Anomalous criticality near semimetal-to-superfluid quantum phase transition in a two-dimensional Dirac cone model

Abstract

We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power-law scaling with anomalous scaling dimensions. The quasi-particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length turns out to be infinite everywhere in the semimetallic ground state.

8 pages, 2 figures, typos corrected

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• The electronic properties of graphene
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum critical transport in clean graphene
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Renormalization group theory of nematic ordering in d-wave superconductors
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Cited by in corpus (4)

• Functional renormalization group approach to correlated fermion systems
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals
• Fluctuation effects at the onset of $2{\mathbf{k}}_{\mathbf{F}}$ density wave order with two pairs of hot spots in two-dimensional metals