Chemical-potential flow equations for graphene with Coulomb interactions

Abstract

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results confirm that the charge carrier density dependence of the Fermi velocity is negligible, validating the comparison of the fRG calculation at zero density of Bauer et al., Phys. Rev. B 92, 121409 (2015) with the experiment of Elias et al., Nat. Phys. 7, 701 (2011).

New point-like sources and a conducting surface in Maxwell–Chern–Simons electrodynamics

“…Theoretical aspects of Maxwell-Chern-Simons electrodynamics have been investigated in Casimir effect [4][5][6][7][8][9], quantum dissipation of harmonic systems [10], quantum electrodynamics (QED 3 ) [11][12][13][14][15], dynamical mass generation [16,17], condensed matter physics (see, for instance, Ref. [18] and references therein), description of graphene properties [19][20][21][22][23][24], noncommutativity [25][26][27][28], strings theory [29], dynamics of vortices [30,31], and with a planar boundary [32][33][34][35][36], to mention just a few. In fact, there is a vast literature concerning this model.…”

Incompressible even denominator fractional quantum Hall states in the zeroth Landau level of monolayer graphene

“…These EDFQH states had not been previously observed in monolayer graphene, although EDFQH states have been seen previously in higher Landau levels (LLs) in single-component systems at ν = 5 2 in GaAs [31], and at ν = 3 2 and 7 2 in ZnO [32]. In multi-component systems, there have been observations of EDFQH states in bilayer graphene at fractions corresponding to n = 1 orbital wavefunctions [33][34][35] and at fractions of ν = 1 2 [36-39] and 1 4 [40,41], corresponding to n = 0 orbital wavefunctions in systems with multiple layers or sub-bands.One of the distinguishing feature of the FQH effect in monolayer graphene that there are four isospin components in the zeroth LL corresponding to two valley and two spin degrees of freedom [42][43][44][45][46][47][48][49][50][51][52][53]. In addition, due to strong electronic interactions in graphene (such as onsite Hubbard repulsion), these states cannot be assumed to be spin polarized.…”

“…Investigation of the excitation spectra for different possible states might also provide ways to discriminate between different orders. The recent construction of a multicomponent Abelian Chern-Simons theory in a functional integral approach is a promising step in this direction [50].…”

“…One of the distinguishing feature of the FQH effect in monolayer graphene that there are four isospin components in the zeroth LL corresponding to two valley and two spin degrees of freedom [42][43][44][45][46][47][48][49][50][51][52][53]. In addition, due to strong electronic interactions in graphene (such as onsite Hubbard repulsion), these states cannot be assumed to be spin polarized.…”

Collective excitations of fractional quantum Hall states in monolayer graphene

“…The fractional quantum Hall effect (FQHE) has also been observed in graphene [4,[8][9][10][25][26][27] and some experiments have revealed an unusual pattern of fractions that follows the standard composite fermion sequence between filling factors ν = 0 and ν = 1 but involves only even-numerator fractions between ν = 1 and ν = 2 [10]. Theoretically, the FQHE in graphene has attracted considerable interest [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. In particular, Refs.…”