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

Arka Bandyopadhyay,Debnarayan Jana,Sujoy Datta,Subhadip Nath,Md Mohi Uddin

doi:10.1038/s41598-020-59262-2

Arka Bandyopadhyay, Debnarayan Jana + Show 3 more

Open Access

https://doi.org/10.1038/s41598-020-59262-2

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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.

Highlights

The first experimental isolation of graphene[1] have revolutionized the field of material science in view of its intriguing electrical, mechanical and optical properties[2]
In section-III we have described an analytical description on the emergence of two Dirac cones in the irreducible Brillouin zone (IBZ) of the S-graphene
Our primary aim is to address the emergence of two Dirac cones and their robustness associated with the lattice shown in Fig. 1 keeping the topology intact

Summary

The RSRG scheme

Our primary aim is to address the emergence of two Dirac cones and their robustness associated with the lattice shown in Fig. 1 keeping the topology intact. The RSRG process has been initiated by evaluating the set of difference equations for the original lattice using Eq 1 given below. The electron’s hopping is restricted between nearest neighbour (NN) only The above relation is valid for the uniform hopping parameter of the complete system With these set of approximations we can substitute the following values to perform the decimation process. The red shaded atomic sites have further been decimated using the following difference equations (E − ε)ψa = t3ψd + tψb + tψf ,.

Emergence of two Dirac points

Dirac cone yes no yes no

Robustness of the Dirac Cones

The Topological Phase Diagram

Conclusion

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