1. Search of a Quantum Critical Point in High Tc Superconductors
Yang Xie
(with great help from Prof. Eun-Ah Kim)

2. Hidden Critical Point
Recall the phase diagram of 1-d quantum Ising model
Non-Fermi liquid: strange power law of resistivity

3. Hidden Critical Point
Compared with phase diagram of 1-d quantum Ising model
We suspect that there is a quantum critical point in the superconducting phase

4. STM Experiment
Electron density of states in a band picture

5. STM Experiment
is density of states (DOS) of quasi-particles, at excitation energies E, at position
Take E=0 at EF , i.e. take E w.r.t EF

6. Cuprate Physics
High Tc Superconductors show d-wave gap, different from s-wave superconductor (metallic superconductor)
d-wave
Peak in DOS
Gap
(BSCCO)
Quasi-particle
density of states
(DOS)
s-wave
(w.r.t EF , i.e. E=0 is the Fermi level)
(NbSe2)

7. Phase Diagram Non-Fermi Liquid:
strange power law behavior of resistivity

8. Non-Fermi Liquid
Strange resistivity: increase linear vs T for a narrow range of doping
Generally, increase as Tx, x ~
Fermi liquid: increase as T2

9. Phase Diagram
To understand Non-Fermi liquid, we need to study regions next to it.
(Fermi liquid is well-understood)

10. Pseudo Gap Tc=85 K Pink line: Fermi liquid (Platinum)
ARPES
Tc=85 K
Pink line:
Fermi liquid (Platinum)
Excitation across the Fermi level (take EF =0)
Black line:
High Tc (BSCCO)
Suppressed excitation below EF in SC phase Tc<85 K
‘Partially’ suppressed excitation above Tc (at T=95K, 120K) – Pseudo Gap

11. STM Experiment DOS evolution for increasing doping
During the experiment, the samples are always in the SC phase
DOS evolution for increasing doping

12. STM Experiment
Fourier Transform
DOS

13. STM Experiment EPG has strong correlation to pseudogap crossover
During the experiment, the samples are always in the SC phase

14. Quantum Critical Point
During the experiment, the samples are always in the SC phase
Power laws
Scaling function

15. Advertisement Prof. Eun-Ah Kim Quantum Nematics Theory
Next Tuesday in class

16. Acknowledgement
James
Eun-Ah & Michael
Stefan, Jeehye & Hitesh