Research

My work focuses on the electronic, transport, thermodynamic, and optical properties of Dirac materials. I also work on excitonic condensation in a variety of materials.

Dirac materials

A Dirac material can be defined as any system which has a low energy effective theory which is described by a massless or massive Dirac equation. Examples include graphene (plus bilayer and multilayer graphenes), other 2D materials such as silicene or layered transition metal dichalcogenides such as MoS₂, and the surface states of 3D topological insulators. The image below shows the linear band structure of graphene, which is typical of a massless Dirac material.

My work on Dirac materials includes:

Optical properties of bilayer graphene, including single and two-photon absorption.
The role of disorder on observable properties of single- and bilayer graphene.
Electronic compressibility of single- and bilayer graphene, and 3D TI surface states.
Role of a nearly-commensurate substrate on the optical properties of single- and bilayer graphene.
Topologically protected interface modes in Dirac materials with strong spin-orbit coupling
Plasmon modes in transition metal dichalcogenides.

Excitonic condensation

A Bose-Einstein condensate occurs when there is macroscopic occupation of the ground state of a bosonic system. Electrons are fermions, but if they pair up, their bound states will behave like bosons.
In condensed matter, it is possible to design a system which has negatively charged electrons and positively charged holes in close proximity to each other. These particles then feel an attractive interaction due to the Coulomb force between them. This force can cause the electrons and holes to bind together, forming bosons (called excitons) which can then condense.
My work on this topic has covered two areas:

The role of extrinsic disorder on excitonic condensation in graphene double layers
The extension of this idea to one-dimensional systems, such as core-shell nanowires.

Topological phase transitions

Topological materials have edge states that are protected by a symmetry. The common understanding is that these edge states only appear when the bulk band gap of insulator continuously closes and then reopens in the topological phase. This assumption is important for various proposed applications of topological materials, including quantum computing.
However, we have shown that this assumption may not always be correct. Specifically, we have shown that it is possible for a discontinuous topological phase transition to occur. In other words, the edge states may appear without the bulk band gap closing.
If this is correct, it has deep implications for how we understand the behaviour of topologically protected phases.

Lateral heterostructures

One particularly interesting aspect of two-dimensional materials is what happens at the one-dimensional interface which forms when two different types of crystal are joined in the same atomic plane. Recently, chemical vapour deposition techniques have allowed the experiments to be conducted on both graphene-boron nitride heterostructures, and interfaces between different types of transition metal dichalcogenides.
If the topological properties of the two materials forming the interface are different, then there may be topologically protected interface modes that live at the junction between the two materials and may carry spin currents. I have recently worked on such systems. I am also interested in the transport and magnetic properties of graphene-BN heterostructures.