Excitonic mass gap in uniaxially strained graphene

Abstract

We study the conditions for spontaneously generating an excitonic mass gap due to Coulomb interactions between anisotropic Dirac fermions in uniaxially strained graphene. The mass gap equation is realized as a self-consistent solution for the self-energy within the Hartree-Fock meanfield and static random phase approximations. It depends not only on momentum, due to the long-range nature of the interaction, but also on the velocity anisotropy caused by the presence of uniaxial strain. We solve the nonlinear integral equation self-consistently by performing large scale numerical calculations on variable grid sizes. We evaluate the mass gap at the charge neutrality (Dirac) point as a function of the dimensionless coupling constant and anisotropy parameter. We also obtain the phase diagram of the critical coupling, at which the gap becomes finite, against velocity anisotropy. Our numerical study indicates that with an increase in uniaxial strain in graphene the strength of critical coupling decreases, which suggests anisotropy supports formation of excitonic mass gap in graphene.

Multilogarithmic velocity renormalization in graphene

“…(2) previously derived by Barnes et al [25]. We note that according to Mishchenko 14 the numerical value of the two-loop coefficient is f ≈ −0.39 is reasonably close to the results of aforementioned calculations 14,17,23,25 . Note that recently Barnes et al 25 found that the three-loop coefficient f…”

“…But certain characteristics of electron-electron interactions in graphene 7 still remain unsettled, as explained below, despite many sincere attempts to unravel the significance of interaction effects [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . An important manifestation of many-body interactions in freely suspended graphene was observed in the quasiparticle velocity, v(k), which was experimentally 22 shown to acquire a logarithmic enhancement close to one of its charge neutrality (Dirac) points.…”

“…Thus, from three-loop order onwards, the higher logarithmic powers start appearing in the perturbative expansion. The numerical value of the one-loop coefficient is known to be f there exist conflicting results 14,17,23,25 . It is clear, however, that the above series in powers of logarithms cannot be resumed to a power law.…”

The recurrent relations for the electronic band structure of the multilayer graphene

“…and 12) and the following valence bands: (5.14) and Note that n-fold degeneracy of bands ε 3 c and ε 3 v begins at n ≥ 2; and (n − 1)-fold degeneracy of bands ε 4 c and ε 4 v begins at n ≥ 3. For even number of layers, and stacking AA .…”

Theory for Strained Graphene Beyond the Cauchy–Born Rule

“…So far the previously reported expressions for as a function on the strain tensor, have been derived without taking into account the effect of the relative displacement vector Δ . However, in order to gain more quantitative knowledge of the strain‐induced effects on graphene, such as optical transmittance modulation, asymmetric Klein tunneling or dynamical gap generation, it is required a precise relationship between strain and the fermion velocity anisotropy.…”