The topology and robustness of two Dirac cones in S-graphene: A tight binding approach

Abstract

Present work reports an elegant method to address the emergence of two Dirac cones in a non-hexagonal graphene allotrope S-graphene (SG). We have availed nearest neighbour tight binding (NNTB) model to validate the existence of two Dirac cones reported from density functional theory (DFT) computations. Besides, the real space renormalization group (RSRG) scheme clearly reveals the key reason behind the emergence of two Dirac cones associated with the given topology. Furthermore, the robustness of these Dirac cones has been explored in terms of hopping parameters. As an important note, the Fermi velocity of the SG system (vF $$\simeq $$≃ c/80) is almost 3.75 times that of the graphene. It has been observed that the Dirac cones can be easily shifted along the symmetry lines without breaking the degeneracy. We have attained two different conditions based on the sole relations of hopping parameters and on-site energies to break the degeneracy. Further, in order to perceive the topological aspect of the system we have obtained the phase diagram and Chern number of Haldane model. This exact analytical method along with the supported DFT computation will be very effective in studying the intrinsic behaviour of the Dirac materials other than graphene.

Dirac Materials in a MatrixWay

“…Therefore, this insulating phase is distinct from the conventional insulators and we call this phase as topologically non-trivial phase. The systems with Chern numbers ±1 are sometimes referred as Chern insulators [27,34].…”

Tetragonal Silicene and Germanene Quantum Dots: Candidates for Enhanced Nonlinear Optical and Photocatalytic Activity

“…In 2012, Wang et al established the stability and electronic characteristics of the armchair and zigzag T-graphene nanoribbons . Besides, extensive research has revealed applications of T-graphene in various intriguing fields, such as in gas sensors, , hydrogen storage, , current rectification devices, and optoelectronic devices. − Similar to graphene, the hexagonal forms of Si and Ge are the next two stable candidates from the same group. − One of the major advantages of working with silicene and germanene is that considering the spin–orbit coupling effects, the zero-band-gap feature can be avoided. , Recently, the tetragonal counterparts of Si and Ge, i.e., T-Si and T-Ge, have been predicted to be stable on satisfying various stability criteria. − Contrary to planar T-graphene, T-Si and T-Ge possess semimetallic band structures with double Dirac cones. , To generate and tune the band gap in these tetragonal systems, several approaches have been taken. , Hence, relative to T-graphene, T-Si and T-Ge are expected to be better candidates for nanodevice applications.…”

Phase transitions of non-Abelian charged nodal links in a spring-mass system

“…Given these new features of non-Abelian charged degeneracies and multi-gap topological physics, a simple, intuitive, and easily tuneable, but experimentally viable system is of interest. A highlight candidate in this regard are classical spring-mass systems [38][39][40][41][42][43][44][45]. Especially because, if a spring-mass system is constituted in three-dimensional real space, it may exhibit nodal line degeneracies that can have an intricate interplay with non-Abelian charges [22,26].…”

“…Here, we predict phase transitions of multi-gap nodal lines quantified by Euler class using a class of simple and easily realizable spring-mass systems. The non-Abelian charged nodal lines are realized using phonon waves in a classical spring-mass system [38][39][40][41][42][43][44][45][68][69][70][71][72][73][74]. A unit cell of our system consists of only one mass and several springs, and the system's mechanical behavior is thus described by classical mechanical equations of motion.…”

“…A unit cell of our system consists of only one mass and several springs, and the system's mechanical behavior is thus described by classical mechanical equations of motion. Some springs concerning on-site potentials [42][43][44][45][72][73][74] eliminate the degeneracy at the Γ-point and enable a three-band nodal link. This heuristically amounts to removing the Nambu-Goldstone zero modes [37] by having different on-site potential.…”