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 ${N}_{f}$ 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.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 ${N}_{f}$ 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.

arXiv:1907.11810Physical review. B./Physical review. BOct 1, 201930 citations

Spinless fermion model with quantum criticality

P. Schlottmann

Physica B Condensed MatterFeb 11, 20062 citations

Quantum Criticality of

3+1

-dimensional massless Dirac fermions

{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.