Research interests

I have a broad interest in the theory of strong correlations in condensed matter systems, but my research mostly focusses on strongly correlated itinerant electron systems (i.e. metals). This is a very exciting field; many of the most pressing questions in condensed matter physics have such a system at their foundation. Some of these questions related to practical applications, such as the use of transition-metal-dichalcogenide materials in new technologies – others pertain to fundamental theory, offering insights into such topics as emergence and non-quasiparticle field theory. I use a number of quantum-field-theoretic techniques to study various metals.

During my PhD, I spent roughly half of my time studying metallic quantum critical points, i.e. points in a metal’s zero-temperature phase diagram at which a second-order phase transition occurs. When this transition is from the disordered metallic (Fermi-liquid) state into an ordered phase, a new disordered state called a non-Fermi liquid may occur at and near the critical point. Non-Fermi liquids, characterized by very strong correlations and the absence of coherent quasiparticle excitations, are notoriously difficult to understand theoretically (particularly in two spatial dimensions). Achieving this understanding is a major goal of the condensed matter community, however; it would give insight into various other important phenomena like high-temperature superconductivity, and could lead to various formal developments in field theory. In my PhD I attempted to develop more robustly predictive approaches to studying certain idealized models of non-Fermi liquids, with the hope that they may be applied to more realistic systems in the future.

The other half of my PhD was devoted to studying the ordered phases adopted by certain models of metals, and it is to this topic that I give the majority of my current research time. Given a microscopic model of electrons hopping and interacting on a lattice, it is often highly non-trivial to accurately predict the behaviour of the low-energy effective field theory. One theoretical tool for doing so is the renormalization group, which starts at the bare, high-energy lattice model and sequentially re-introduces degrees of freedom in order of decreasing energy, thereby allowing the development of ordering instabilities to be studied in a controlled fashion. There are in fact many renormalization-group methods, one of which – the truncated-unity functional renormalization group (TUFRG) – is particularly suited to finite-density fermionic systems at weak coupling. I use TUFRG to gain understanding of particular materials, with the aim of explaining experimental observations. One such material is monolayer vanadium diselenide, which features a charge-density-wave state whose origin and wavevector are the subject of much debate.

In this PostDoc I intend to apply TUFRG to a wide range of materials, particularly those featuring exotic correlated phenomena that defy our current methods. This will involve producing robust theoretical explanations (with clear microscopic foundations) of experimental observations, but would also hopefully entail some qualitative (and even quantitative!) predictions that could be tested by experiment. TUFRG is a very powerful tool, and has much potential to do this; however, it will likely also be necessary to sometimes use methods that go beyond TUFRG’s approximations. Efficient incorporation of electron self-energies, as well as electron-phonon interactions, is an active field of research, and I hope use my experience in other field-theoretic techniques to contribute to it.

Educational and professional record

• 2026-present: postdoctoral research position at the University of St Andrews.
• 2021-2025: PhD in theoretical condensed matter physics at the University of St Andrews. Conducted under Chris Hooley and Bernd Braunecker.
• 2020-2021: MSc in Mathematical and Theoretical Physics at the University of Oxford.
• 2016-2020: BSc in Physics and Mathematical Sciences at University College Cork.

Awards

• One of two research awards for “Best publication of the Year involving an Undergraduate student as an author”, University College Cork, 2021.
• A Hamilton Prize in mathematics, Royal Irish Academy, 2019.
• A Quercus entrance scholarship, University College Cork, 2016.

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