Excited spin density waves in zigzag graphene nanoribbons

Abstract

In addition to the well-known anti-ferromagnetic and ferromagnetic edge states in zigzag graphene nanoribbons (GNR), we find that there also exist some excited spin density wave (ESDW) states, the energies of which are close to the anti-ferromagnetic state (ground state). We thus argue that these ESDW states may coexist in experiment. Our numerical results from the self-consistent mean-field method as well as the first-principles calculations indicate that the allowed ESDWs are commensurate; and their dispersion curves are linear in the long wave limit. The coupling of the two edge portions in an ESDW becomes very weak in a wide GNR, in which case these ESDW portions may have different phases. Finally our calculations in the non-equilibrium Green's function theory combined with the Hubbard model show that these ESDW states can also exist in some localized (middle or terminal) region of GNR.

Topological and magnetic phase transition in silicene-like zigzag nanoribbons

“…We know that the band gap in zSiNR/zGNR result from the flat bands, which reflect the Coulomb repulsion of the edge electrons [31,35]. In a very wide zGNR, the band gap becomes small [23,24], which means the Coulomb interaction is relatively weak.…”

“…The self-consistent (SC) calculation is employed in the Hubbard system for the electron density a ( ) n k i [31,34]…”

“…So the number of spin-down electron becomes more than the spin-up electron and the system exhibit a weak FM property. Because the final steady state has a local minimum of the total energy [31], in the iteration calculation process the intersected bands will rise and fall until they merge with their respective 'same-spin' counterpart in the conduction and valence band regions ( figure 3(d)). Figure 4(d) shows the energy evolution in this iteration.…”

“…Similar edge states in graphene nanoribbons (GNR) have been deeply studied with the Hubbard model and the firstprinciples models [23][24][25][26][27][28][29][30]. Our previous study also shows there exist various excited spin density waves (ESDW) in GNR [31]. For the zSiNR, someone uses the Hubbard model to study magnetic band structures and the thermoelectric properties [32][33][34].…”

“…We find near these transitions, the energy drops suddenly and some spin bands merge after the critical field. We give a detailed explanation of these transition processes based on the principle of the local minimum of the total energy in the configuration space [31]. With a strong electric field, there exists a paramagnetic state without any magnetism.…”