A route to strain-engineering electron transport in graphene
Downs, Christopher Stephen Charles
Date: 7 September 2015
University of Exeter
PhD in Physics
Graphene, a single atomic layer of graphite, has many exciting electronic and mechanical properties. On a fundamental level, the quasi-relativistic behaviour of the charge carriers in graphene arises from the honeycomb-like atomic structure. Deforming the lattice changes the lengths of the carbon-carbon bonds, breaking the hopping ...
Graphene, a single atomic layer of graphite, has many exciting electronic and mechanical properties. On a fundamental level, the quasi-relativistic behaviour of the charge carriers in graphene arises from the honeycomb-like atomic structure. Deforming the lattice changes the lengths of the carbon-carbon bonds, breaking the hopping symmetry between carbon sites. Mathematically, elastic strain in a graphene membrane can be described by additional terms in the low-energy effective Hamiltonian, analogous to the vector potential of an external magnetic field. Hence, certain non-uniform strain geometries produce so-called `pseudo-magnetic fields', leading to a predicted zero-field quantum Hall effect. These fictitious magnetic fields are distinct from an external magnetic field in that they are only observed by charge carriers within the membrane, and have opposing polarity for electrons in the K and K' valleys, preserving time-reversal symmetry of the lattice as a whole. Deforming graphene in the non-uniform manner required to produce a homogeneous pseudo-magnetic field has proven to be a huge technological challenge, however, restricting experimental evidence to scanning tunnelling spectroscopy measurements on, for example, highly deformed nanobubbles formed by the thermal expansion of an epitaxially grown sheet on a platinum substrate. These results stimulated a large amount of interest in strain-engineering electron transport in graphene, partly due to the extreme magnitude of the observed pseudo-magnetic field, a direct consequence of the strain components strongly varying over the space of a few nanometres, but the formation of nanobubbles is a highly stochastic process which cannot be reliably reproduced. Subsequent research found a way to fabricate nanobubbles with a high degree of consistency, but the measurements were still limited to local-probe techniques due to the nanoscale size of the devices. As such, a method to reliably induce a homogeneous pseudo-magnetic field within a micron-sized membrane would be an attractive proposition, and is the basis for the work presented within this thesis. The non-uniform strain required precludes a simple bending or elongation of the substrate, hence a more local method is required. A novel nanostructure consisting of suspended gold beams surrounding a graphene membrane will deform upon cooling to cryogenic temperatures, and crucially, the actuation mechanism can be designed to produce any configuration of strain, including uniaxial strain, triaxial strain and a fan-shaped deformation, the latter two of which are predicted to create homogeneous pseudo-magnetic fields within a membrane. Strain patterns which are predicted to produce experimentally significant pseudo-magnetic fields (~1 T) may be generated with complex actuation beams that are physically achievable. Furthermore, the actuation mechanisms may be utilised as electrical contacts to the membrane, allowing its conductivity to be measured in the context of a two- or multi-terminal measurement, in conjunction with an external magnetic field. The design of the devices was developed using finite-element analysis, and the behaviour verified by low-temperature imaging of prototypes. While, after careful annealing, some conventional two-terminal suspended devices exhibited quantum Hall features at very low fields, the fabricated strain-inducing devices did not display pseudo-Landau quantisation, nor Landau quantisation, due to the difficulties of using current annealing to clean devices post-fabrication. The presented work, however, could pave the way towards observing signatures of pseudo-magnetic fields in a range of experimental measurements, as well as creating alternative strain geometries.
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