High T c Superconductors & QED 3 theory of the cuprates

1. High Tc Superconductors & QED3 theory of the cuprates Tami Pereg-Barnea UBC tami@physics.ubc.ca QED3

2. outline • High Tc – Known and unknown • Some experimental facts and phenomenology • Models • Attempts to solve the problem • The inverted approach • QED3 – formulations and consequences

3. Facts • The parent compounds are AF insulators. • 2D layers of CuO2 • Superconductivity is the condensation of Cupper pairs with a D-wave pairing potential. • The cuprates are superconductors of type II • The “normal state” is a non-Fermi liquid, strange metal.

4. YBCO microwave conductivity BSCCOARPES

5. Neutron scattering – (p,p) resonance in YBCO Underdoped Bi2212

6. Phenomenology • The superconducting state is a D-wave BCS superconductors with a Fermi liquid of nodal quasiparticles. • The AF state is well described by a Mott-Hubbard model with large U repulsion. • The pseudogap is strange! • Gap in the excitation of D-wave symmetry but no superconductivity • Non Fermi liquid behaviour – anomalous power laws in verious observables.

7. Phase diagram AF AF AF

8. Theoretical approaches • Starting from the Hubbard model at ½ filling. • Slave bosons SU(2) gauge theories • Spin and charge separation • Stripes • Phenomenological • SO(5) theory • DDW competing order

9. The inverted approach • Use the phenomenology of d-SC as a starting point. • “Destroy” superconductivity without closing the gap and march backwards along the doping axis. • The superconductivity is lost due to quantum/thermal fluctuations in the phase of the order parameter.

10. Vortex Antivortex unbinding Emery & Kivelson Nature 374, 434 (1995) Franz & Millis PRB 58, 14572 (1998)

11. Phase fluctuations • Assume D0 = |D|= const. • Treat exp{if(r)} as a quantum number – sum over all paths. • Fluctuations in f are smooth (spin waves) or singular (vortices). • Perform the Franz Tešanović transformation - a singular gauge transformation. • The phase information is encoded in the dressed fermions and two new gauge fields.

12. Formalism • Start with the BdG Hamiltonian • FT transformation – in order to avoid branch cuts.

13. The transformed Hamiltonian The gauge field am couples minimallym am The resulting partition function is averaged over all A, B configurations and the two gauge fields are coarse grained.

14. The physical picture • RG arguments show that vm is massive and therefore it’s interaction with the Toplogical fermions is irrelevant. • The am field is massive in the dSC phase (irrelevant at low E) and massless at the pseudogap. • The kinetic energy of am is Maxwell - like.

15. Quantum “Electro” Dynamics • Linearization of the theory around the nodes. • Construction of 2 4-component Dirac spinors.

16. Dressed QP’s Optimally doped BSCCO Above Tc T.Valla et al. PRL (’00) QED3 Spectral function

17. Chiral Symmetry Breaking  AF order • The theory of Quantum electro dynamics has an additional symmetry, that does not exist in the original theory. • The Lagrangian is invariant under the global transformation where G is a linear combination of

18. The symmetry is broken spontaneously through the interaction of the fermions and the gauge field. • The symmetry breaking (mass) terms that are added to the action, written in the original nodal QP operators represent: • Subdominant d+is SC order parameter • Subdominant d+ip SC order parameter • Charge density waves • Spin density waves

19. Antiferromagnetism • The spin density wave is described by: where ,  labels denote nodes. • The momentum transfer is Q, which spans two antipodal nodes. • At ½ filling, Q → (,) – commensurate Antiferromagnetism. _

20. Summary • Inverted approach: dSC → PSG → AF • View the pseudogap as a phase disordered superconductor. • Use a singular gauge transformation to encode the phase fluctuation in a gauge field and get QED3 effective theory. • Chirally symmetric QED3 Pseudogap • Broken symmetry  Antiferromagnetism