Dynamical fermion mass generation and exciton spectra in graphene

Abstract

The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than the width of dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.

Absence of dynamical gap generation in suspended graphene

“…For these reasons, the dynamical gap generation and the resultant semimetal-insulator transition have attracted intense theoretical interest in recent years. Many analytical and computational tools, including the Dyson-Schwinger (DS) gap equation [19][20][21][22][23][24][25][26][27][28][29], the Bethe-Salpeter equation [30,31], renormalization group (RG) [32][33][34] and large-scale Monte Carlo simulation [35][36][37][38][39][40], have been applied to study this problem. A critical interaction strength α c and a critical fermion flavor N c are found in almost all these investigations: a dynamical gap is opened only when α > α c and N < N c .…”

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

“…(44), (68), (69), and (70), respectively. In the RG schemes 2, 3, and 4, the fermion self-energy can still be written as Eq.…”

“…Because different RG schemes might give rise to unidentical results [49,50], we feel it helpful to revisit the effect of Coulomb interaction by employing the four RG schemes defined by Eq. (44), and (68), (69), and (70) respectively. Detailed analytic calculations lead us to…”

“…Since Nambu and Jona-Lasinio [68], the DS equation approach has been widely applied to study DCSB in QCD [123,124] and QED 3 [125][126][127][128][129][130][131]. It also has been used to examine whether an excitonic gap can be dynamically generated by the Coulomb interaction in graphene [65,[69][70][71][72][73][74][75][76][77][78][79][80][81][82][83] and other closely related materials [41,46,82]. The role played by the DS equation in the studies of excitonic gap generation is similar to that played by the gap equation in the studies of the formation of superconductivity in BCS theory.…”

“…If the ground state of suspended graphene is an excitonic insulator, there would be more practical applications of graphene in the design of electronic devies [5,66]. From a theoretic point of view, this provides an ideal laboratory to test some important concepts of high energy physics [69], and also gives us a nice platform to study the rich quantum critical phenomena.…”