THE SPIN GAP
The problem of the crossover from a BCS superconductor to a condensate of pre-formed bosons has attracted renewed attention recently. Given their very short coherence lengths, the high Tc materials are likely to be in an intermediate regime between these two limits. Rather little is known about how the normal (non-superconducting) state of a system of fermions with attractive interactions evolves from a Fermi liquid-like regime to a Bose regime as a function of increasing attraction. Independent of the microscopic mechanism, the question of how the resulting attractive interaction affects the normal state properties is of considerable interest.
We studied the normal state of the 2D attractive Hubbard model using quantum Monte Carlo. We found that singlet pairing correlations develop in the normal state, and the system evolves from a Fermi liquid-like state for small U to a non-degenerate Bose liquid at large U. In the intermediate U regime, the spin susceptibility chi is strongly temperature dependent, and the low frequency spectral weight, as measured by the NMR relaxation rate 1/T1T, is shown to track chi. This provides a natural explanation for the spin-gap behavior observed in several high Tc systems.
CHARGE TRANSFER MECHANISMS
The CuO2 sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The 3-band Hubbard model with an onsite Cu Coulomb interaction Ud which is large compared to the difference in energy Delta between the O and Cu sites provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a CuO2 lattice described by a 3-band Hubbard model.[2,3] For Ud large compared with Delta, and Delta comparable or larger than the bandwidth of the lower hole band, we found strong antiferromagnetic correlations and evidence for a charge transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decreased with either hole or electron doping, and we showed that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole doped system exhibited a charge transfer instability. As V is reduced, this was reflected as a peak in the charge-transfer susceptibility near Ep+2V = Ud, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended s-wave channels near the antiferromagnetic boundary.
We also calculated the ground state energy as a function of magnetic flux in one-dimensional "CuO" rings. When the intersite repulsion V is of order of the charge transfer gap, we found flux quantization with charge 2e and a slow algebraic decay of singlet superconducting correlation functions, suggesting a transition into a paired state.
[29.] "Antiferromagnetic, Charge-Transfer, and Pairing Correlations in the Three-Band Hubbard Model", R.T. Scalettar, S.R. White, D.J. Scalapino, and R.L. Sugar, Phys. Rev. B44, 770 (1991).
[44.] "Pairing and Spin Gap in the Normal State of Short Coherence Length Superconductors," M. Randeria, N. Trivedi, A. Moreo, and R.T. Scalettar, Phys. Rev. Lett. 69, 2001 (1992).
[34.] "Quantum Monte Carlo Simulations of a CuO2 Molecule," R.T. Scalettar, D.J. Scalapino, R.L. Sugar, and S.R. White, International Journal of Supercomputing Applications 5, 36 (1991).
[45.] "Flux Quantization and Pairing in One-Dimensional Copper-Oxide Models," A. Sudbo, C.M. Varma, T. Giamarchi, E.B. Stechel, and R.T. Scalettar, Phys. Rev. Lett. 70, 978 (1993).
[51.] "Magnetic and Pairing Correlations in Coupled Hubbard Planes," R.T. Scalettar, J.W. Cannon, D.J. Scalapino, and R.L. Sugar, Phys. Rev. B50, 13419 (1994).
[55.] "Magnetism and Spin Liquid Behavior in a Two Layer Hubbard Model," R.T. Scalettar, J. of Low Temp. Phys. 99, 499 (1995).
[75.] "Variational Monte Carlo Study of an Interacting Electron-Phonon Model", B.J. Alder, K.J. Runge, and R.T. Scalettar, Phys. Rev. Lett. 79, 3022 (1997).
[82.] "The Phase Diagram of Disordered Vortices from London Langevin Simulations", A. van Otterlo, R.T. Scalettar, and G.T. Zimanyi, Phys. Rev. Lett. 81, 1497 (1998).
[83.] "Dynamic Phases and the Peak Effect in Dirty Type II Superconductors", A. van Otterlo, R.T. Scalettar, G.T. Zimanyi, R. Olsson, A. Petrean, W. Kwok, and V. Vinokur, Phys. Rev. Lett. 84, 2493 (2000).
[96.] "Effect of Splayed Pins on vortex creep and critical currents", C.J. Olson, R.T. Scalettar, G.T. Zimanyi, and N. Gronbech-Jensen, Phys. Rev. B62, 3612 (2000).
[99.] "Metastability and Transient Effects in Vortex Matter Near a Disorder Driven Transition", C.J. Olson, C. Reichhardt, R.T. Scalettar, G.T. Zimanyi, and N. Gronbech--Jensen, Phys. Rev. B67, 184523 (2003).
[175.] K. Bouadim, M. Enjalran, F. Hebert,
G.G. Batrouni, and R.T. Scalettar,
Sign change of the extended s-wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study,
Phys. Rev. B77, 014516 (2008).
B. Moritz, F. Schmitt, W.. Meevasana, S. Johnston, E.M. Motoyama,
M. Greven, D.H. Lu, C. Kim, R.T. Scalettar, Z.-X. Shen, and T.P.
"Cuprate ``Waterfalls" Redux: n-type vs. p-type Materials,"
New Journal of Physics, to appear.
Simone Chiesa, Prabuddha B. Chakraborty,
Warren E. Pickett, and Richard T. Scalettar,
"Disorder-induced stabilization of the pseudogap in strongly correlated systems,"
Phys. Rev. Lett. 101, 086401 (2008).
E. Khatami, K. Mikelsons, D. Galanakis, A. Macridin, J. Moreno,
R.T. Scalettar, and M. Jarrell,
"Quantum Criticality Due to Incipient Phase Separation in the 2D Hubbard Model,"
submitted to Phys. Rev. Lett.