Uryszek, MD; Christou, E; Jaefari, A; Krüger, F; Uchoa, B; (2019) Quantum criticality of semi-Dirac fermions in 2 + 1 dimensions. Physical Review B , 100 (15) 10.1103/PhysRevB.100.155101.

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Abstract

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions toward charge and spin density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell renormalization group. We generalize to a large number Nf of fermion flavors to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including 1/Nf corrections. The latter depend on the specific form of the bosonic infrared propagator in 2+1 dimensions, which needs to be included to regularize divergencies. The 1/Nf corrections are surprisingly small, suggesting that the expansion is well controlled in the physical dimension. The order parameter correlations inherit the electronic anisotropy of the semi-Dirac fermions, leading to correlation lengths that diverge along the spatial directions with distinct exponents, even at the mean-field level. We conjecture that the proximity to the critical point may stabilize novel modulated order phases.

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