Two ways to destroy a Fermi liquid

1
Dynamic variational principle and the phase
diagram of high-temperature superconductors
André-Marie Tremblay
2
Some basic Solid State Physics non-interacting
electrons
3
Electronic states in d2
Angle Resolved Photoemission Spectroscopy (ARPES)
4
The non-interacting case
EDC
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
5
Electron-doped, non-interacting
MDC
6
Interacting case The Fermi liquid
A(k,w)f(w)
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
7
A Fermi liquid in d 2
T-TiTe2
U / W 0.8
Perfetti, Grioni et al. Phys. Rev. B 64, 115102
(2001)
8
Destroying the Fermi liquid at half-fillingLatti
ce interactions
A-Long-range order
Introduce frustration
Will resist LRO until critical U
9
Destroying the Fermi liquid at half-fillingLatti
ce interactions
B-Strong on-site repulsion (Mott transition)
10
Question What happens away from n 1?
A- Long-Range Order (U large enough)
Hole pockets Still FL
B- Mott transition DMFT
If gapped, gapped everywhere
11
Two ways to destroy a Fermi liquid hole and
electron-doped cuprates.

• I. Introduction
• Fermi liquid
• II. Experimental results from cuprates model
• III. Strong and weak coupling pseudogap (CPT)
• IV. Weak coupling pseudogap (QMC,TPSC)
• V. d-wave superconductivity
• VI. Conclusion

12
CuO2 planes
YBa2Cu3O7-d
13
Phase diagram
n, electron density
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
14
Fermi surface, electron-doped case
Armitage et al. PRL 87, 147003 88, 257001
15
Fermi surface, hole-doped case 10
16
The  Hubbard model 
17
Weak vs strong coupling, n1
T
w
U
w
U
Mott transition
U 1.5W (W 8t)
18
Question quantitative and qualitative

• How do we go from a Mott insulator to a conductor
  as a function of doping?
• Hot spots and pseudogaps in the Hubbard model
  (like experiment) ?
• Close to understood in e-doped case.

19
Two ways to destroy a Fermi liquid hole and
electron-doped cuprates.

• I. Introduction
• Fermi liquid
• II. Experimental results from the cuprates and
  model
• III. Strong and weak coupling pseudogap (CPT)
• IV. Weak coupling pseudogap (QMC,TPSC)
• V. d-wave superconductivity
• VI. Conclusion