A group of Lancaster Undergraduates have discovered a new type of symmetry in topological insulators called nonsymmorphic chiral symmetry. Becky Allen, Holly Gibbons, Alex Sherlock and Harvey Stanfield undertook their research during third-year Theoretical Physics Group Projects and have published their work in the journal Physical Review B. This new symmetry has consequences for the properties of topological insulators.

A topological insulator is a new state of matter, widely studied over the last 15 years, which behaves as an insulator except for the presence of metallic states at its edges. Such edge states have the potential for holding information as a quantum bit, or qubit, in topological quantum information processing.

In one dimension, topological insulators require the presence of chiral symmetry which is alternatively called sublattice symmetry because it may be realised in a solid with a periodic arrangement of two types of atoms and, hence, two sublattices. Becky, Holly, Alex and Harvey found a topological insulator that has nonsymmorphic chiral symmetry – meaning the chiral symmetry consists of the usual sublattice symmetry combined with a translation of the lattice. This unusual feature has repercussions for the existence of metallic edge states, and their paper details conditions under which metallic states can exist on solitons, a certain type of domain wall, and whether the resulting qubits are stable in the presence of perturbations.

Alex said, “The Theoretical Group Project module here at Lancaster gave us the opportunity to work together on a particular problem in physics. We worked as a team on a particularly new area of physics, that of topological insulators, under the supervision of a lecturer who specialises in the field. Our project made use of extremely new research, and to that end, we were able to build on some of the contemporary models and theories. Our work during the module culminated in a publication to the journal Physical Review B, as a contribution to the rapidly-developing field of research.”

In the Department of Physics at Lancaster University, undergraduate students take a succession of projects, with third-year group projects following a computer project in second year. Students on the MPhys/MSci programmes also take an individually supervised research project in their final year.

In third-year Theoretical Physics Group Projects, students work as part of a team of four or five. There is a strong emphasis on an open-ended investigation, so the projects aren’t tightly restrained by defined limits, and students have to make decisions about the direction of their research. Recently, projects have covered a range of topics including using cellular automata for modelling the spread of Covid-19, machine learning, simulating quantum computers, chaos and topology.

The project supervisor, Ed McCann, said “In these projects, students get their first taste of open-ended research. Their enthusiasm is infectious, and it never fails to surprise me how far a group can progress with their research by supporting each other and working together. Becky, Holly, Alex and Harvey are a great example of this, and it’s wonderful that they’ve published the results of their work.”