# Dresden 2017 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 19: Transport: Graphene and Carbon Nanostructures (jointly with DY, DS, HL, MA, O)

### HL 19.9: Vortrag

### Montag, 20. März 2017, 17:15–17:30, HSZ 204

**Interaction induced Dirac fermions from quadratic band touching in bilayer graphene** — •Thomas C. Lang^{1}, Sumiran Pujari^{2}, Ganpathy Murthy^{2}, and Ribhu K. Kaul^{2} — ^{1}Institute for Theoretical Physics, University of Innsbruck, Austria — ^{2}Department of Physics & Astronomy, University of Kentucky, Lexington, KY

We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite *U*/*t*, despite the *U*=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with *z*=1 as expected for Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and there is a finite-coupling phase transition out of this phase to a symmetry-broken state.