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Topological solitons in anisotropic superconductors

PGR-P-1127

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Project start date
Tuesday 1 October 2024
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Source of funding
University of Leeds
Supervisors
Professor Martin Speight
Schools
School of Mathematics
Research groups/institutes
Algebra, geometry and integrable systems, Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

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.

<h2 class="heading hide-accessible">Full description</h2>

<p>Examples of recent work in this vein by the supervisor&rsquo;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>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;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>&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Topological Solitons in Anisotropic Superconductors</strong></em>&nbsp;as well as <a href="https://eps.leeds.ac.uk/maths/staff/4079/professor-martin-speight">Martin Speight</a>&nbsp;as your proposed supervisor&nbsp;and in the finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;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 after the closing. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;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 in support of your application by the closing date of 3 April 2024 for&nbsp;Leeds Opportunity Research Scholarship and 8 April 2024 for Leeds Doctoral Scholarship:</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> </ul>

<h2 class="heading heading--sm">Entry requirements</h2>

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.

<h2 class="heading heading--sm">English language requirements</h2>

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.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a><span style="font-size:11.0pt"><span style="line-height:107%"><span style="font-family:&quot;Calibri&quot;,sans-serif">&nbsp;</span></span></span>are available to UK applicants (open from October 2023). <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 &ndash;&nbsp;The&nbsp;<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>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;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>&nbsp; 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>

<h2 class="heading">Contact details</h2>

<p>For further information about your application, please contact Doctoral College Admissions by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For further information about this project, please contact Professor Martin Speight by email to&nbsp;<a href="mailto:j.m.speight@leeds.ac.uk">j.m.speight@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>