The discovery of graphene and other atomically thin quantum materials has defined a new paradigm in nanoscience. Electrons in these materials behave as light shining through window glass, propagating ballistically, unimpeded by disorder and defects. This leads to record-high electric conduction and other unique properties, which enable new directions for device engineering and have the potential to radically transform the performance of electronic devices. Remarkably, the quantum phenomena underlying these excellent electronic properties persist even at room temperature, changing the rules for signal processing and opening new avenues for quantum electronics and calling for innovative approaches to nanoelectronics that exploit new physical ideas rather than the conventional schemes.

Electron fluid (e-fluid) is a new state of matter that may help to address this challenge. In e-fluids, the flow of electric charge mimics that of viscous fluids, such as water, honey, or air, in a radical departure from textbook Ohm's law seen in conventional metals and semiconductors. In 20th century, viscous fluids were employed to engineer fluidic circuits and even simple but fully functional hydraulic computers operating at low frequencies. (For example, such devices found their use in automatic transmissions systems in vehicles.) E-fluids in quantum materials, in particular graphene, a one-atom-thin layer of carbon, move much faster and on much shorter scales. Extending fluidic designs to e-fluids will lead to logic gates and integrated circuits that operate a billion times faster, and are 10000 times smaller. Can the performance of fluidic circuits surpass that of conventional semiconductor transistors?

We believe that the answer to this question is in the affirmative: fluidic circuit components employing e-fluids in novel materials may operate faster, on a smaller scale, and provide novel functionalities. E-fluids will enable ultrafast low-power transistors, low-resistivity interconnects, and direct-current transformers. The fluidic architectures will provide support to modern technologies such as machine learning through achieving energy-efficient operation of analogue nanoscale devices at ultrahigh frequencies. To put these ideas on a firm ground and to unleash the potential of e-fluidics, a deeper understanding of the physics of e-fluids must be developed.

This project is a condensed-matter theorist's answer to the demands of nanoscale electronics. In the PI's preliminary work, an interesting and potentially useful regime, the onset of fluidity was identified. We shall focus our efforts on the onset of fluidity, describing it via mathematical models, and employing these to suggest design ideas for applications in nanoscale electronics.

The onset of fluidity occurs when the frequency of collisions between charge carriers reaches a certain threshold such that a current flow can drag ambient particles. In this regime, nonlocal effects and nonlinear couplings between currents are expected to be maximal. The latter is very beneficial for potential applications: electric current can be employed to manipulate the flow of another current. More detailed recent analysis demonstrate that the onset is not just a threshold for fluid-mechanical behaviour but an entirely new regime, in which injected currents propagate through the fluid via directed jets comprised of electrons and holes.

We will study theoretically the key phenomena occurring at the fluidity onset in graphene: charge flows, formation of jets, nonlinear coupling between the currents, energy transport, sensitivity to external magnetic field, response to fast electric fields. The research will be linked to experimental efforts done by project partners. The insights into the physics of fluidity will eventually help, via interaction with other teams, to propose novel designs of elements of nanoelectronic circuits based on the principles of e-fluidics.

Potential Impact:
Modern economy and society are rapidly transformed by the ongoing BigData revolution. Developments in machine learning, in particular, deep neural network algorithms, made it possible to analyse vast amounts of data to identify patterns and make informed decisions improving all aspects of our lives and well-being, including e.g. preventive healthcare. Computations underpinning these algorithms are very complex and costly, and a further progress in hardware development is required for this revolution to proceed: the new technologies in electronics should provide fast, energy-efficient, and scalable computing architectures.

Our research is a basic-science answer to this challenge: it aims to develop understanding of electron fluidity in graphene and other quantum materials with an eye on applications in nanoscale electronics. Fluidity in high-mobility quantum materials, such as graphene, is characterised by low resistances, which addresses the issue of energy efficiency. The outstanding characteristics of graphene allow logical operations at a higher clock rate, and hence enhance computational power. The proposed project will put these ideas on a firm ground, and will facilitate progress in nanoelectronic technologies. We will interact with other teams involving engineers (such as our partner team at Massachusetts Institute of Technology) to transform our fluidics-inspired vision into practical design ideas. This way, our research will contribute both to global prosperity and to the UK's prosperity as a productive and connected nation.

The research will be popularised via outreach events including those organised by the University of Exeter, events run by the Institute of Physics, and others. This will help members of the general public to understand the principles of modern technologies and how these will change in the future for the benefit of the economy. Public outreach activities of our interdisciplinary research will excite interest of general audience in both applied and fundamental science, from new concepts in nanoelectronics to the physics of fluids and relativistic physics of interacting particles. This will encourage younger members of society to work in physics or engineering research, and to stay informed about how basic science helps the development of modern technologies.

Participating in this project will provide a valuable training for the Postdoctoral Researcher and will equip them with quantitative skills required for a career in academia. (Such skills are also in high demand in high-tech industries, in particular in the recently emerged field of data science, as well as in the financial sector.) Our research will result in offspring projects pursued by PhD students at Exeter. This, together with smaller projects attempted by MPhys students, will further contribute to the development of skilled labour force.