Classically electrons in a three-dimensional solid can change their momentum in all possible directions. However, electrons in semiconductors can be manipulated so that they are constrained to move in lower dimensions. One of the perfect examples of such a system is a semiconductor heterostructure of GaAs/AlGaAs forming a plane of electrons, only a few nanometer thick, at its junction where electrons possessing quantised energy and freedom to change momentum in the plane. Such remarkable ensemble of non-interacting electrons is known as the two-dimensional electron gas (2DEG). The electrons in a 2DEG system are highly mobile and at low temperatures their motion is mainly scattering free due to the reduction in the interaction with lattice vibrations (phonons) and there is little impurity scattering. When the 2D electrons are electrostatically squeezed to form a narrow, 1D channel whose effective size is less than the electron mean free path for scattering then quantum phenomena associated with the electrons becomes resolved. In this situation, the energy of 1D electrons becomes quantised and discrete levels are formed. At a low carrier concentration of electrons, if the potential which is confining the 1D electrons is relaxed then electrons can arrange themselves into a periodic zig- zag manner forming a Wigner Crystal, named after Wigner who first predicted such a phenomenon in metal in 1936. Recently the distortion of a line of electrons into a zig-zag and then into two separate rows of electrons was observed and associated rich spin and charge phases. A very subtle change in confinement can result in two rows emerging from a zig-zag state which indicates that there is a narrow range where wavefunctions separate and form entangled states. Entanglement is a remarkable phenomenon in which a change in state of one electron will introduce a change in state of another. This amazing property forms the basis for quantum information processing with practical consequences related to quantum technologies, which will be investigated in this proposal. Another most important aspect of my Fellowship proposal is investigating the zig-zag regime or relaxed 1D system in search of fractional quantum states in the absence of a magnetic field. In the presence of a large magnetic field the energy of a 2DEG is quantized to form Landau levels which gave rise to two celebrated discoveries of the Integer and fractional quantum Hall effects in 1980 and 1982 respectively. Such unexpected revelations then pose a question whether fractional quantised states in the absence of any magnetic field in any lattice or topological insulators could ever be observed? However, there were no reports of observations of any fractional states without a magnetic field until the recent discovery of fractional charges of e/2 and e/4 arising from the relaxed zig-zag state in a Germanium-based 1D system. The proposal is inspired by this and the recent experimental finding of non-magnetic self-organised fractional quantum states in tradition GaAs based 1D quantum wires, which was completely unanticipated. The research aim is to introduce new insights, and new aspects of quantum physics, by exploiting the interaction effects in low-dimensional semiconductors by manipulating electron wavefunctions in a controllable manner to allow technological exploitation of basic quantum physics. The major challenges to be investigated: spin and charge manipulation, demonstrating electron entanglement and detection, mapping self-organised fractional states and their spin states, controlled manipulation and detection of hybrid fractional states and establishing if they are entangled. This research proposal opens up a new area in the quantum physics of condensed matter with the generation of Non-Abelian fractions which can be used in a Topological Quantum Computation scheme.

International research suggests that in response to climate change global cities are now engaging in strategic efforts to effect a low carbon transition. That is, to enhance resilience and secure resources in the face of the impacts of climate change, resource constraints and in relation to new government and market pressures for carbon control. But significant questions remain unexplored. First, limited research has been undertaken internationally to comparatively examine how different cities in the north and south are responding to the challenges of climate change. Second, it is not clear whether the strategic intent of low carbon transitions can be realised in different urban contexts. Consequently, we propose to establish an international network, to be undertaken between leading scholars on urban climate change responses as an important step towards addressing these deficits. The network will focus on the research and policy issues involved in comparing and researching the broader dynamics and implications of low carbon urbanism. This network includes Australia, China, India, South Africa and the US and builds on existing scholars and research teams with whom we currently have bilateral and ad hoc collaborations. Our proposed collaboration is designed to create greater density of network connections and enhancing the depth of each connection by three sets of initiatives: 1. International Networking Opportunities: The first element of the ESRC initiative will be to support significant international research opportunities for UK researchers. We will undertake programmed and structure visits to each national context to: increase knowledge of one another's research and plans; to gain intelligence about the research landscape in the partner countries in this field in order to build up a global picture of research expertise; to exchange ideas about possible future collaborative research projects; and to build personal relationships that are at the heart of successful long-distance research partnerships. 2. International Comparative Collaboration: The second element of the network is to facilitate interaction between the partners in the research network and with a wider group of UK and international researchers through two connected forum that will meet four times. A. International Research Workshops (Network partners plus other relevant UK and international researchers). These meetings will focus primarily on enhancing comparison and collaboration with a wider group of researchers but will also serve as an important opportunity for developing publications in the form of special issues and edited collections. B. Network Partners Research Forum (Network partners only). The network will also sponsor a number of much smaller research forums, focused on the network partners. These workshops will enable a structured and protected space for the partners to share the findings from their ongoing work, and to explore and examine the implications of the issues and themes emerging from the larger workshops in this context. 3. International Network Infrastructure: The third element will focus on establishing the necessary infrastructure for promoting effective international research collaboration. The network will pursue two projects. A. Information Infrastructure: Durham will establish a website that facilitates collaboration among international partners. All partner researchers and institutions will have the opportunity to present and regularly update information about their ongoing research. The website will also serve as a base for communicating about events, visits, awards, etc. The website will also host audio and video recordings of workshops. B. International Network Coordinator: Additionally Durham will support a 20% network coordinator to manage and organize the visits, workshops, teleconferences and the website.

