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arXiv:1607.02512 · Physical review. B./Physical review. B

Superconductivity from doublon condensation in the ionic Hubbard model

Abhisek Samanta, Rajdeep Sensarma

Published Dec 27, 2016• 11 citations
arXivHTMLPDF

Abstract

In the ionic Hubbard model, the on-site repulsion $U$, which drives a Mott insulator, and the ionic potential $V$, which drives a band insulator, compete with each other to open up a window of charge fluctuations when $U\ensuremath{\sim}V$. We study this model on square and cubic lattices in the limit of large $U$ and $V$, with $V\ensuremath{\sim}U$. Using an effective Hamiltonian and a slave-boson approach with both doublons and holons, we find that the system undergoes a phase transition as a function of $V$ from an antiferromagnetic Mott insulator to a paramagnetic insulator with strong singlet correlations, which is driven by a condensate of ``neutral'' doublon-holon pairs. On further increasing $V$, the system undergoes another phase transition to a superconducting phase driven by condensate of ``charged'' doublons and holons. The superfluid phase, characterized by the presence of a coherent (but gapped) fermionic quasiparticle and $hc/e$ flux quantization, has a high ${T}_{c}\ensuremath{\sim}t$, which shows a dome-shaped behavior as a function of $V$. The paramagnetic insulator phase has a deconfined U(1) gauge field and associated gapless photon excitations. We also discuss how these phases can be detected in the ultracold-atom context.

DOI
10.1103/physrevb.94.224517

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In the ionic Hubbard model, the on-site repulsion UUU, which drives a Mott insulator, and the ionic potential VVV, which drives a band insulator, compete with each other to open up a window of charge fluctuations when U\ensuremath∼VU\ensuremath{\sim}VU\ensuremath∼V. We study this model on square and cubic lattices in the limit of large UUU and VVV, with V\ensuremath∼UV\ensuremath{\sim}UV\ensuremath∼U. Using an effective Hamiltonian and a slave-boson approach with both doublons and holons, we find that the system undergoes a phase transition as a function of VVV from an antiferromagnetic Mott insulator to a paramagnetic insulator with strong singlet correlations, which is driven by a condensate of neutral'' doublon-holon pairs. On further increasing $V$, the system undergoes another phase transition to a superconducting phase driven by condensate of charged'' doublons and holons. The superfluid phase, characterized by the presence of a coherent (but gapped) fermionic quasiparticle and hc/ehc/ehc/e flux quantization, has a high Tc\ensuremath∼t{T}_{c}\ensuremath{\sim}tTc​\ensuremath∼t, which shows a dome-shaped behavior as a function of VVV. The paramagnetic insulator phase has a deconfined U(1) gauge field and associated gapless photon excitations. We also discuss how these phases can be detected in the ultracold-atom context.
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle-point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On a half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from a paramagnetic semimetal/metal to an antiferromagnetic-ordered Slater insulator with coherent quasiparticles at Uc1{U}_{c1}Uc1​, followed by a Mott transition into an electron-fractionalized AF∗{}^{*}∗ phase without coherent excitations at Uc2{U}_{c2}Uc2​. Such a phase structure appears to be generic for bipartite lattices without frustration. We show that doublon-holon binding unites the three important ideas of strong correlation: coherent quasiparticles, incoherent Hubbard bands, and deconfined Mott insulator.
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number (zzz) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-zzz limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the 2N2^N2N-fold degeneracy of the local moments in the insulating phase. We show that the spinons are coupled to doublons/holons by a dissipative compact U(1) gauge field that is in the deconfined phase, stabilizing the spin-charge separated gapless spin liquid Mott insulator.
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number zzz that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in 1/z1/\sqrt{z}1/z​ and becomes exact on the infinite-zzz Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard Uc{U}_{c}Uc​ and the corresponding doublon density ndc{n}_{d}^{c}ndc​, hopping ${\ensuremath{\chi}}_{d}^{c}$ and doublon-holon pairing ${\mathrm{\ensuremath{\Delta}}}_{d}^{c}$ amplitudes. We find ${U}_{c}={U}_{\mathrm{BR}}[1\ensuremath{-}2{n}_{d}^{c}\ensuremath{-}\sqrt{z}({\ensuremath{\chi}}_{d}^{c}+{\mathrm{\ensuremath{\Delta}}}_{d}^{c})]\ensuremath{\simeq}0.8{U}_{\mathrm{BR}}$, where UBR{U}_{\mathrm{BR}}UBR​ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a U(1)U(1)U(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-zzz limit and lifts the 2N{2}^{N}2N-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact U(1)U(1)U(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half-filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction UUU, we can identify a hidden critical point UMott{U}_{\mathrm{Mott}}UMott​, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of UUU), where magnetism induces a potential energy gain, and a Mott insulator (at large values of UUU), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott{U}_{\mathrm{Mott}}UMott​ has crucial consequences when doping the system: We observe a tendency for phase separation into hole-rich and hole-poor regions only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott{U}_{\mathrm{Mott}}UMott​, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott{U}_{\mathrm{Mott}}UMott​ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.
Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.