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Dynamic variational principle and the phase diagram of high-temperature superconductors. c = -1 Perfect diamagnetism (Shielding of magnetic field) (Meissner effect). André-Marie Tremblay. k y. w. w. k x. k. r. -p/ a. p/ a. Some basic Solid State Physics : non-interacting electrons.

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Presentation Transcript
slide1

Dynamic variational principle and the phase diagram of high-temperature superconductors

c = -1

Perfect diamagnetism (Shielding of magnetic field)

(Meissner effect)

André-Marie Tremblay

slide3

e

Photon

2

k

= E +w + m- W

ph

2m

k

Electronic states in d=2

Angle Resolved Photoemission Spectroscopy (ARPES)

the non interacting case
The non-interacting case

EDC

Damascelli, Shen, Hussain, RMP 75, 473 (2003)

interacting case the fermi liquid
Interacting case: The Fermi liquid

A(k,w)f(w)

Damascelli, Shen, Hussain, RMP 75, 473 (2003)

a fermi liquid in d 2
A Fermi liquid ind = 2

T-TiTe2

U / W = 0.8

Perfetti, Grioni et al. Phys. Rev. B64, 115102(2001)

destroying the fermi liquid at half filling lattice interactions

w

Q

D

k

-p/a

p/a

Destroying the Fermi liquid at half-filling:Lattice + interactions

A-Long-range order

Introduce “frustration”

Will “resist” LRO until critical U

destroying the fermi liquid at half filling lattice interactions1

w

w

w

U

W

W

r

r

r

U

w

w

w

W

W

U

U

DMFT- Georges, Kotliar, Rosenberg, 1986.

r

r

r

Destroying the Fermi liquid at half-filling:Lattice + interactions

B-Strong on-site repulsion (Mott transition)

question what happens away from n 1
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

two ways to destroy a fermi liquid hole and electron doped cuprates
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
cuo 2 planes
CuO2 planes

YBa2Cu3O7-d

phase diagram

Hole doping

Electron doping

Optimal doping

Optimal doping

Phase diagram

n, electron density

Damascelli, Shen, Hussain, RMP 75, 473 (2003)

fermi surface electron doped case

15%

10%

10%

15%

4%

Pseudogap at hot spots

4%

Fermi surface, electron-doped case

Armitage et al. PRL 87, 147003; 88, 257001

slide16

Simplest microscopic model for Cu O planes.

t’

t’’

m

U

LSCO

t

  • Size of Hilbert space :
  • With N=16, It takes 4 GigaBits just to store the states

(N = 16)

The « Hubbard model »

slide17

A(kF,w)

A(kF,w)

LHB

UHB

t

Effective model, Heisenberg: J = 4t2 /U

Weak vs strong coupling, n=1

T

w

U

w

U

Mott transition

U ~ 1.5W (W= 8t)

question quantitative and qualitative
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.
two ways to destroy a fermi liquid hole and electron doped cuprates1
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