International research suggests that in response to climate change global cities are now engaging in strategic efforts to effect a low carbon transition. That is, to enhance resilience and secure resources in the face of the impacts of climate change, resource constraints and in relation to new government and market pressures for carbon control. But significant questions remain unexplored. First, limited research has been undertaken internationally to comparatively examine how different cities in the north and south are responding to the challenges of climate change. Second, it is not clear whether the strategic intent of low carbon transitions can be realised in different urban contexts. Consequently, we propose to establish an international network, to be undertaken between leading scholars on urban climate change responses as an important step towards addressing these deficits. The network will focus on the research and policy issues involved in comparing and researching the broader dynamics and implications of low carbon urbanism. This network includes Australia, China, India, South Africa and the US and builds on existing scholars and research teams with whom we currently have bilateral and ad hoc collaborations. Our proposed collaboration is designed to create greater density of network connections and enhancing the depth of each connection by three sets of initiatives: 1. International Networking Opportunities: The first element of the ESRC initiative will be to support significant international research opportunities for UK researchers. We will undertake programmed and structure visits to each national context to: increase knowledge of one another's research and plans; to gain intelligence about the research landscape in the partner countries in this field in order to build up a global picture of research expertise; to exchange ideas about possible future collaborative research projects; and to build personal relationships that are at the heart of successful long-distance research partnerships. 2. International Comparative Collaboration: The second element of the network is to facilitate interaction between the partners in the research network and with a wider group of UK and international researchers through two connected forum that will meet four times. A. International Research Workshops (Network partners plus other relevant UK and international researchers). These meetings will focus primarily on enhancing comparison and collaboration with a wider group of researchers but will also serve as an important opportunity for developing publications in the form of special issues and edited collections. B. Network Partners Research Forum (Network partners only). The network will also sponsor a number of much smaller research forums, focused on the network partners. These workshops will enable a structured and protected space for the partners to share the findings from their ongoing work, and to explore and examine the implications of the issues and themes emerging from the larger workshops in this context. 3. International Network Infrastructure: The third element will focus on establishing the necessary infrastructure for promoting effective international research collaboration. The network will pursue two projects. A. Information Infrastructure: Durham will establish a website that facilitates collaboration among international partners. All partner researchers and institutions will have the opportunity to present and regularly update information about their ongoing research. The website will also serve as a base for communicating about events, visits, awards, etc. The website will also host audio and video recordings of workshops. B. International Network Coordinator: Additionally Durham will support a 20% network coordinator to manage and organize the visits, workshops, teleconferences and the website.

The subject of electron transport when states are localized by disorder has been an important topic in physics for a considerable time. It was first realized in 2006 that a closed quantum system in which there is both disorder and many body interactions shows a completely new regime of behaviour termed Many Body Localization, MBL. This regime is characterised by a breakdown of equilibrium statistical mechanics, it predicts a zero conductance state at a finite temperature, entanglement can spread although there is a lack of thermalisation due to the breakdown of ergodicity expressed as a violation of the Eigenstate Thermalisation Hypothesis, ETH. Ergodicity is assumed in many areas of condensed matter science, namely that a sub-system of the whole is typical of the whole and that the behaviour averaged over time is identical to that averaged over space. Consequently the fact that it does not hold in this situation allows new phenomena as does the lack of equilibration due to the ETH no longer holding. Possible new states can be formed by the application of high frequencies to MBL and these will be investigated in the project. To date there has been no sustained experimental investigation of these predictions in condensed matter systems although there is considerable activity using cold atoms which naturally form a closed quantum system. Enormous theoretical interest has been expressed in the hundreds of papers published on the topic. It is in the area of condensed matter that this new state of matter would have a major impact if realised - which is the purpose of the project. We will comprehensively investigate this regime of behaviour using semiconductor technology and the fabrication techniques used in investigating mesoscopic devices and semiconductor nanostructures. By fabricating free standing nanostructures we will ensure a closed system by drastically reducing the coupling to the phonons which act as a heat bath. The temperature of measurements will be down the milliKelvin region and the length scale of the disorder will be varied as will other parameters such as dimensionality. Electrical and thermal techniques will be utilised as probes of the MBL state. In addition to the importance for basic physics this work will be extremely significant in quantum information and topological physics as this new state provides a means of quantum protection not presently available.