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arXiv:1606.04129 · Physical review. B./Physical review. B

d -wave superconductivity in boson+fermion dimer models

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Published May 18, 2017• 8 citations
arXivHTMLPDF

Abstract

We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk et al. [Proc. Natl. Acad. Sci. USA 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge $e$ fermion pockets whose total area is equal to the hole doping $p$ for a range of parameters consistent with the $t\ensuremath{-}J$ model for high-temperature superconductivity. Here we find that the dimers are unstable to $d$-wave superconductivity at low temperatures. The region of the phase diagram with $d$-wave rather than $s$-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.

DOI
10.1103/physrevb.95.174511

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We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk et al. [Proc. Natl. Acad. Sci. USA 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge eee fermion pockets whose total area is equal to the hole doping ppp for a range of parameters consistent with the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model for high-temperature superconductivity. Here we find that the dimers are unstable to ddd-wave superconductivity at low temperatures. The region of the phase diagram with ddd-wave rather than sss-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.
We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.
Two of the iconic phases of the hole-doped cuprate materials are the intermediate temperature pseudogap metal and the lower temperature ddd-wave superconductor. Following the suggestion of P. W. Anderson, there were early theories of these phases as doped quantum spin liquids. However, these theories have had difficulties with two prominent observations: (i) angle-dependent magnetoresistance measurements (ADMR) in the pseudogap metal, including observation of the Yamaji effect, present convincing evidence of small hole pockets which can tunnel coherently between square lattice layers (Fang et al., Nature Physics 18, 558 (2022); Chan et al., Nature Physics 21, 1753 (2025)) and (ii) the velocities of the nodal Bogoliubov quasiparticles in the ddd-wave superconductor are highly anisotropic, with vF≫vΔv_F \gg v_ΔvF​≫vΔ​ (Chiao et al., Phys. Rev. B 62, 3554 (2000)). These notes review how the fractionalized Fermi Liquid (FL*) state, which dopes quantum spin liquids with gauge-neutral electron-like quasiparticles, resolves both difficulties. Theories of insulating quantum spin liquids employing fractionalization of the electron spin into bosonic or fermionic partons are discussed. Doping the bosonic parton theory leads to a holon metal theory: while not appropriate for the cuprate pseudogap, this theory is argued to apply to ultracold atom experiments on the Lieb lattice. Doping the fermionic parton theory leads to a ddd-wave superconductor with nearly isotropic quasiparticle velocities. The construction of the FL* state in a single band Hubbard-type model is described using a quantum dimer model, followed by a more realistic description using the Ancilla Layer Model (ALM), which is then used to obtain the theory of the pseudogap and the ddd-wave superconductor. The ALM also leads to a wavefunction for the FL* state of the Hubbard model, which agrees with ultracold atom observations.
We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. We argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the ddd-wave superconducting pairing amplitude when antiferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.
We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates. The model contains bosonic dimers, representing a spin-singlet valence bond between a pair of electrons, and fermionic dimers, representing a quasiparticle with spin-1/2 and charge +e+e+e. By density matrix renormalization group calculations on a long but finite cylinder, we obtain the ground-state density distribution of the fermionic dimers for a number of different total densities. From the Friedel oscillations at open boundaries, we deduce that the Fermi surface consists of small hole pockets near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$, and this feature persists up to a doping density of 1/16. We also compute the entanglement entropy and find that it closely matches the sum of the entanglement entropies of a critical boson and a low density of free fermions. Our results support the existence of a fractionalized Fermi liquid in this model.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
We study the phases of doped spin S=1∕2S=1∕2S=1∕2 quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0S=0S=0 sector. We extend the dimer model to include fermionic S=1∕2S=1∕2S=1∕2 excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the S=0S=0S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1S=1S=1 excitations and their coupling to superflow and density-wave fluctuations.