Disorder induced superconductivity in quasi 1-D strongly correlated systems
Lead Research Organisation:
Aston University
Department Name: Sch of Engineering and Applied Science
Abstract
Abstract
The 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.
Context
Attraction 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.
Objectives
To 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.
Method
A 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.
The 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.
Context
Attraction 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.
Objectives
To 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.
Method
A 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.
People |
ORCID iD |
| Igor Yurkevich (Primary Supervisor) | |
| Adam Lowe (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509425/1 | 01/10/2016 | 30/09/2021 | |||
| 2003683 | Studentship | EP/N509425/1 | 01/10/2017 | 30/09/2020 | Adam Lowe |
| Description | The award has yielded two pieces of key research; the first is the paper that has already been outlined, where a novel topological superconductor was found from a theoretical perspective by both analytical and numerical methods. If this system is realised experimentally, it could be used in the design and development of quantum computers. This is since one of the main methods for developing quantum computers is the use of superconducting qubits. The added benefit of the topological properties, further helps prevent the quantum state becoming entangled with the classical state. A particularly interesting finding from this model is the contiuum of Cooper pairs along the diagonals of the Brillouin zone when the system is at half filling and for the lowest energy eigenvalue. The second piece of research is currently unpublished, but will submitted in the next few months, and answers the main research question of the project. We have found the disorder can induce superconductivity when considering a quasi 1D strongly correlated system. This was done by using an array of coupled Luttinger liquid wires, and introducing disorder into this system. We can see from the renormalisation group analysis, that for certain values, an increase of disorder leads to an increase in the critical temperature of the system. Moreover, numerical analysis is used to model the system, so that all facets of the model can be studied, and these can be compared with the experiment that motivated the research. The significance of this result should not be underestimated as this the first theory which accurately describes observed experiment for disorder raising the critical temperature of superconductivity. The reason why it is important to have a controllable technique to raise the critical temperature, is that it could be utilised for room temperature superconductivity. However, this is only possible when the theory is fully understood. Our research has taken the first steps to understanding this. |
| Exploitation Route | For this first paper, hopefully an experimental team can try and reproduce the model and see if they see the non trivial topology predicted. This would be done by measuring the specific heat and seeing if there is a certain type of jump at the phase transition. If such a material is found, it could be used a potential material for quantum computers, so that would be the next step. If a team could make practical use of the material, the research would be fully justified. For the second paper, the topology of the system could be studied. This could yield a very interesting link between disorder and topology, and this could potentially be exploited in future theoretical and experimental work with the potential for the realisation of quantum computers which perform at a high level. Another line of investigation is to continue to investigate the link between disorder and other models of superconductivity both experimentally and theoretically. Our research could be used as avenue of determining what experiments may be suitable for disorder enhanced superconductivity. Additionally, the theory could be extended to try understand the microscopic mechanism underlying the superconductivity. Consequently, there are many avenues for different research to explore from our project. |
| Sectors | Electronics,Energy |
| URL | https://arxiv.org/abs/1902.04599 |
| Title | DIsorder Induced Superconductivity in a Quasi-1D Strongly Correlated System |
| Description | This model consists of an array of Luttinger liquid wires which are weakly coupled. From this, Josephson coupling is allowed to occur, and disorder is introduced. Using this formalism, the effective action is written for the system. Consequently, a renormalisation group (RG) analysis calculation is performed so that the physics of the system can be understood as the temperature varies. From these RG equations, it is clearly seen that disorder can enhance the critical temperature of the superconductor. There is still more analysis to be performed on the RG equations such that we can consider the model to be fully consistent with the observed experiment, which explains why the work is not yet published. This will be resolved within the next few months and consequently will be published then. |
| Type Of Material | Data analysis technique |
| Year Produced | 2019 |
| Provided To Others? | No |
| Impact | This model is extremely relevant in the field since it is the first theory which describes how disorder can enhance superconductivity whilst being consistent with observed experiment. Consequently, by using controllable techniques, such as adding disorder to the system, we can enhance the critical temperature of a superconductor. In the future, this could reveal a signature for increasing the critical temperature of a superconductor, and thus could one day yield room temperature superconductors which could revolutionise the modern world. |
| Title | Finding a topological superconductor by looking at model that has mirror symmetry |
| Description | The model was developed by considering a very simple condensed matter system, namely a 2D square lattice, and then attempting to uncover the physics of such a system. The novel methodology was determining the non trivial topology through a mixture of computational and analytical techniques. The analytical techniques were based on using a Hubbard-Stratonovich transformation, such that the gap function for the system could be found. From this, the type of superconductivity was determined, and analytical calculations could be performed on this gap function. The numerical techniques, consisted of finding the minimum eigen energies for the system, since a non analytic integral needed to be computed. It was using these techniques that revealed unknown physics, and thus justifies the research methodology. The DOI for the article is 10.1088/1361-648X/ab467d |
