- Type of research degree
- Application deadline
- Ongoing deadline
- Country eligibility
- International (open to all nationalities, including the UK)
- Competition funded
- Professor Martin Speight
- School of Mathematics
- Research groups/institutes
- Algebra, geometry and integrable systems, Applied Mathematics
Superconductors subjected to a magnetic field can host topological solitons called vortices, spatially localized tubes of magnetic flux and energy that cannot dissipate for topological reasons. Their dynamics and properties are key to understanding many important effects in superconductivity. <br /> <br /> The conventional mathematical model of superconductivity treats vortices as solutions of a nonlinear field theory, called Ginzburg-Landau theory, that is homogeneous and isotropic in space, with a single field (or order parameter) representing a single condensate of electron pairs. However, real superconductors often have highly anisotropic crystal structures, and can support electron condensates in more that one pairing state, so a more realistic model should have several fields and be spatially anisotropic. The behaviour of vortices (and domain walls, and Skyrmions) in these anisotropic multicomponent Ginzburg-Landau models is more richer and less well understood than in the simpler, conventional model. <br /> <br /> The purpose of this project is to study the properties of these various topological solitons in multicomponent Ginzburg-Landau theory, guided by a mixture of computer simulation, analytic approximation and geometry.
<p>Examples of recent work in this vein by the supervisor’s research group can be found in the following preprints:</p> <p><a href="https://arxiv.org/abs/2106.00475">https://arxiv.org/abs/2106.00475</a></p> <p><a href="https://arxiv.org/abs/2004.13171">https://arxiv.org/abs/2004.13171</a></p> <p><a href="https://arxiv.org/abs/1908.07969">https://arxiv.org/abs/1908.07969</a></p> <p><a href="https://arxiv.org/abs/1905.07296">https://arxiv.org/abs/1905.07296</a></p>
<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Topological Solitons in Anisotropic Superconductors</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4079/professor-martin-speight">Martin Speight</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p style="margin-bottom:11px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered on an ongoing basis. Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents at the point you submit your application:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> <li>Funding information including any alternative sources of funding that you are applying for or if you are able to pay your own fees and maintenance</li> </ul>
Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.
The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.
<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> are available to UK applicants. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>Non-UK – The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Important:</strong> Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are <strong>not </strong>covered under these studentships.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>
<p>For further information about your application, please contact Doctoral College Admissions: e: <a href="mailto:firstname.lastname@example.org">email@example.com</a></p> <p>For further information about this project, please contact Professor Martin Speight: e: <a href="mailto:firstname.lastname@example.org">email@example.com</a></p>
<h3 class="heading heading--sm">Linked research areas</h3>