**Electronic Structure and Topological Quantum Phase Transitions in Strained Graphene Nanoribbons**

Fanyao Qu, Ginetom S. Diniz and Marcos R. Guassi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64493

#### **Abstract**

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e2011-20384-6

56 Recent Advances in Graphene Research

2009.09.028

2013.1039

1763. DOI: 10.1143/JPSJ.69.1757

10.1016/j.ssc.2009.02.053

10.1007/978-3-662-02753-0

DOI: 10.1038/nmat3245

In this chapter, we discuss the new classes of matter, such as the quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states, that have been theoretically predicted and experimentally observed in graphene and beyond graphene systems. We further demonstrate how to manipulate these states using mechanical strain, internal exchange field, and spin‐orbit couplings (SOC). Spin‐charge transport in strained graphene nanoribbons is also discussed assuming the system in the QAH phase, exploring the prospects of topological devices with dissipationless edge currents. A remarkable zero‐field topological quantum phase transition between the time‐reversal‐ symmetry‐broken QSH and quantum anomalous Hall states is predicted, which was previously thought to take place only in the presence of external magnetic field. In our proposal, we show as the intrinsic SOC is tuned, how it is possible to two different helicity edge states located in the opposite edges of the graphene nanoribbons exchange their locations. Our results indicate that the strain‐induced pseudomagnetic field could be coupled to the spin degrees of freedom through the SOC responsible for the stability of a QSH state. The controllability of this zero‐field phase transition with strength and direction of the strain is also explored as additional phase‐tuning parameter. Our results present prospect of strain, electric and magnetic manipulation of the QSH, and QAH effect in these novel two‐dimensional (2D) materials.

**Keywords:** Graphene, graphene nanoribbon, quantum spin Hall, quantum anomalous Hall, topological insulator, 2D materials, strain
