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arXiv:cond-mat/0401160 · Physical Review B

Study of the triangular lattice tV model near x=13

Olexei I. Motrunich, Patrick A. Lee

Published Jul 22, 2004• 50 citations
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Abstract

We study the extended Hubbard model on a triangular lattice near doping $x=\frac{1}{3}$, which may be relevant for the recently discovered superconductor ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}y{\mathrm{H}}_{2}\mathrm{O}$. By generalizing this model to $N$ fermionic species, we formulate a meanfield description in the limit of large $N$. In meanfield, we find two possible phases: a renormalized Fermi liquid and a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ charge density wave state. The transition between the two phases is driven by increasing the nearest-neighbor repulsion and is found to be first order for doping $x=\frac{1}{3}$, but occurs close to the point of the local instability of the uniform liquid. We also study fluctuations about the uniform meanfield state in a systematic $1∕N$ expansion, focusing on the residual interaction of quasiparticles and possible superconducting instabilities due to this interaction. Upon moving towards the charge density wave instability, the increasing charge fluctuations favor a particular $f$-wave triplet state. (This state was recently discussed by Tanaka et al., cond-mat/0311266.) We also report a direct Gutzwiller wave function study of the spin-$\frac{1}{2}$ model.

DOI
10.1103/physrevb.70.024514

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Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction UUU at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (ttt being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For U>Uc2U>{U}_{\mathrm{c}2}U>Uc2​, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For Uc1<U<Uc2{U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}Uc1​<U<Uc2​, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K\mathrm{K}K and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing UUU and thus the superconductivity is unlikely in the intermediate phase.
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