Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Abstract

We show that fermion charge fractionalization can take place in a recently proposed chiral gauge model for graphene even in the absence of Kekulé distortion in the graphene honeycomb lattice. In this model, electrons couple in a chiral way to a pseudomagnetic field with a vortex profile in such a way that it can be used to describe the influences of topological defects, such as disclinations, on the electronic states. We also extend the model by adding the coupling of fermions to an external magnetic field and show that the fermion charge can be fractionalized by means of only gauge potentials. It is shown that the chiral fermion charge can also have fractional value. We also relate the fractionalization of the fermion charge to the parity anomaly in an extended quantum electrodynamics, which involves vector and axial-vector gauge fields.

Induced fractional valley number in graphene with topological defects

“…We have also wondered if similar effects could also take place in strained samples of graphene under microstresses, as those reported in [10] where uniform (pseudo)magnetic fields up to 300T seems to be realized. In view of the results in [25], we conclude that particles associated to the different valleys would describe orbits with different cyclotron frequencies, namely ω ± = |eB ± B A | /2 and each Landau level, say √ 2eBn, is split in two levels with energies |eB + B A | n and |eB − B A | n, each one contains representative of only one of the valleys. The zero-energy level still persists with representatives of both valleys, but since they have different cyclotron frequencies, there will be an induced valley number given by N v = ±Φ/2π (the ambiguity of the sign is attributed to the zero-energy particles be assigned to the valence or to the conduction band), which is no longer fractional, neither is finite once the pseudomagnetic field is uniform and the sample is taken to be infinitely…”

“…Motivated by many of the works cited above, we have shown [25] that vector and axialvector gauge potentials by themselves can bind zero-energy electrons and that fractional charge may be induced even in the absence of Kekulé distortions. In this vein, we have also discussed the relation of such induced fractional charge to the parity anomaly which would be realized in gapped graphene as proposed almost thirty years ago [3] and in gapped graphene whose parity symmetry breaking term is provided by the Haldane energy [26].…”

Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

“…Nontrivial topological properties of space-time/gauge field lead to appearance of fermion zero modes [24]. In turn, this may cause induced vacuum fermion current [8,[25][26][27][28]. Recently, in [25], the effect of vacuum polarization in the field of a solenoid at distances much larger than its radius was investigated.…”

“…This equation is obtained by linearizing the energy as a function of a momentum near Dirac points. The topological properties in this framework were accounted for in [27,29,30].…”

Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''

“…In that section, the authors analyzed the topological response generated by one-loop radiative corrections to the two-point function of the gauge and DKP fields in 2 + 1 dimensions. As it is known from usual QED 2+1 , such topological term -called Chern-Simons term -comes from the first-order in external momentum contribution of the vacuum polarization diagram [11]. In Physics of Condensed Matter (perhaps its most notable application), this emergent Chern-Simons theory naturally leads to the transverse conductivity observed from the Hall effect.…”