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Physical review. B, Condensed matter

Energies of the staggered flux phase: A numerical study

Ting-Kuo Lee, Lay Nam Chang

Published Nov 1, 1990• 9 citations
Publisher

Abstract

Kinetic and magnetic energies of the staggered flux phase, with a fictitious flux of equal magnitude but opposite direction in adjacent square plaquettes, are calculated for the two-dimensional t-J model using the variational Monte Carlo method. They are compared to the energies of the resonating-valence-bond state, the flux phase with half a quantum per plaquette, and the projected Fermi-liquid state. For about 10% hole concentration the staggered flux phase has the lowest energy of the nonsuperconducting states, but its energy is still higher than that of the superconducting d-wave state.

DOI
10.1103/physrevb.42.8720

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The stability of a staggered flux (SF) or d-density wave state is studied in a d-p model using a variational Monte Carlo (VMC) method. This state possesses a local circular current and possibly causes the pseudogap phase in high-Tc cuprate superconductors. We introduce into the trial function a configuration dependent phase factor, which was recently shown to be indispensable to stabilize current-carrying states. We pay attention to the energy gain as a function of adjacent O-O hopping and Cu-site coulomb repulsion U. It is found the SF state becomes stable for hole doping rates of and , owing to the reduction in kinetic energy, but seems fragile because the energy gain rapidly decays on doping holes for any . The loop current tends to increase as increases.

Physics Procedia•Jan 1, 2015•0 citations
Kinetic and magnetic energies of the staggered flux phase, with a fictitious flux of equal magnitude but opposite direction in adjacent square plaquettes, are calculated for the two-dimensional t-J model using the variational Monte Carlo method. They are compared to the energies of the resonating-valence-bond state, the flux phase with half a quantum per plaquette, and the projected Fermi-liquid state. For about 10% hole concentration the staggered flux phase has the lowest energy of the nonsuperconducting states, but its energy is still higher than that of the superconducting d-wave state.
The authors have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP+d) of the extended t-J model at various hole densities ( delta ). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. They found that the SFP is stable against the projected Fermi liquid up to delta approximately=20%. For moderately large J, J/t>or=0.4, the SFP+d state may be favoured against the pure d-wave state but only at very low hole density ( delta approximately 20%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.
Kinetic and magnetic energies are calculated for the two-dimensional Hubbard model using the variational Monte Carlo method and including a fictitious flux phase. In contrast to earlier results for the two-dimensional t-J model, we found all the flux phases studied lie higher in energy than the paramagnetic or the antiferromagnetic states. Near half-filling, the t-J model with no double occupancy on a lattice site is dominated by the magnetic energy, while the Hubbard model with partial double occupancy is dominated by the kinetic energy. When flux phases are introduced into the Hubbard model, the decrease in the magnetic energy is not nearly enough to offset the cost in kinetic energy.
A normal (nonsuperconducting) ground state of the t-J model may be variationally approximated by a Gutzwiller-projected wave function. Within this approximation, at small hole doping near half-filling, the normal state favors staggered-flux ordering. Such a staggered-flux state may occur in vortex cores of underdoped high-temperature cuprate superconductors. From comparing the energies of the staggered-flux state and of the superconducting state, we numerically obtain the condensation energy. Extracting the superfluid density directly from the projected superconducting wave function, we can also estimate the coherence length at zero temperature.
We calculate the energy of flux states described by Slater determinants of single-particle levels in a uniform magnetic field with p/q flux quanta per plaquette and with no double occupancy. We find the exchange energy of flux states is lower than that of the Gutzwiller wave function by 10%--20%. The minimum kinetic energy is obtained by introducing phases associated with the holes. The phases are calculated by mapping onto a classical frustrated XY model. At 10% doping, the 1/2 flux state (\ensuremath{\pi} phase) is stabilized for the parameter regime J/t\ensuremath{\gtrsim}0.2. At about 20% doping, the time-reversal-breaking (1/3 flux state has the lowest energy for J/t\ensuremath{\gtrsim}1.0.
The stability of a staggered flux (SF) or d-density wave state is studied in a d-p model using a variational Monte Carlo (VMC) method. This state possesses a local circular current and possibly causes the pseudogap phase in high-Tc cuprate superconductors. We introduce into the trial function a configuration dependent phase factor, which was recently shown to be indispensable to stabilize current-carrying states. We pay attention to the energy gain as a function of adjacent O-O hopping and Cu-site coulomb repulsion U. It is found the SF state becomes stable for hole doping rates of and , owing to the reduction in kinetic energy, but seems fragile because the energy gain rapidly decays on doping holes for any . The loop current tends to increase as increases.