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arXiv:cond-mat/0702118 · Physical Review Letters

Quantum Phases in a Doped Mott Insulator on the Shastry-Sutherland Lattice

Jun Liu, Nandini Trivedi, Yongbin Lee, Bruce N. Harmon, Jörg Schmalian

Published Nov 30, 2007• 23 citations
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Abstract

We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.

DOI
10.1103/physrevlett.99.227003

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We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.
We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the S=1∕2S=1∕2S=1∕2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a ddd-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.
Motivated by recent experiments on SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​, we investigate the ground states of the doped Mott insulator on the Shastry-Sutherland lattice. To provide a unified theoretical framework for both the valence-bond solid state found in undoped SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ and the doped counterpart being pursued in on-going experiments, we analyze the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model via the bond-operator formulation. It is found that superconducting states emerge upon doping with their properties crucially depending on the underlying valence-bond order. Implications to future experiments are discussed.
We study possible paramagnetic phases of antiferromagnets on the Shastry-Sutherland lattice by a gauge-theoretic analysis of fluctuations in a theory with Sp(2N)\mathrm{Sp}(2N)Sp(2N) symmetry. In addition to the familiar dimer phase, we find a confining phase with plaquette order and a topologically ordered phase with deconfined S=1/2S=1/2S=1/2 spinons and helical spin correlations. The deconfined phase is contiguous to the dimer phase and in a regime of couplings close to those found in the insulator SrCu2(BO3)2.{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}.SrCu2​(BO3​)2​. We suggest that a superconductor obtained by doping this insulator with mobile charge carriers will be an attractive candidate for observing the anomalous magnetic flux properties associated with topological order.
We define a suitable quantity Zc{Z}_{c}Zc​ that measures the pairing strength of two electrons added to the ground-state wave function by means of the anomalous part of the one-particle Green's function. Zc{Z}_{c}Zc​ discriminates between systems described by one-electron states, like ordinary metals and band insulators, for which Zc=0{Z}_{c}=0Zc​=0, and systems where the single particle picture does not hold, like superconductors and resonating valence bond insulators, for which ${Z}_{c}\ensuremath{\ne}0$. By using a quantum Monte Carlo projection technique for the Hubbard model at U∕t=4U∕t=4U∕t=4, a finite Zc{Z}_{c}Zc​, with ddd-wave symmetry, is found at half filling and in the lightly doped regime, thus emphasizing a qualitatively new feature coming from electronic correlation.
A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t–J model, just as a BCS state satisfies the Fermi–Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fractionalization with neutral spinons and 'backflow' spinons forming a two-component RVB structure. While the former spinon is bosonic, originating from the superexchange correlation, the latter spinon is found to be fermionic, accompanying the hopping of bosonic holons. The low-lying emergent gauge fields associated with such a specific fractionalization are of mutual Chern–Simons type. Corresponding to this superconducting ground state, three types of elementary excitations are identified. Among them a Bogoliubov nodal quasiparticle is conventional, while the other two are neutral excitations of non-BCS type that play crucial roles in higher-energy/temperature regimes. Their unique experimental implications for the cuprates are briefly discussed.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion UUU from a Gossamer superconductor at small UUU. At the critical value U=UcU={U}_{c}U=Uc​, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>UcU>{U}_{c}U>Uc​ to a Gossamer SC state at U<UcU<{U}_{c}U<Uc​ at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.