Santos Group Advances Frontier of Topological Phases in Graphene Superlattices

Prof. Luiz Santos and his graduate student Jian Wang have proposed a new framework for the realization of topological phase transitions in graphene superlattices. Two-dimensional superlattices, where electrons experience a long length scale periodic potential, have emerged in recent years as versatile platforms to realize exotic forms of quantum matter. A remarkable example of such electronic phases is a Hofstadter-Chern insulator, which is a bulk insulating phase of matter supporting topologically protected chiral electronic edge currents that are immune to disorder and deformations of the sample. Such electronic phases form because of a “competition” between an external magnetic field and the superlattice potential, which gives rise to fractal electronic bands. Through analytical and numerical methods, Wang and Santos have established the existence of a vast number of topological transitions between Hofstadter-Chern insulators. The researchers have shown that these transitions are tuned by changes of the superlattice in the presence of a fixed background magnetic field, establishing a surprising connection between geometrical effects of the lattice and the topological response of the electrons. Wang and Santos showed that the system is very susceptible to a topological transition when it is in the vicinity of van Hove singularities (spikes in the density of states), and, that the topological changes induced by the superlattice manifest through the onset of exotic Dirac fermions and large changes in quantized conductance. This research opens a new venue for the exploration of entangled electronic states that may serve as quantum information building blocks.

Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices, Jian Wang and Luiz H. Santos, Phys. Rev. Lett. 125, 236805 (2020). DOI:

The research has been published in Physical Review Letters and has been featured in the Physics ViewPoint section of APS. Physics ViewPoint: Topological Phases Beyond the Hofstadter Butterfly, Vidar Gudmundsson, Physics 13, 187 (2020).

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