| Type Of Material | Data analysis technique |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| Impact | A potential non trivial topological superconductor. If this can be realised experimentally, it could be an avenue to better performing quantum computers. This is since one of the most promising candidates for quantum computers relies on using topological superconducting qubits. If a material was found that enabled this to be manufactured, the computational power of quantum computers could vastly increase. |
| URL | https://arxiv.org/abs/1902.04599 |
| Description | Disorder Induced Superconductivity in a Quasi-1D Strongly Correlated System |
| Organisation | Sami Shamoon College of Engineering |
| Country | Israel |
| Sector | Academic/University |
| PI Contribution | The contributions made by Adam Lowe and Igor Yurkevich consisted of the formulation of the problem in terms of Luttinger liquid theory and Josephson coupling, whilst adding disorder to the effective action. Once this effective action was written, a renormalisation group (RG) analysis was performed which led to the RG equations for the system. The results of these equations implied that for certain values disorder could enhance the critical temperature of the superconductor. However, the full nature of this system needed to be explored further, thus requiring numerical analysis when solving the differential equations. |
| Collaborator Contribution | The contributions made by Prof. Victor Kagalovsky consisted of useful discussions when formulating the correct model for the system. However, the main contribution has come from helping to solve the RG equations numerically, and importantly how to interpret the results. This has been particularly useful having extra members of the team due to the sensitivity of the system to the initial starting conditions. By having multiple people exploring the different ways the physics of the system changed when the initial conditions were adjusted helped us understand the circumstances under which disorder helped the critical temperature increase the most. |
| Impact | The result of this collaboration will be an article that will be submitted in the next few months outlining the methodology that was undertaken, and concluding the results concisely. The title of this paper will emphasise that disorder induced superconductivity is theoretically understood for a certain scenario. |
| Start Year | 2019 |
| Description | Topological Phase Transition in Superconductors with Mirror Symmetry |
| Organisation | University of Murcia, Spain |
| Country | Spain |
| Sector | Academic/University |
| PI Contribution | We provided the analytical framework for the toy model proposed in the paper. The toy model is a square lattice with nearest neighbour coupling. From this, the Hamiltonian and therefore action were written for this system. The wavefunction for the superconducting pairs was written, and this was used to calculate the Chern number which found the non-trivial topology. This was done entirely by Adam Lowe and Igor Yurkevich, and was performed analytically except for basic numerics computed by both Adam Lowe and Igor Yurkevich. |
| Collaborator Contribution | The contribution by our collaborator was entirely numerical, due to their expertise at numerical simulations. The purpose of the simulation was to calculate the minimum eigen energies when the chemical potential is zero (half filling). This is since our initial simulations suggested a continuum of Cooper pair energies along the diagonals of the Brillouin zone. However, since this is an unusual phenomenon, we decided to have the simulation check rigorously by an expert. The expert in question was Prof. Miguel Ortuno. He found using his numerical simulations that the system did in fact exhibit a continuum of Cooper pair energies along the diagonals. This accurate confirmation allowed us to claim the results in a paper that was published. |
| Impact | Published Article: Topological Phase Transition in Superconductors with Mirror Symmetry, A Lowe and M Ortuno and I V Yurkevich, Journal of Physics: Condensed Matter, 32, 3, 035603 (2019) The collaboration is not multi-disciplinary. |
| Start Year | 2018 |
| Description | Understanding the Literature of the Field Resulting in the Direction for the Project |
| Organisation | University of Electronic Science and Technology of China (UESTC) |
| Country | China |
| Sector | Academic/University |
| PI Contribution | Adam Lowe and Igor Yurkevich spent time at the institute. Initially Igor presented a talk at a conference, and then returned to Aston University. Whereas Adam stayed at the University for approximately one month, primarily conducting a literature review. Since this was in the first month of the project, it allowed a comprehensive understanding of what had already been done in the field, and thus revealed what path to take for the future research. Furthermore, this especially helped the student gain a wider understanding of the type of techniques that were used in both superconducting systems, and low dimensional systems. |
| Collaborator Contribution | The contribution of the partners was hosting the student and supervisor for a sufficient amount of time. They also enabled an excellent research facility for the research team, and thus led to a productive working environment. Additionally, due to the variety of different scientists at the conference and the institute, it helped wider understanding of the research currently being undertaken within the physics community. |
| Impact | 10.1088/1361-648X/ab467d |
| Start Year | 2017 |
| Description | Talk within the Mathematics Group at Aston University |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Other audiences |
| Results and Impact | The purpose of the talk was to give an introduction into the field of research, and highlight the goals of the project. Importantly, the wider impact of the aims of the project was discussed, including how room temperature superconductors could enhance the worldwide community. Additionally, an emphasis was put on how the development of the materials that were proposed could be used for quantum computers due to their topological nature. The talk was to the Mathematics group within Aston University, and approximately 20 people were there to witness it. Consequently, the outreach primarily was within academia, however it would not be limited to just research, due to connections between lecturers and undergraduate students. |
| Year(s) Of Engagement Activity | 2018 |