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2. Model of strongly correlated electrons
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Magnetism and Superconductivity in the t-J model on the triangular
lattice. We have investigated the phase diagram of the t-J Model on a triangular
lattice using a variational Monte Carlo approach. We used an extended set of
Gutzwiller projected fermionic trial wave-functions allowing for simultaneous
magnetic and superconducting order parameters, which were extended by using
Pfaffian matrices. We obtained energies at zero doping for the spin-1/2
Heisenberg model in very good agreement with the best estimates. Upon
electron doping this phase is surprisingly stable variationally up to electronic
density n=1.4, while the d+id order parameter is rather weak. For hole doping
the coplanar magnetic state is almost immediately destroyed and the d+id
superconductivity survives down to n=0.8. Moreover, there are evidences for a
narrow spin density wave phase and ferromagnetism [6].
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Bond-order wave instability in the t-J model on the square lattice.
Motivated by the observation of inhomogeneous patterns in some high- T c
cuprate compounds, several variational Gutzwiller-projected wave functions
with built-in charge and bond-order parameters are proposed for the extended t-
J-V model on the square lattice at low doping. In this work, we investigate, as a
function of doping and Coulomb repulsion the relative stability of a wide
variety of modulated structures. It is found that the 4×4 bond-order wave
function with staggered-flux pattern (and small charge and spin current density
wave) is a remarkable competitive candidate for hole doping around 1⁄8 in
agreement with scanning tunneling microscopy observations in the underdoped
regime of some cuprates. This wave function is then optimized accurately and
its properties studied extensively using a variational Monte Carlo scheme.
Moreover, we find that under increasing the Coulomb repulsion, the d -wave
superconducting RVB wave function is rapidly destabilized with respect to the
4×4 bond-order wave function [8,9].
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Scanning-tunneling microscopy. Low temperature (3.9 K) scanning-tunneling
spectroscopy on a Ag(111) surface has revealed that for some concentration of
Cerium ad-atoms on-top of the surface, a superstructure (hexagonal) of ad-atom
could be stabilized. Using a tight-binding model, we could relate the overall
spectral structures to the scattering of Ag(111) surface-state electrons by the Ce
ad-atoms. Also the site dependence could be related to the disorder induced by
imperfections of the superlattice, and the opening of a gap in the local density of
states could explain the observed stabilization of superlattices with ad-atom
distances in the range of 2.3-3.5nm. For more details see ref. [2].