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Topological band theory and Majorana fermions: With focus on self-consistent lattice models
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the most central concepts in condensed matter physics is the electronic band structure. Although band theory was established more than 80 years ago, recent developments have led to new insights that are formulated in the framework of topological band theory. In this thesis a subset of topological band theory is presented, with particular focus on topological supercon- ductors and accompanying Majorana fermions. While simple models are used to introduce basic concepts, a physically more realistic model is also studied intensely in the papers. Through self- consistent tight-binding calculations it is confirmed that Majorana fermions appear in vortex cores and at wire end points when the superconductor is in the topologically non-trivial phase. Many other properties such as the topological invariant, experimental signatures in the local density of states and spectral function, unconventional and odd-frequency pairing, the precense of spin-polarized currents and spin-polarization of the Majorana fermions, and a local π-phase shift in the order parameter at magnetic impurities are also investigated. 

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. , 144 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1441
Keyword [en]
Topology, Majorana, superconductivity, material physics, numerical calculations, tight-binding, mean-field
National Category
Condensed Matter Physics Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-305212ISBN: 978-91-554-9728-6OAI: oai:DiVA.org:uu-305212DiVA: diva2:1034719
Public defence
2016-12-09, Häggsalen, Ångströmslaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2016-11-15 Created: 2016-10-12 Last updated: 2016-11-23
List of papers
1. Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures
Open this publication in new window or tab >>Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures
2013 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 88, no 2, 024501- p.Article in journal (Refereed) Published
Abstract [en]

We study the energy spectrum of a vortex core in a two-dimensional semiconductor with Rashba spin-orbit interaction and proximity coupled to a conventional superconductor and a ferromagnetic insulator. We perform self-consistent calculations using the microscopic tight-binding Bogoliubov-de Gennes method on a lattice and confirm the existence of Majorana fermions in the nontrivial topological phase. We also find two different topologically trivial bulk superconducting phases, only differing in the type of vortex core structure they support and separated by a zero-energy excitation. Furthermore, we find an asymmetry in the energy spectrum with respect to both Zeeman splitting and vortex rotation direction and explain its physical origin.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-204775 (URN)10.1103/PhysRevB.88.024501 (DOI)000321270100003 ()
Available from: 2013-08-15 Created: 2013-08-12 Last updated: 2016-10-12Bibliographically approved
2. Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
Open this publication in new window or tab >>Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
2014 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 13, 134518- p.Article in journal (Refereed) Published
Abstract [en]

We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor-superconductor heterostructures. We show that in the nontrivial topological phase, characterized by a nonzero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyrmion classification can be extended to the equivalent one-dimensional topological superconductors.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-227201 (URN)10.1103/PhysRevB.89.134518 (DOI)000335498000004 ()
Available from: 2014-06-26 Created: 2014-06-24 Last updated: 2016-10-12Bibliographically approved
3. Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures
Open this publication in new window or tab >>Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 21, 214514Article in journal (Refereed) Published
Abstract [en]

We investigate the local density of states, spectral function, and superconducting pair amplitudes for signatures of Majorana fermions in vortex cores in ferromagnetic and spin-orbit coupled semiconductor/superconductor heterostructures. We show that the Majorana fermion quasiparticle momentum distribution is always symmetrically distributed at a finite radius around a high-symmetry point, thereby providing a necessary condition for a low-energy state to be a Majorana fermion. In real-space profiles of the local density of states through the vortex core the Majorana fermion, together with other finite-energy vortex states, forms a characteristic X-shape structure only present at nontrivial topology. Moreover, we find that the Mexican hat band structure property of the topologically nontrivial phase translates into multiple high-intensity band edges and also vortex core states located above the superconducting gap in the local density of states. Finally, we find no strong correlation between odd-frequency pairing and the appearance of Majorana fermions, but odd-frequency pairing exists as soon as ferromagnetism is present. In fact, we find that the only vortex superconducting pair amplitude directly related to any phase transition is the appearance of certain spin-triplet p-wave pairing components in the vortex core at a pre-topological vortex core widening transition.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-258333 (URN)10.1103/PhysRevB.91.214514 (DOI)000356477400004 ()
Funder
Swedish Research Council
Available from: 2015-07-15 Created: 2015-07-13 Last updated: 2016-10-12Bibliographically approved
4. Currents Induced by Magnetic Impurities in Superconductors with Spin-Orbit Coupling
Open this publication in new window or tab >>Currents Induced by Magnetic Impurities in Superconductors with Spin-Orbit Coupling
2015 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 115, no 11, 116602Article in journal (Refereed) Published
Abstract [en]

We show that superconducting currents are generated around magnetic impurities and ferromagnetic islands proximity coupled to superconductors with finite spin-orbit coupling. Using the Ginzburg-Landau theory, T-matrix calculation, as well as self-consistent numerical simulation on a lattice, we find a strong dependence of the current on the direction and magnitude of the magnetic moment. We establish that in the case of point magnetic impurities, the current is carried by the induced Yu-Shiba-Rusinov (YSR) subgap states. In the vicinity of the phase transition, where the YSR states cross at zero energy, the current increases dramatically. Furthermore, we show that the currents are orthogonal to the local spin polarization and, thus, can be probed by measuring the spin-polarized local density of states.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-264046 (URN)10.1103/PhysRevLett.115.116602 (DOI)000361040800005 ()26406845 (PubMedID)
Funder
EU, European Research Council, DM-321031Swedish Research CouncilSwedish Foundation for Strategic Research
Available from: 2015-10-06 Created: 2015-10-05 Last updated: 2016-10-12Bibliographically approved
5. Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors
Open this publication in new window or tab >>Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 92, no 21, 214501Article in journal (Refereed) Published
Abstract [en]

We investigate the persistent currents, spin-polarized local density of states, and spectral functions of topological superconductors constructed by placing ferromagnetic impurities on top of an s-wave superconductor with Rashba spin-orbit interaction. We solve self-consistently for the superconducting order parameter and investigate both two-dimensional blocks and one-dimensional wires of ferromagnetic impurities, with the magnetic moments pointing both perpendicular and parallel to the surface. We find that the topologically protected edge states of ferromagnetic blocks give rise to spin-polarized edge currents, but that the total persistent current flows in opposite direction to what is expected from the dispersion relation of the edge states. We also show that the Majorana fermions at the end points of one-dimensional wires are spin polarized, which can be directly related to the spin polarization of the edge currents of two-dimensional blocks. Connections are also made to the physics of the Yu-Shiba-Rusinov states for zero-dimensional impurities.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-270955 (URN)10.1103/PhysRevB.92.214501 (DOI)000365773700002 ()
Funder
Swedish Research CouncilGöran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologySwedish Foundation for Strategic Research EU, European Research Council, DM-321031
Available from: 2016-01-05 Created: 2016-01-05 Last updated: 2016-10-12Bibliographically approved
6. Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
Open this publication in new window or tab >>Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
2016 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 94, no 10, 100501Article in journal (Refereed) Published
Abstract [en]

We consider a wire network of ferromagnetic impurities on the surface of an s-wave superconductor with a strong Rashba spin-orbit interaction. Within the topological phase, zero-energy Majorana fermions appear at the wire end points as well as at junctions between an odd number of wire segments, while no clearly isolated subgap states are present at junctions between an even number of wire segments, providing strong, experimentally accessible signatures for Majorana fermions. We also investigate the quasiparticle energy gap with respect to varying the Rashba spin-orbit coupling and magnetic impurity strength. 

National Category
Condensed Matter Physics Physical Sciences
Identifiers
urn:nbn:se:uu:diva-305208 (URN)10.1103/PhysRevB.94.100501 (DOI)000383231600002 ()
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-19Bibliographically approved
7. Superconducting order parameter π-phase shift in magnetic impurity wires
Open this publication in new window or tab >>Superconducting order parameter π-phase shift in magnetic impurity wires
(English)Manuscript (preprint) (Other academic)
Abstract [en]

It has previously been found that a magnetic impurity in a conventional s-wave superconductor can give rise to a local π-phase shift of the superconducting order parameter. By studying a finite wire of ferromagnetic impurities, we are able to trace the origin of the π-phase shift to a resonance condition for the Bogoliubov-de Gennes quasiparticle states. When non-resonating states localized at the impurity sites are pulled into the condensate for increasing magnetic strength, the superconducting order parameter is reduced in discrete steps, eventually resulting in a π-phase shift. We also show that for a finite spin-orbit coupling, the π-phase shift is preserved and occurs in a large portion of the topologically non-trivial phase.

National Category
Condensed Matter Physics Physical Sciences
Identifiers
urn:nbn:se:uu:diva-305210 (URN)
Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-12

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