Dimensionality is hugely important in low-temperature physics, the study of materials and the behaviour of electrons and other excitations in solid crystals. The underlying mathematics and the resulting observed behaviour of a material or system is hugely and fundamentally different and exotic if its character becomes two-dimensional rather than the familiar 3D. Even more fascinating and elusive is the fuzzy halfway ground of how a system behaves as it is pushed from one regime to the other - '2.5D'. A nascent revolution in alternatives to silicon-based electronics is increasingly turning to the physics of 2D materials to design new devices to overcome the challenges of ever-increasing miniaturisation and an ever-mounting drive to become more energy efficient. 2D layered crystals have unique advantages in this regard, as they can be cleanly and easily thinned down to single layers of atoms (as with the famous example of graphene), then stacked together in nigh-unlimited complex configurations to combine their exotic properties. To design and use these systems at an application level, it is essential that the underlying physics, and with it both the limitations and possibilities intrinsic to the materials are fundamentally understood and tested. Furthermore, this research can inform potential new avenues to explore and the synthesis of new designer materials to fulfil established criteria. A large volume of recent work on low-dimensional physics has focused on thickness control, to tune towards the `true 2D' limit of the atomic monolayer. A complementary approach is to tune the interactions from 2D to 3D by applying hydrostatic pressure - an extremely clean and powerful tuning parameter in a van-der-Waals (vdW) material. These materials are formed of strongly-bonded flat planes of atoms, linked only by the extremely weak van-der-Waals chemical bond - akin to static electric attraction. Applying pressure to such a system overwhelmingly has the effect of pushing the crystal planes together, strengthening bonds between them and allowing ever-increasing crosstalk. This will often have profound effects on the conductivity and magnetism seen in the system, including the discovery of exotic new states of matter. I will use extremes of low temperature, high pressure, magnetic and electric fields to search for new functional and multifunctional quantum materials and tune existing systems into novel states, focussing on fundamental properties of transport and of magnetic and charge order in 2D materials. I will focus on fundamental properties of transport and magnetism in low-dimensional van-der-Waals materials, and then to nanoscale devices built from stacking individual atomic layers of different 2D materials together. Extreme-conditions tuning of these nanodevices is a completely new and exciting research direction that brings together two very different fields of research with essentially no overlap - my unique background across these two areas, and quantum computing, will allow me to build a new interdisciplinary programme to explore exciting new physics. These devices additionally harbour great potential for new technologies as well as blue-skies science interest. I am partnering with industry, and academic collaborators in electrical engineering, chemistry and materials science, to explore pathways to practical applications of the new materials, behaviours and architectures to be discovered. Potential uses are in new times of electronics and memory such as spintronics or low-power transistors, flexible electronics and precision sensors. I will also look to harness the exotic 'topological' properties of new 2D materials to build fault-tolerant new qubits for quantum computing, drawing on my expertise and contacts in this field.

