arXiv subjects

Yasufumi Araki

Publications and source records attributed to Yasufumi Araki.

39 records · Page 3Linked to original sources

arXiv2010

Chiral symmetry of graphene and strong coupling lattice gauge theory

We model the electrons on a monolayer graphene in terms of the compact and non-compact U(1) lattice gauge theories. The system is analyzed by the strong coupling expansion and is shown to be an insulator due to dynamical gap formation in/around the strong coupling limit. This is similar to the spontaneous chiral symmetry breaking in strong coupling gauge theories. The results from the compact and non-compact formulations are compared up to the next-to-leading order of the strong coupling expansion. Excitonic modes and their dispersion relations in the insulating phase are also investigated: it is found that there arises a pseudo-Nambu--Goldstone mode obeying the Gell-Mann--Oakes--Renner type formula.

cond-mat.str-el↗

arXiv2010

Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories

Due to effective enhancement of the Coulomb coupling strength in the vacuum-suspended graphene, the system may turn from a semimetal into an insulator by the formation of a gap in the fermionic spectrum. This phenomenon is analogous to the spontaneous breaking of chiral symmetry in the strong-coupling relativistic field theories. We study this "chiral symmetry breaking" and associated collective excitations on graphene in the strong coupling regime by taking U(1) lattice gauge theory as an effective model for graphene. Both compact and non-compact formulations of the U(1) gauge action show chiral symmetry breaking with equal magnitude of the chiral condensate (exciton condensate) in the strong coupling limit, while they start to deviate from the next-to-leading order in the strong coupling expansion. Phase and amplitude fluctuations of the order parameter are also investigated: in particular, a mass formula for the pseudo-Nambu--Goldstone mode ($π$-exciton), which is analogous to Gell-Mann--Oakes--Renner relation for the pion in quantum chromodynamics (QCD), is derived from the axial Ward-Takahashi identity. To check the applicability of the effective field theory description, typical energy scales of fermionic and bosonic excitations are estimated by identifying the lattice spacing of the U(1) gauge theory with that of the original honeycomb lattice of graphene.

cond-mat.str-el↗

arXiv2010

Chiral Gap and Collective Excitations in Monolayer Graphene from Strong Coupling Expansion of Lattice Gauge Theory

Using the strong coupling expansion of the compact and non-compact U(1) lattice gauge theory for monolayer graphene, we show analytically that fermion bandgap and pseudo Nambu--Goldstone exciton (pi-exciton) are dynamically generated due to chiral symmetry breaking. The mechanism is similar to the generation of quark mass and pion excitation in quantum chromodynamics (QCD). We derive a formula for the pi-exciton analogous to the Gell-Mann--Oakes--Renner (GOR) relation in QCD. Experimental confirmation of the GOR relation on a suspended monolayer graphene would be a clear evidence of chiral symmetry breaking.

cond-mat.str-el↗