arXiv:cond-mat/0509520 · Physical Review B

Magnetism and superconductivity of strongly correlated electrons on the triangular lattice

Cédric Weber, Andreas Martin Läuchli, Frédéric Mila, Thierry Giamarchi

Published Jan 20, 2006• 53 citations

Abstract

We investigate the phase diagram of the $t\text{\ensuremath{-}}J$ model on a triangular lattice using a variational Monte Carlo approach. We use an extended set of Gutzwiller projected fermionic trial wave functions allowing for simultaneous magnetic and superconducting order parameters. We obtain energies at zero doping for the spin-$1∕2$ Heisenberg model in very good agreement with the best estimates. Upon electron doping (with a hopping integral $t<0$) this phase is surprisingly stable variationally up to $n\ensuremath{\approx}1.4$, while the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ order parameter is rather weak and disappears at $n\ensuremath{\approx}1.1$. For hole doping, however, the coplanar magnetic state is almost immediately destroyed and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ superconductivity survives down to $n\ensuremath{\approx}0.8$. For lower $n$, between $0.2$ and $0.8$, we find saturated ferromagnetism. Moreover, there is evidence for a narrow spin density wave phase around $n\ensuremath{\approx}0.8$. Commensurate flux phases were also considered, but these turned out not to be competitive at finite doping.

DOI: 10.1103/physrevb.73.014519

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arXiv:cond-mat/0509520 · Physical Review B

Magnetism and superconductivity of strongly correlated electrons on the triangular lattice

Cédric Weber, Andreas Martin Läuchli, Frédéric Mila, Thierry Giamarchi

Published Jan 20, 2006• 53 citations

arXiv HTML PDF

Abstract

We investigate the phase diagram of the

t\text{\ensuremath{-}}J

model on a triangular lattice using a variational Monte Carlo approach. We use an extended set of Gutzwiller projected fermionic trial wave functions allowing for simultaneous magnetic and superconducting order parameters. We obtain energies at zero doping for the spin-

1∕2

Heisenberg model in very good agreement with the best estimates. Upon electron doping (with a hopping integral

t<0

) this phase is surprisingly stable variationally up to

n\ensuremath{\approx}1.4

, while the

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}

order parameter is rather weak and disappears at

n\ensuremath{\approx}1.1

. For hole doping, however, the coplanar magnetic state is almost immediately destroyed and

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}

superconductivity survives down to

n\ensuremath{\approx}0.8

. For lower

n

, between

0.2

and

0.8

, we find saturated ferromagnetism. Moreover, there is evidence for a narrow spin density wave phase around

n\ensuremath{\approx}0.8

. Commensurate flux phases were also considered, but these turned out not to be competitive at finite doping.

DOI: 10.1103/physrevb.73.014519

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Thierry Giamarchi, C. Lhuillier

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Physical review. B, Condensed matterJun 1, 1991167 citations

We investigate the phase diagram of the

t\text{\ensuremath{-}}J

1∕2

Heisenberg model in very good agreement with the best estimates. Upon electron doping (with a hopping integral

t<0

) this phase is surprisingly stable variationally up to

n\ensuremath{\approx}1.4

, while the

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}

order parameter is rather weak and disappears at

n\ensuremath{\approx}1.1

. For hole doping, however, the coplanar magnetic state is almost immediately destroyed and

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}

superconductivity survives down to

n\ensuremath{\approx}0.8

. For lower

n

, between

0.2

and

0.8

, we find saturated ferromagnetism. Moreover, there is evidence for a narrow spin density wave phase around

n\ensuremath{\approx}0.8

. Commensurate flux phases were also considered, but these turned out not to be competitive at finite doping.

J/t=0.4\pm0.2

K>0

and the ferromagnetic (FM) order for

K<0

, both vanish at sufficiently large doping, beyond which we find regimes with chiral

d\pm i d

singlet pairing and

p\pm ip

triplet pairing respectively. Our tensor network computations however reveal that the superconducting correlations are strongly suppressed; while FM order stubbornly persists for the doped

K<0

model, the doped

K>0

model features emergent spin-charge modulated stripe orders. At higher hole doping for

K > 0

, where AFM order is more strongly suppressed than for the electron doped case, incorporating a sufficiently strong nearest-neighbor attraction yields evidence for singlet

d

-wave superconductivity with Luttinger parameter

K_{\rm sc} < 1

. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as NaRuO

_2

which feature bond-dependent exchange interactions.