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arXiv:1708.07256 · Physical review. B./Physical review. B

Unconventional pairing symmetry of interacting Dirac fermions on a π -flux lattice

Huaiming Guo, Ehsan Khatami, Yao Wang, Thomas Devereaux, Rajiv R. P. Singh, Richard T. Scalettar

Published Apr 20, 2018• 14 citations
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Abstract

The pairing symmetry of interacting Dirac fermions on the $\ensuremath{\pi}$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The ${s}^{*}$- (i.e., extended $s$-) and $d$-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional $d{s}^{*}$-wave phase consisting of alternating stripes of ${s}^{*}$- and $d$-wave phases. A complementary mean-field analysis shows that while the ${s}^{*}$- and $d$-wave symmetries individually have nodes in the energy spectrum, the $d{s}^{*}$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral $d$-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

DOI
10.1103/physrevb.97.155146

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The pairing symmetry of interacting Dirac fermions on the \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s∗{s}^{*}s∗- (i.e., extended sss-) and ddd-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds∗d{s}^{*}ds∗-wave phase consisting of alternating stripes of s∗{s}^{*}s∗- and ddd-wave phases. A complementary mean-field analysis shows that while the s∗{s}^{*}s∗- and ddd-wave symmetries individually have nodes in the energy spectrum, the ds∗d{s}^{*}ds∗ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral ddd-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.
The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s*- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds*-wave phase consisting of alternating stripes of s*- and d-wave phases. A complementary mean-field analysis shows that while the s*- and d-wave symmetries individually have nodes in the energy spectrum, the ds* channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.
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We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s -wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.
We show the chiral d-wave RVB state on honeycomb lattice stands as a natural generalization of the staggered flux phase on square lattice. Although the state is generated from a time reversal symmetry broken mean field ansatz, it actually represents a fully symmetric spin liquid state with a positive definite wave function in the sense of Marshall sign rule for unfrustrated antiferromagnets. The evolution of the state with the parameter Δ/χΔ/χΔ/χ follows exactly the same manner as that of the staggered flux phase on square lattice. The critical pairing strength corresponding to the πππ-flux phase is found to be Δ/χ=2Δ/χ=\sqrt{2}Δ/χ=2​. As a result of the geometric frustration between neighboring plaquette on honeycomb lattice, a direct generalization of the U(1) staggered flux pattern on square lattice to honeycomb lattice is impossible. Replacing it is the chiral d-wave state with Z2Z_{2}Z2​ gauge structure. However, this Z2Z_{2}Z2​ gauge structure is found to be ineffective after Gutzwiller projection and the system does not support topological degeneracy. The chiral d-wave RVB state is also found to be a rather good variational state for the Heisenberg model on honeycomb lattice. The spin correlation of the chiral d-wave state is found to be greatly enhanced as compared to the mean field prediction.
The effect of electron-phonon coupling on Dirac fermions was recently explored numerically on a honeycomb lattice, leading to precise quantitative values for the finite temperature and quantum critical points. In this paper, we use the unbiased determinant quantum Monte Carlo method to study the Holstein model on a half-filled staggered-flux square lattice and compare the results with the honeycomb lattice geometry, presenting results for a range of phonon frequencies $0.1\ensuremath{\leqslant}\ensuremath{\omega}\ensuremath{\leqslant}2.0$. We find that the interactions give rise to charge density wave order, but only above a finite coupling strength ${\ensuremath{\lambda}}_{\mathrm{crit}}$. The transition temperature is evaluated and presented in a ${T}_{c}\text{\ensuremath{-}}\ensuremath{\lambda}$ phase diagram. An accompanying mean-field theory calculation also predicts the existence of a quantum phase transition, but at a substantially smaller coupling strength.
We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components N=8N=8N=8 in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a ddd-wave pairing field, inducing Dirac cones in the single-particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, which is the canonical model for graphene, despite the unit cells being apparently different (e.g., they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting NNN and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the N=8N=8N=8 chiral Heisenberg universality class are $\ensuremath{\nu}=1.05(5)$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}=0.75(4)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.23(4)$, which are compared with the previous numerical estimations.