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arXiv · 1907.11810

Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions

Mikolaj D. Uryszek·Elliot Christou·Akbar Jaefari·Frank Krüger·Bruno Uchoa
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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 towards charge, 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 RG. We generalize to a large number $N_f$ of fermion flavors to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including $1/N_f$ 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 $1/N_f$ 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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Mikolaj D. Uryszek, Elliot Christou, Akbar Jaefari, Frank Krüger, Bruno Uchoa. 2019-07-26. Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions. https://doi.org/10.1103/physrevb.100.155101

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