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arXiv:0810.0738 · Physical Review Letters

Supersolid Phases of a Doped Valence-Bond Quantum Antiferromagnet: Evidence for a Coexisting Superconducting Order Parameter

Marcin Raczkowski, Didier Poilblanc

Published Jul 6, 2009• 10 citations
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Abstract

Motivated by numerical evidence of the valence-bond ground state of the two-dimensional Heisenberg pyrochlore lattice, we argue using a t-J model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-Tc cuprates as well as possible relevance to frustrated noncuprate superconductors such as spinels and pyrochlores is discussed.

DOI
10.1103/physrevlett.103.027001

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Motivated by numerical evidence of the valence-bond ground state of the two-dimensional Heisenberg pyrochlore lattice, we argue using a t-J model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-Tc cuprates as well as possible relevance to frustrated noncuprate superconductors such as spinels and pyrochlores is discussed.
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Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.
Motivated by the recently observed pattern of unidirectional domains in high-Tc{T}_{c}Tc​ superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the ddd-wave superconducting resonating valence bond phase using the ttt-JJJ model at x=1∕8x=1∕8x=1∕8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axes, leading to modulated superconductivity with out-of-phase ddd-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations reveal that the energies of modulated and uniform phases are very close to each other.
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