Competition of edge effects on the electronic properties and excitonic effects in short graphene nanoribbons

Abstract

We explore the electronic properties and exciton effects in short graphene nanoribbons (SGNRs), which have two armchair edges and two zigzag edges. Our results show that both of these two types of edges have profound effects on the electronic properties and exciton effects. Both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states are alternatively changed between the bulk and the edge states as the lengths of the zigzag edges increase, due to the competition between the states of the two types of edges. The energy gaps, as a function of the lengths of the armchair edges, will then induce two kinds of trends. Furthermore, two kinds of exciton energies and exciton binding energies are found, which can be understood through the two kinds of HOMO and LUMO states in SGNRs. In addition, we find that the three triplet exciton states are not totally energy degenerate in SGNRs due to the spin-polarized states on the zigzag edges.

Role of impurities on the optical properties of rectangular graphene flakes

“…We set the on-site repulsion parameter to U = 8.29 eV for all calculations 38 . While some researchers [33][34][35]37 have used heavily screened values for U, we base our choice of this parameter on recent calculations of the Coulomb repulsion parameter in graphene 38,52,53 . The parameters we use in this article have been shown to result in a semi-metal solution for the ground state of graphene-like systems [54][55][56] , and are also similar to values used in calculations for other organic systems 49 .…”

“…While the optical properties of graphene have been extensively studied [18][19][20][21][22] including some finite size [23][24][25] and impurity [26][27][28] effects , the optical properties of finite size graphene flakes have not been, partly due to the shortcomings of mean field theory in finite systems. Previous studies 11,[29][30][31][32][33][34][35][36][37] have demonstrated that the size, shape, and the nature of the edges have an impact on the optical properties of these GFs.…”

“…Rectangular flakes inevitably contain both types of edges, and can display unique behavior due to the competition between effects associated with each kind of edge. Research on these flakes has so far been at the mean field level 35,38,39 , and there is still little understanding of the optical properties of these flakes as the size of zig-zag or armchair edges are increased.…”

Correlation effects on topological end-states in finite-size graphene nanoribbons in the GW approximation

“…In particular, graphene nanoribbons (GNRs) are of special interest since they can be synthesized with atomic precision [4][5][6][7][8][9][10][11]. The development of synthesis processes and theoretical studies [12][13][14][15] have opened new research directions where the electronic properties of GNRs can be tuned and engineered by structuring the GNRs. For instance, heterojunctions of different types of GNRs or chevron-types GNRs have prompted much interest in this field [16][17][18][19][20].…”

“…Armchair GNRs (AGNRs) are often categorized into three families, based on their specific electronic band-gap versus width dependence [12][13][14]22] and defined by N a = 3p, 3p + 1, or 3p + 2 where N a is the number of atoms across the width of the unit cells (UCs) and p is an integer. However, tightbinding (TB) and k • p approximations predict a zero bandgap (i.e.…”