Renormalised field theory for ideal molecular-beam epitaxy

• Main Author: Sherman, Edward
• Other Authors: Pruessner, Gunnar
• Published: Imperial College London 2013
• Subjects: 510
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.570065

In this thesis an overview is given of the renormalisation group as it is applied to equilibrium systems; the methods of field theory are extended to non-equilibrium systems, described by a Langevin equation in the stead of a Hamiltonian; this analysis is applied to a well known model of surface growth driven by molecular-beam epitaxy. The renormalisation group is a celebrated technique in both hard and soft condensed matter physics for probing the asymptotic behaviour of a model, though in this thesis no examination is made of quantum effects. Several distinct methods exist under the banner of renormalisation, most famously the approaches of Wilson and field theory. The renormalisation group is explored through a comparison of these approaches. The approach of field theory, with its methods being applied to an equilibrium system where a model is defined by a Hamiltonian, can be extended to analyse non-equilibrium systems, where a model is described by a Langevin equation. One class of the non-equilibrium condensed matter systems which have received extensive attention is that of surface growth. For the last two decades the Villain-Lai-Das Sarma equation has been used to understand conserved surface growth processes such as molecular-beam epitaxy. However, the theory has some aspects that seem incomplete. The mound formation observed experimentally and numerically lacks a complete theoretical narrative for its mechanism. Also, no clear picture has emerged over a disagreement in the literature about the alleged exactness of scaling relations. Using field theory to analyse the original derivation of the Villain-Lai-Das Sarma equation reveals that terms responsible for mound formation are generated under renormalisation, further these terms should have been included initially on symmetry grounds. It is possible to recover several widely studied Langevin equations at the trivial fixed point of the full theory, allowing a more complete theoretical picture to be presented for conserved epitaxial surface growth.