Heat engines form one of the cornerstones of classical thermodynamics. By converting heat into mechanical work they powered the industrial revolution in the 19th century. Molecular heat engines have the potential to convert thermal energy to electrical power and vice versa with efficiency close to the thermodynamic limit. The topic of single-molecule thermoelectricity is therefore of fundamental importance for the development of on-chip cooling and heat-to-electricity energy harvesting technologies that could power the quantum revolution of the 21st century. The key challenge in harnessing the thermoelectric energy conversion capabilities of single molecules is gaining a better understanding of the quantum mechanical interactions between molecular electronic and vibrational degrees of freedom, which could prove transformative for experiments in the research area of open quantum systems. These experiments will deliver impact in two ways: by exploring new science and by laying the foundation for new technologies. New science: Molecular heat engines form an ideal platform for exploring the dialogue between quantum mechanics and thermodynamics. While some theoretical efforts have been undertaken towards this end, many predictions remain to be verified by experiments. New insights into thermodynamics on the molecular scale will also raise further questions: Does quantum coherence boost the thermoelectric efficiency of single-molecule heat engines? What happens if the Born-Oppenheimer approximation breaks down? Can molecular vibrational modes be electrically cooled to their ground state? New technologies: Thermoelectrics have a long history of providing simple, reliable power generation. Yet, the use of thermoelectric materials to recover waste heat has remained limited due to their scarcity and toxicity, and the unfortunate fact that the properties that determine their efficiency - the electrical conductance, the thermal conductance, and the Seebeck coefficient - are contra-indicated, meaning that an improvement to one will deteriorate another. Quantum effects in single-molecule heat engines lift the link between these contra-indicated properties, thereby opening up the possibility for highly efficient thermoelectric generators that could provide a low-cost, environmentally-friendly means of scavenging waste heat that would drastically decrease global energy consumption. This proposal seeks to develop the instrumentation and experimental methodology to investigate controlled thermoelectric heat-to-energy conversion in a single molecule, where the emphasis is on controlling the molecular interactions. This control will be achieved by using two-dimensional networks of nanoparticles linked via molecular junctions. Building on recent ground-breaking experiments, I will use electric-field control to tune the molecular energy level alignment with respect of the Fermi level of the substrate, while simultaneously controlling the tunnel coupling and applied bias voltage. A local heater will drive a thermally generated flow of electrons through a single molecule, which I will be able to optimize thanks to the unprecedented degree of tunability in the system. By probing the thermoelectric efficiency over a wide parameter space, I will establish the intrinsic thermodynamic limits to single-molecule energy conversion.

The proposed CDT will address the UK's need for a pipeline of highly skilled scientists and engineers who will be able to secure the country's position as the global leader in the science and technology of two-dimensional materials (2DMs). Having started with the discovery of graphene at the University of Manchester, this research field now encompasses a vast number of 2DMs, 2DM-based devices, composites, inks, and complex heterostructures with designer properties. Numerous proposals for applications have emerged from research groups worldwide, some of them already picked up and being developed by big established companies and a large number of start-ups (30+ spin-outs just from the two partner universities, Manchester and Cambridge). Many of the ideas put forward require further research and validation and many more are expected to emerge, thanks to the unique properties of this new class of advanced materials and the ability to use modelling to predict new useful combinations of 2DMs or design conditions that bring about new properties. The CDT will support and enable new avenues of research and the development of 2DM-based technologies and work with industry partners to accelerate lab-to-market development of products and processes that leverage the exceptional properties of 2DMs. 2DMoT CDT will be an important part of graphene and 2D Materials eco-system centred on the Manchester and Cambridge innovation networks. It will contribute to the plans by the local authorities, in particular, of the Greater Manchester Combined Authority, to pilot Manufacturing Innovation Networks focused on graphene & nanomaterials, coatings and technical textiles. Industrial co-supervision of research projects will accelerate realisation of new products and technologies enabled by 2DMs, which is key to competitiveness. The CDT will implement a new approach to PhD research training by incorporating individual research projects into several overarching, multidisciplinary research missions with 2-3 CDT students a year joining each research mission, either at Manchester or Cambridge, and gradually forming 8-10 researcher teams incorporating CDT students at different stages of their PhD and involving several research groups with complementary expertise, working collaboratively and sharing ideas and knowledge. All students will have opportunities to shape their own projects and overall research missions, creating an inclusive environment, ideal for peer-to-peer learning and innovation. A 6-months-long formal taught programme at the start of PhD will be complemented by further advanced skills training during the research phase, transferrable skills training and research schools and workshops organised jointly with leading international research centres and the CDT business partners. Environmental sustainability of the developed products and technologies will be a focal point of the CDT programme, with specialist training and considerations of sustainability embedded in all research missions. Training in innovation and commercialization of research, project management, responsible research and innovation, and dealing with the media will be mandatory for all CDT students. To ensure that the benefits of CDT training are available to a wider group of PhD researchers, a range of CDT events - residential conferences, seminars, research workshops, commercialisation training - as well as some of the courses, will be open to non-CDT students whose research interests are aligned with the CDT research missions. Outreach events will form an important part of CDT activities, in particular participation in Science festivals, British Science weeks, Bluedot, Science X, with exhibits showcasing the science of 2DMs and their developing applications.