**4. Conclusion**

In summary, we have performed a systematic investigation of the effects of uniaxial strains, exchange field, staggered sublattice potential, and SOC on the electronic and transport properties of graphene and graphene nanoribbons. We have employed the tight‐binding approximation, and Green's function formalism in order to fully describe the electronic and transport properties of these interesting nanostructures.

Using an effective low energy approximation, we were able to describe the Berry curvature and the associated Chern numbers for different orientation and uniaxial strain strength, as function of exchange field interaction. The QSH–QAH phase transition associated to the tunability of Chern number for the bulk graphene displays an interesting behavior accord‐ ing to specific directions of strains: an increase in the critical exchange field *Mc* for the QAHE phase transition for *θ*=*π* / 2 as the strain modulus is enhanced, in contrast to the *θ* =0, which shows a reduction (above a limiting strain modulus of approximately *ε* =0.078) in the critical exchange field *Mc* fortheQAHE phase [32]. The investigated spin‐resolved electronic transport and LDOS of GNR devices have demonstrate that it is possible to achieve a total electron transmission suppression of specific spin specie, which can be further tailored by uniaxial tensile strain on specific directions [86]. In addition, we have implemented a formalism to describe the zero‐field topological QPT between QSH and QAH states in GNRs in the presence of internal EX, uniaxial strain, and intrinsic and Rashba SOCs [49].

Our results demonstrated in this Chapter offer the prospect to efficiently manipulate the electronic structure, transport properties, and consequently the QAHE by strain engineering of the graphene. We also envision that our work can be extended to other layered materials (for instance, transition metal dichalcogenides), with a great potential application on novel electronic devices with the focus on dissipationless charge current.
