Disorder induced superconductivity in quasi 1-D strongly correlated systems

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AbstractThe long-lasting search for superconducting materials where the phase transition temperature can be increased by the introduction of disorder has been unsuccessful until recently. Only recently, advances in controlled incorporation of disorder in quasi-one-dimensional materials proved the existence of such materials. The discovery of new materials where superconducting pairing is enhanced by disorder opens a path to controlling (increasing) the transition temperature. Such systems are not described by standard mean-field theories of phase transitions. We will develop a new quantum field theory for quasi-one-dimensional strongly correlated disordered superconductors required to understand the nature of the new superconducting state.ContextAttraction between electrons leads to the formation of a superconductor. Disorder localises electrons and, therefore, suppresses their transport, leading to the formation of an 'antipode' state with infinite resistance, insulator. The competition between these two mechanisms is usually formulated as disorder-induced suppression of superconductivity. This fact has been known for decades and the main open question which was "how exactly the temperature of the transition into a superconducting state is suppressed by the disorder". Unexpectedly, recent experiments on different materials demonstrated an increase in the transition temperature, so-called 'critical temperature enhancement'. These materials turned out to be one-dimensional chains with extremely weak couplings between them. In one dimension there can be no true superconductivity and any disorder localises electrons. Nevertheless, it seems that a weak coupling between one-dimensional chains creates a new state with superconducting behaviour which is enhanced by the disorder. There is no theory at the moment capable of explaining the observed behaviour. This project is focused on developing such a theory; the aim is to understand the nature of disorder-induced enhancement of phase transition temperature, open the path to controlling the superconducting properties, and to guide the search for novel high-temperature superconductors.ObjectivesTo understand the nature of disorder-induced emergence and enhancement of superconductivity, we will implement an exhaustive theoretical study of phase transitions taking place in novel quasi-one-dimensional materials. The research objectives are: 1. Formulation of the effective field theory describing disordered system of coupled one-dimensional electron liquids with superconducting pairing. 2. Theoretical analysis of the multi-fractal nature of many-electron wavefunctions in quasi-one-dimensional systems of coupled electron liquids. 3. Theoretical test of the hypothesis that enhancement of phase transition temperature is related to the topology of the wavefunctions support in different network-like structures and materials. MethodA description of phase transitions in low-dimensional systems (where almost all interactions lead to non-perturbative effects) requires application of quantum field theory in a form suitable to dealing with condensed matter problems. A one-dimensional electron liquid is treated by the bosonisation technique. To describe a set of coupled one-dimensional electron liquids we will have to build corresponding field-theoretic model that generalizes bosonisation approach and includes disorder and superconductivity. The presence of disorder will require statistical averaging that will be performed with the use of the Keldysh-based or replica approach. To analyse different mechanisms leading to formation of a new state, we will use renormalisation group analysis. For the analysis of superconductivity onset in lattices with non-trivial topology (Bethe lattice and scale-free networks) we will use a combination of non-linear sigma model and the cavity method.