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Condensed matter is the field of Physics that combines quantum mechanics with many-body theory in order to understand the properties of matter from its microscopic components. My research is of a theoretical nature and focuses on the solution of the equations of quantum mechanics in order to understand a range of phenomena, from the properties of every-day materials to those of astrophysical objects. My work encompasses both the development of new methods and their applicaion to physical systems. Below I describe some projects in greater detail.





Anharmonic properties of periodic systems
with Prof Richard Needs and Dr Neil Drummond





This diagram shows the temperature dependence of the thermal band gap E_g of diamond, caused by electron-phonon interactions. The red curve is our theoretical prediction and the black diamonds are experimental data from Clark et al. Proc. R. Soc. London, Ser. A 277, 312 (1964).

The vibrational properties of solids are usually studied within the harmonic approximation, which is valid when the motion of the atomic nuclei is restricted to the neighbourhood of their equilibrium positions. This approximation is usually very good when investigating standard solids under normal conditions. However, for the lighter nuclei and at high temperatures, atoms explore larger regions far away from their equilibrium positions, and the harmonic approximation is no longer valid.

We have worked on a methodology to study the vibrational properties of periodic solids beyond the harmonic approximation. We map the Born-Oppenheimer energy surface on which the atoms move by a principal axes approach, and then solve the resulting equations self-consistently within a mean-field formalism. We then use the anharmonic phonon wave function for the calculation of phonon expectation values. This allows us to investigate physical properties such as the electronic band gap renormalisation due to electron-phonon coupling, or thermal expansion using the stress tensor [ PRB 87, 144302 (2013) ].





Kinetic Monte Carlo of epitaxial growth with an intermediate species
with Prof Dimitri Vvedensky and Jonathan Lloyd-Williams


The growth of crystals at high temperatures is a dynamical process which can be studied by means of Kinetic Monte Carlo (KMC), a stochastic method for the time-evolution of discrete components. Normal crystals grow directly from the independent components which are deposited on the substrate, but experiments on graphene growth suggest that for graphene an intermediate cluster of carbon atoms is formed before joining the growing crystal. We have extendend the KMC formalism to include an intermediate polyatomic species, and we have shown how the growth dynamics can be dominated by it [ PRB 85, 161402(R) (2012) ].




The first four diagrams represent the equilibrium distribution of islands from a KMC simulation with increasing bonding energy between components. The last diagram is an experimental picture of epitaxial graphene islands from Loginova et al. New J. Phys. 10, 093026 (2008).





Basis sets for first-principles calculations
with Prof Peter D. Haynes


First-principles calculations in condensed matter are calculations that attempt to investigate the properties of systems by solving the corresponding equations of Quantum Mechanics. Within Quantum Theory, the wavefunction plays a central role, as it contains all the physical information about the system. When attempting to solve these equations numerically, the wavefunction is represented in terms of a basis of functions with some nice properties, for example the existence of some intermediate analytical results. We have investigated a basis set of truncated spherical waves first proposed by P.D. Haynes and M.C. Payne, and we have presented some analytical results for several matrix elements [ J. Phys. A: Math. Theor. 43, 465205 (2010) ].

by B. Monserrat