Electron-electron interactions and topology in the electronic properties of gated graphene nanoribbon rings in Möbius and cylindrical configurations

Abstract

We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Möbius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Möbius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings.

Wigner crystallization at graphene edges

“…In our case, this means that for N = 15, the total spin is S max = 15/2. However, away from charge neutrality, correlation effects are expected to strongly affect the magnetization [36]. In Fig.…”

“…In order to model the interaction effects at the zigzag edges, we start with a graphene ribbon with a periodic boundary condition [36], consisting of N a = 1456 atoms, with a length of L = 12.8 nm and a width of W = 2.9 nm. This gives a total of n s = 30 edge states [see Fig.…”

“…In particular, room-temperature magnetic properties of the zigzag edge state in graphene nanoribbons were recently investigated experimentally [42]. However, for the design of carbon-based next-generation devices such as nanoribbons [29][30][31][32][33][34][35][36] and quantum dots [37][38][39][40][41], an in-depth understanding of Wigner crystallization at graphene edges is necessary and a focused investigation of the liquid to crystal crossover is lacking.…”

“…Electrons populating these edge states constitute a particularly interesting many-body system since their relative kinetic energy is close to zero, thus the properties are dominated by Coulomb interactions. So far, most of the previous literature on interaction effects due to edge states in various graphene systems focused on magnetic properties [28][29][30][31][32][33][34][35][36][37][38][39][40][41]. In particular, room-temperature magnetic properties of the zigzag edge state in graphene nanoribbons were recently investigated experimentally [42].…”

Electronic and Magnetic Properties of Graphene M?bius Strips: Density Functional Theory Approach

“…Topological insulators have remarkable physical properties and have potential applications in quantum computing and spintronics [18]. The effect of Möbius topology on the electronics properties of graphene nanoribbon rings has been studied [19]. Also, the effect of twisted angle on the electronic and magnetic properties of Möbius strips has been reported [20].…”