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Among many remarkable qualities of graphene, its electronic propertiesattract particular interest due to a massless chiral character of chargecarriers, which leads to such unusual phenomena as metallic conductivity in thelimit of no carriers and the half-integer quantum Hall effect (QHE) observableeven at room temperature [1-3]. Because graphene is only one atom thick, it isalso amenable to external influences including mechanical deformation. Thelatter offers a tempting prospect of controlling graphene's properties bystrain and, recently, several reports have examined graphene under uniaxialdeformation [4-8]. Although the strain can induce additional Raman features[7,8], no significant changes in graphene's band structure have been eitherobserved or expected for realistic strains of approx. 10% [9-11]. Here we showthat a designed strain aligned along three main crystallographic directionsinduces strong gauge fields [12-14] that effectively act as a uniform magneticfield exceeding 10 T. For a finite doping, the quantizing field results in aninsulating bulk and a pair of countercirculating edge states, similar to thecase of a topological insulator [15-20]. We suggest realistic ways of creatingthis quantum state and observing the pseudo-magnetic QHE. We also show thatstrained superlattices can be used to open significant energy gaps ingraphene's electronic spectrum.

Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering