{"title":"各向异性超导体中涡旋周围的量子化束缚态","authors":"Ke Xiang, Da Wang, Qiang-Hua Wang","doi":"10.1007/s11433-023-2353-6","DOIUrl":null,"url":null,"abstract":"<p>The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue. In this work, we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface. In the case of circular Fermi surface, the effective Schrödinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago. Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors. More importantly, we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schrödinger equation, going beyond the quasiclassical Eilenberger results, which, as we find, are sensitive to the scattering rate. For the case of isotropic Fermi surface, the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions, in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory. Moreover, as a consequence of the pairing anisotropy, the quantized wave functions develop a peculiar distribution of winding number, which reduces stepwise towards the vortex center. Our work provides a flexible way to study the vortex bound states in the future.</p>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantized bound states around a vortex in anisotropic superconductors\",\"authors\":\"Ke Xiang, Da Wang, Qiang-Hua Wang\",\"doi\":\"10.1007/s11433-023-2353-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue. In this work, we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface. In the case of circular Fermi surface, the effective Schrödinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago. Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors. More importantly, we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schrödinger equation, going beyond the quasiclassical Eilenberger results, which, as we find, are sensitive to the scattering rate. For the case of isotropic Fermi surface, the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions, in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory. Moreover, as a consequence of the pairing anisotropy, the quantized wave functions develop a peculiar distribution of winding number, which reduces stepwise towards the vortex center. Our work provides a flexible way to study the vortex bound states in the future.</p>\",\"PeriodicalId\":774,\"journal\":{\"name\":\"Science China Physics, Mechanics & Astronomy\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Physics, Mechanics & Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s11433-023-2353-6\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s11433-023-2353-6","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Quantized bound states around a vortex in anisotropic superconductors
The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue. In this work, we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface. In the case of circular Fermi surface, the effective Schrödinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago. Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors. More importantly, we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schrödinger equation, going beyond the quasiclassical Eilenberger results, which, as we find, are sensitive to the scattering rate. For the case of isotropic Fermi surface, the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions, in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory. Moreover, as a consequence of the pairing anisotropy, the quantized wave functions develop a peculiar distribution of winding number, which reduces stepwise towards the vortex center. Our work provides a flexible way to study the vortex bound states in the future.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
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