{"id":890,"date":"2013-04-19T10:51:10","date_gmt":"2013-04-19T10:51:10","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/?p=890"},"modified":"2014-03-03T16:56:06","modified_gmt":"2014-03-03T16:56:06","slug":"anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/","title":{"rendered":"Anomalous thermodynamic power laws near topological transitions in nodal superconductors"},"content":{"rendered":"<ul class=\"kent-social-links\"><li><a href='http:\/\/www.facebook.com\/sharer.php?u=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;t= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-facebook' title='Share via Facebook'><\/i><\/a><\/li><li><a href='http:\/\/twitter.com\/home?status= Anomalous thermodynamic power laws near topological transitions in nodal superconductors%20https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/' target='_blank'><i class='ksocial-twitter' title='Share via Twitter'><\/i><\/a><\/li><li><a href='https:\/\/plus.google.com\/share?url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/' target='_blank'><i class='ksocial-google-plus' title='Share via Google Plus'><\/i><\/a><\/li><li><a href='http:\/\/linkedin.com\/shareArticle?mini=true&amp;url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;title= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-linkedin' title='Share via Linked In'><\/i><\/a><\/li><li><a href='mailto:content=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;title= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-email' title='Share via Email'><\/i><\/a><\/li><\/ul><p><a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Dispersion_relations.png\"><img loading=\"lazy\" class=\"aligncenter\" alt=\"Dispersion_relations\" src=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Dispersion_relations-300x47.png\" width=\"300\" height=\"47\" \/><\/a><\/p>\n<p>We have just put out a generalisation of the theory of nodal quasiparticles and used it to derive a bulk thermodynamic signature of certain topological transitions.<\/p>\n<p>The theory of nodal quasiparticles has a wide range of applications, from unconventional superconductors to topological superconductors and graphene. At low temperatures, their linear dispersion away from a nodal point or line on the Fermi surface (a Dirac point or a Dirac line), leads to a characteristic power-law dependence of the specific heat:<\/p>\n<p style=\"text-align: center\"><a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Screenshot-from-2013-04-19-120348.png\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-897\" alt=\"Screenshot from 2013-04-19 12:03:48\" src=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Screenshot-from-2013-04-19-120348.png\" width=\"102\" height=\"33\" \/><\/a><\/p>\n<p>In superconductors, such behaviour can be used to detect experimentally whether the order parameter has line nodes (<em>n<\/em> = 2) or point nodes (<em>n<\/em> = 3) and therefore to identify the Cooper pairing symmetry. In our recent preprint, [Note added: now published, see <a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/12\/13\/anomalous-power-laws-paper-published\/\">http:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/12\/13\/anomalous-power-laws-paper-published\/<\/a>]<\/p>\n<blockquote>\n<h1>Anomalous thermodynamic power laws near topological transitions in nodal superconductors<\/h1>\n<div><a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Mazidian_B\/0\/1\/0\/all\/0\/1\">B. Mazidian<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Quintanilla_J\/0\/1\/0\/all\/0\/1\">J. Quintanilla<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Hillier_A\/0\/1\/0\/all\/0\/1\">A.D. Hillier<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Annett_J\/0\/1\/0\/all\/0\/1\">J.F. Annett<\/a><\/div>\n<div><a href=\"http:\/\/arxiv.org\/abs\/1302.2161\">arXiv:1302.2161<\/a><\/div>\n<\/blockquote>\n<p>we show that other, non-integer exponents are possible. These occur when line nodes cross or near topological transitions where point nodes, line nodes, or line node crossings either appear, disappear or re-configure themselves in a non-trival way on the Fermi surface (e.g., at a line reconnection transition where the number of rings of line nodes on the Fermi surface changes). Such anomalous exponents thus provide <em>bulk <\/em>thermodynamic signatures of the topological transitions in question &#8211; which should come in handy to experimentalists wishing to study topological matter as until recently the emphasis has been on <em>surface <\/em>phenomena in topological insulators i.e. topologically-protected edge states.<\/p>\n<p>Interestingly, you don&#8217;t need to be exactly at the topological transition in order to observe the anomalous exponent &#8211; merely being near the transition is enough to observe the anomalous power law down to some characteristic temperature scale <a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Screenshot-from-2013-04-19-120215.png\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-896\" alt=\"Screenshot from 2013-04-19 12:02:15\" src=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/04\/Screenshot-from-2013-04-19-120215.png\" width=\"35\" height=\"25\" \/><\/a>, below which the more conventional behaviour is found &#8211; a behaviour strongly reminiscent of a quantum critical endpoint (QCEP):<\/p>\n<p style=\"text-align: center\"><a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-1007\" alt=\"Screenshot from 2013-12-13 14:59:12\" src=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912-300x79.png\" width=\"300\" height=\"79\" srcset=\"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912-300x79.png 300w, https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912-1024x270.png 1024w, https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912-500x132.png 500w, https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2013\/12\/Screenshot-from-2013-12-13-145912.png 1085w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<ul class=\"kent-social-links\"><li><a href='http:\/\/www.facebook.com\/sharer.php?u=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;t= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-facebook' title='Share via Facebook'><\/i><\/a><\/li><li><a href='http:\/\/twitter.com\/home?status= Anomalous thermodynamic power laws near topological transitions in nodal superconductors%20https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/' target='_blank'><i class='ksocial-twitter' title='Share via Twitter'><\/i><\/a><\/li><li><a href='https:\/\/plus.google.com\/share?url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/' target='_blank'><i class='ksocial-google-plus' title='Share via Google Plus'><\/i><\/a><\/li><li><a href='http:\/\/linkedin.com\/shareArticle?mini=true&amp;url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;title= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-linkedin' title='Share via Linked In'><\/i><\/a><\/li><li><a href='mailto:content=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2013\/04\/19\/anomalous-thermodynamic-power-laws-near-topological-transitions-in-nodal-superconductors\/&amp;title= Anomalous thermodynamic power laws near topological transitions in nodal superconductors' target='_blank'><i class='ksocial-email' title='Share via Email'><\/i><\/a><\/li><\/ul>","protected":false},"excerpt":{"rendered":"<p>We have just put out a generalisation of the theory of nodal quasiparticles and used it to derive a bulk thermodynamic signature of certain topological &hellip; 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