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arXiv:1809.07903 · Physical Review Letters

Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons

Chuang Chen, Xiao Yan Xu, Zi Yang Meng, Martin Hohenadler

Published Feb 19, 2019• 75 citations
arXivHTMLPDF

Abstract

The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.

DOI
10.1103/physrevlett.122.077601

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We study the boundary criticality for the Gross-Neveu-Yukawa (GNY) models. Employing interacting Dirac fermions on a honeycomb lattice with armchair boundaries, we use determinant quantum Monte Carlo simulation to uncover rich boundary criticalities at the quantum phase transition to a charge density wave (CDW) insulator, including the ordinary, special, and extraordinary transitions. The Dirac fermions satisfy a Dirichlet boundary condition, while the boson field, representing the CDW order, obeys Dirichlet and Neumann conditions at the ordinary and special transitions, respectively, thereby enriching the critical GNY model. We develop a perturbative 4-ε renormalization group approach to compute the boundary critical exponents. Our framework generalizes to other GNY universality class variants and provides theoretical predictions for experiments.