Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

Abstract

Among many remarkable qualities of graphene, its electronic properties attract particular interest due to a massless chiral character of charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no carriers and the half-integer quantum Hall effect (QHE) observable even at room temperature [1-3]. 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 ~10% [9-11]. 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 pseudo-magnetic QHE. We also show that strained superlattices can be used to open significant energy gaps in graphene's electronic spectrum.If a mechanical strain Δ varies smoothly on the scale of interatomic distances, it does not break the sublattice symmetry but rather deforms the Brillouin zone in such a way that the Dirac cones located in graphene at points K and K' are shifted in the opposite directions [2]. This is reminiscent of the effect induced on charge carriers by magnetic field B applied perpendicular to the graphene plane [2,[12][13][14]. The strain-induced, pseudo-magnetic field B S or, more generally, gauge field vector potential A have opposite signs for graphene's two valleys K and K', which means that elastic deformations, unlike magnetic field, do not violate the time-reversal symmetry of a crystal as a whole [12][13][14]21,22].Based on this analogy between strain and magnetic field, we ask the following question: Is it possible to create such a distribution of strain that it results in a strong uniform pseudo-field B S and, accordingly, leads to a "pseudo-QHE" observable in zero B? The previous attempts to engineer energy gaps by applying strain [5][6][7] seem to suggest a negative answer. Indeed, the hexagonal symmetry of the graphene lattice generally implies a highly anisotropic distribution of B S [21,22]. Therefore, the strain is expected to contribute primarily in the phenomena that do not average out in a random magnetic field such as weak localization [13,14]. Furthermore, a strong gauge field necessitates the opening of energy gaps due to Landau quantization, δE ≈ 400K B ⋅ (>0.1 eV for B S =10T) whereas no gaps were theoretically found for uniaxial strain as large as ≈25% [4]. The only way to induce significant gaps, ...

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