Developing the fermionic quantum order by disorder approach to understanding novel quantum phases.

Lead Research Organisation: University College London
Department Name: London Centre for Nanotechnology


In recent years the Green group has developed a new approach to understanding how quantum fluctuations can induce new phases of electrons in solids with possibly useful properties. This approach - known as fermionic quantum order by disorder is largely analytical providing a good qualitative account of a range of quantum phenomena. Whilst analytically tractable models play an important role in the qualitative understanding of new phenomena, sometimes numerically precise predictions are needed - particularly when guiding experiment through a delicate balance of competing possibilities.
Presently, the calculation of fluctuation-induced effects, such as superconductivity, is carried out in parallel with ab initio band structure calculations; the latter providing spin susceptibilities that are used in field theoretical Eliashberg type equations. It would be appealing if these calculations could be performed in concert. QOBD suggests a natural way to do so. It sits nicely within the a framework , which places DFT, DMFT and Baym-Kadanoff theory in a unified context. Our formulation of QOBD is essentially a restriction of Baym-Kadanoff theory where the variational parameter - the Green's function - is itself characterised by a restricted set of parameters.
We aim to incorporate QOBD into DFT, enabling us to study density wave, electron nematic, and spatially modulated magnetic order, and superconductivity all within the same numerical framework. To pursue this possibility, Prof Chris Pickard (CJP Cambridge) and AGG will combine their complementary numerical and analytical skills in joint supervision of the PhD project. This project will be a pilot study to asses the viability of this approach. No immediate commercialisation is expected.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509577/1 01/10/2016 30/09/2021
1904745 Studentship EP/N509577/1 26/09/2017 30/09/2021 Adam Harold Walker
Description We have used the fermionic order-by-disorder method to develop a theory that describes superconductivity that is driven by magnetic fluctuations in materials. We have made comparisons to ascertain how exactly this new theory compares to preexisting descriptions of superconductors. Furthermore we have worked out how this theory can be interfaced with density functional theory, which is an effective and widely-used theory that is used to simulate materials. This combined theory provides a computational method of simulating materials which superconduct due to magnetic fluctuations. We have started implementing this joint theory in code.
Exploitation Route This work can be taken forward primarily by finishing the implementation into software. Once completed this software can be used to study through simulation novel materials that exhibit fluctuation-driven superconductivity, such as the iron pnictides, and for example calculate their critical temperatures. It could also be used to predict new superconducting materials, for example as part of a random structure searching protocol (c.f AIRSS). This work also prescribes a way of introducing other types of novel electronic phenomena, such as spin nematic order, into materials simulations.
Sectors Electronics,Energy