Majorana Fermions and Topological Superconductivity 1D Topological classification of CII phases
Typ
Examensarbete för masterexamen
Program
Physics and astronomy (MPPAS), MSc
Publicerad
2019
Författare
Erkensten, Daniel
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
In the last decades, topology has established itself as a fundamental principle in condensed
matter physics. Not only does topology explain the incredible robustness of
certain physical quantities such as the Hall conductivity, but as a result of the bulkboundary
correspondence it also accounts for robust exotic fermionic edge states, e.g.
Majorana zero modes in superconductors. In this thesis the field of topological quantum
matter is reviewed with particular emphasis on one-dimensional non-interacting
superconducting systems and symmetry-protected topological phases. By taking off
from Kitaev’s model of p-wave superconductivity and the tenfold classification of
topological superconductors and insulators, we also investigate the notion of gapless
phases of matter addressing the issue what happens at a topological phase transition
in one dimension. For the symmetry classes BDI and CII, which both are known to
host topological superconductors in 1D, we obtain an N×Z-classification of gapless
phases. In addition to the conventional topological Z-invariant, the other classification
is provided by conformal field theory, a framework frequently used when
studying critical phenomena.
Beskrivning
Ämne/nyckelord
topological superconductors , Majorana zero modes , Majorana bound states , symmetry classes , gapless phases of matter