2.30 ky= 0.00 ε k 2 + Δ k Campuzano, et al., PRB 53(96) R14797 (k F ) Binding energy (ev) Binding energy (ev)

12 Shape of the superconducting gap 40 M 1 Y Shen, et al. PRL 70, 1553 (93) Γ 15 1 M Ding, et el., PRL 73, 3302 (94) e- along diagonal to Cu-O bond not paired FS angle phase sensitive experiments van Harlingen (1993, 95) Tsuei & Kirtley (1994, 95) k y k x

13 Pseudogap: Supression of spectral weight at E F 4 Temperature x 10 2 K Optimal doping 2 200K Pseudo Gap K SC order 0.2 Doping 14K Beyond BCS: thermodynamic transition NOT mean field Ding, et al., Nature 382, 51 (96) Loeser, et al. Science 273, 325 (96)

14 Contrast the UD and OD regime Pseudogap same 2ΔPG as SC gap QP! Strange Metal No Q.P. Metal Pseudo-Gap S.C. Beyond BCS: SC state does NOT arise from a Fermi liquid

15 Pseudogap leaves behind Fermi arcs SC state PG state 2! Fermi Arc! Binding Energy(eV) 0 0! 2! Norman, et al., Nature 392 (98) Binding Energy(eV)

16 Scaling properties of the Fermi arcs T c =90K, T=140K T c =70K, T=110K T=110K T c =25K, T=50K As the doping decreases, the Fermi arcs get shorter! Binding Energy(eV) Binding energy (ev) Energy (ev)

17 Scaling properties of the Fermi arcs T=110K T=200K As the 0.1 T=200K Tc=70K temperature decreases, the arcs also Anti-node Node get shorter! T=110K Tc=70K (π/a) x

18 Scaling of the Fermi arcs t = T/T*(x) Kanigel, et al. Nature Physics, 2, 447 (06) b 100 Fermi Arc Length(%) "Node" Hot Spot k y t=t/t * If you could go down to T=0 in the PG state, it would have four point nodes, just like a d-wave SC, but its NOT a SC! k x

19 Are the Fermi arcs just a T-effect? Arcs Co'apse! Beyond BCS: Δ shows NO T-dependence

20 Temperature evolution of Δ Kanigel, et al., PRL 99 (07) Beyond BCS: NO relation between the gap and tbe order parameter!

21 Fermi arc collapse controlled by transition width 0.8 Fermi Arc Length (%) 0.6 Tc=67 T*=170K Tc=80 T*=132K Kanigel, et al., PRL, 99, (07) t=t/t*

22 Pseudogap in parts like a metal and in other parts akin to a SC, but no LRO Metal Superconductor a Arc region 2!! 0 0! 2! Binding energy (ev)

23 Fluctuating Diamagnetism in the PG phase Wang, et al., PRL 95, (05) Underdoped Bi 2212 Parabolic behavior at highest T due to Less than parabolic due to diamagnetism T c

24 Properties of the pseudogap PG same magnitude as Δ. Anisotropy is T-dependent, leading to disconnected Fermi arcs below T* PG at same k F of the SC gap and of the normal state Fermi arc collapses below T c. There is fluctuating diamagnetism in the PG PG is a precursor to the SC gap

25 Temperature Summary: What ARPES te's us Phase diagram exhibits the failure of three paradigms of 20 th Band theory fails for the x=0 parent insulator BCS fails for the Unconventional SC for x<optimal A F M Century Solid State Physics! Pseudo Gap Strange metal d-wave superconductor Normal Metal Doping Landau s Fermi liquid theory fails for the strange metal and pseudogap regimes!ank y" for y"r a#ention