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Novel Quantum Criticality of Dirac Semimetals

Frank Krüger

Mardi 29 octobre 2019 à 11h
LPS, bât 510, Moyen Amphi

Nodal metals with point-like Fermi surfaces are the simplest setting to study fermionic quantum criticality. In the half-filled honeycomb lattice the low-energy quasiparticles are Dirac fermions. Strong on-site or nearest-neighbour repulsions give rise to SDW or CDW order, respectively. Interestingly, the universal critical behaviour is outside the Landau-Ginzburg-Wilson paradigm : the Wilson-Fisher fixed point is unstable, leading to a novel critical point with universal behaviour known as Gross-Neveu-Yukawa (GNY) criticality [1]. 
I will discuss the effects of a second-neighbour repulsion, which might lead to quantum anomalous Hall or quantum spin Hall states [2]. Such interaction-driven “topological Mott insulators” are found in mean-field theory [3]. We include fluctuations using an effective low-energy field theory, demonstrating that the topological states are suppressed by a charge modulated CDW3 state with a six-site unit cell. Our findings agree with numerical studies [4].
The lattice-symmetry breaking in the CDW3 state can give quasiparticles dispersing quadratically in one and linearly in the other direction. This suggests a universal behaviour distinct from GNY criticality.
We study the quantum phase transition by renormalisation group analysis in 2+1 dimensions using a large number N of fermion flavours. In the effective field theory the CDW3 order parameters couple as both conventional mass fields and emergent gauge fields, the latter being responsible for the novel criticality.

[1] I. Herbut, PRL 97, 146401(2006) ; F. Assaad & I. Herbut, PRX 3, 031010(2013)
[2] S. Raghu, X.-L. Qi, C. Honerkamp, and S.-C. Zhang, PRL 100, 156401(2008)
[3] A. Grushin, et al., PRB 87, 085136(2013) ; 
[4] M.Daghofer et al., PRB 89, 035103(2014) ; S.Capponi et al. PRB 92, 085146 ; J.Motruk et al. PRB 92, 085147 ; D.Scherer et al., PRB 92, 155137 (2015)


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