Curved space acts as gauge field in graphene

a, Distortion of a graphene disc which is required to generate uniform B_S. The original shape is shown in blue. b, Orientation of the graphene crystal lattice with respect to the strain. Graphene is stretched or compressed along equivalent crystallographic directions 100. Two graphene sublattices are shown in red and green. c, Distribution of the forces applied at the disc’s perimeter (arrows) that would create the strain required in a. The uniform colour inside the disc indicates strictly uniform pseudomagnetic field. d, The shown shape allows uniform B_S to be generated only by normal forces applied at the sample’s perimeter. The length of the arrows indicates the required local stress.

Among many remarkable qualities of graphene, its electronic properties attract particular interest owing to the chiral character of the charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no carriers and the half-integer quantum Hall effect observable even at room temperature^{1, 2, 3}. Because graphene is only one atom thick, it is also amenable to external influences, including mechanical deformation. The latter offers a tempting prospect of controlling graphene’s properties by strain and, recently, several reports have examined graphene under uniaxial deformation^{4, 5, 6, 7, 8}. Although the strain can induce additional Raman features^{7, 8}, no significant changes in graphene’s band structure have been either observed or expected for realistic strains of up to ~15% (refs 9, 10, 11). Here we show that a designed strain aligned along three main crystallographic directions induces strong gauge fields^{12, 13, 14} that effectively act as a uniform magnetic field exceeding 10 T. For a finite doping, the quantizing field results in an insulating bulk and a pair of countercirculating edge states, similar to the case of a topological insulator^{15, 16, 17, 18, 19, 20}. We suggest realistic ways of creating this quantum state and observing the pseudomagnetic quantum Hall effect. We also show that strained superlattices can be used to open significant energy gaps in graphene’s electronic spectrum.