Novel X-ray methods for studying correlated quantum matter in the strong spin-orbit coupling limit

Although it is one of the most prosaic properties of a material, the response to an applied electrical voltage can be one of its most profound. Initial insight into why some materials are electrical conductors while others are insulators came from the early application of quantum mechanics. In this view, electrons in "simple" materials are treated as independent, and solids are classified according to the number of electrons filling the quantum states: for an even number the states are filled, resulting in an insulator, whereas for an odd number the states are partly filled allowing the electrons to conduct. Although this rule of thumb works for many "simple" materials, including e.g. aluminum and silicon on which a large fraction of our current technologies are based, it fails spectacularly for others. Simple oxides of transition metals, for example, exist with partially filled electron states. Mott first proposed that it was only by including electron interactions, which in materials such as oxides can be dominant, that the metal-insulator transition can be understood. Hubbard later proposed a deceptively simple model with just two parameters, describing the tendency of electrons either to localize (insulating behaviour) or delocalize (metallic). For more than 50 years, the Mott-Hubbard paradigm has provided the abiding theoretical framework for rationalizing the electronic and magnetic properties of "complex" quantum solids defined as those that exhibit explicit collective quantum effects, such as high-temperature superconductivity.

More recently, the relativistic coupling of an electron's intrinsic spin with its orbital motion - the spin-orbit interaction (SOI) - has come sharply into focus with the discovery that it can lead to qualitatively new types of electronic state. It has been shown that even for certain "simple" materials the SOI leads to surface metallic states on materials that in the bulk are insulating. These surface states are non-trivial, in that they are protected by symmetries - or topology - and therefore cannot be easily destroyed. The question then naturally arises as to the consequences of including relativistic effects in "complex" quantum materials in which the electrons interact strongly. The answer requires developing a new paradigm - beyond the Mott-Hubbard one - that treats interactions and the SOI on an equal footing. This proposal is to perform experiments that will be key to establishing this new paradigm. This new frontier has attracted considerable theoretical attention, and a plethora of predictions have been made for exotic electronic and magnetic states, some of which in the long run may lead to new technologies. Examples include novel types of insulators, metals, superconductors, quantum spin liquids, etc. However, history shows that although theory provides a useful guide, it cannot anticipate all possibilities, and many exciting discoveries will no doubt be made through experimentation.

Revealing the nature of the electronic and magnetic correlations in complex "quantum matter" through experimentation is very challenging, requiring techniques with extremely high sensitivity and specificity. A major theme of this proposal is the development of novel X-ray techniques which will offer unprecedented insights into the atomic scale order and excitations in solids. The techniques will be developed at large-scale central facilities, both nationally and internationally, which have dedicated particle accelerators for producing ultra intense X-ray beams. The recent advent of X-ray laser sources represent the pinnacle of this technology which deliver 20 orders of magnitude higher intensity than conventional sources in femto-second pulses (i.e. the time taken for light to transit a molecule). These sources are transformational enabling novel non-equilibrium electronic and magnetic states to be created and their evolution to be studied in real-time.

The main impacts of the Fellowship will come from the significant advances in knowledge that will be achieved on both scientific and technical fronts.

Scientifically, the proposal is positioned at the new frontier between strongly correlated electron materials and strong spin-orbit coupling. This frontier is attracting considerable interest in the academic community as numerous predictions have been made for the realization of exotic electronic phases with new functionalities. The scientific results of the Fellowship will therefore have an impact on the broad academic communities working on the electronic and magnetic properties of functional materials.

Technically, novel X-ray techniques will be developed in collaboration with the central facilities Project Partners (Diamond, ESRF, PETRA III). These range from the significant enhancement of existing techniques to the development of entirely new methods for probing the non-equilibrium states of correlated quantum matter. These techniques will bring unprecedented insights into the electronic and magnetic correlations that endow functional materials with their properties. The new capabilities will uniquely reveal the evolution of the electronic and magnetic correlations in the vicinity of phase transitions induced by extreme conditions,
and in the non-equilibrium, transient states created in response to ultrafast laser stimulation. They will thus have considerable impact on the capabilities of the central facilities themselves, including allowing the UK to obtain better returns on the large investments it makes in X-ray sources, and will be of benefit to the wider community of central facilities' users across the physical and engineering sciences.

The Fellowship will also have a significant positive impact on the training and careers of early career researchers. The postdoctoral research assistants and PhD students will receive excellent training through the experience of working closely with world-leading laboratories for X-ray science.

The ongoing large-scale investments in central facilities for X-ray science demands active and effective advocacy by working with both research councils, learned societies, government agencies, etc., and also by explaining to the general public the exciting science that the facilities enable. Award of a prestigious EPSRC Established Career Fellowship will also allow me to significantly enhance my activities in advocacy and public engagement.

Finally, the Fellowship will have considerable impact on my career allowing me to achieve international leadership in the rapidly developing field of X-ray physics applied to understand quantum materials.