Leumer, Nico and Marganska, Magdalena and Muralidharan, Bhaskaran and Grifoni, Milena (2020) Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties. JOURNAL OF PHYSICS-CONDENSED MATTER, 32 (44): 445502. ISSN 0953-8984, 1361-648X
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We present a comprehensive, analytical treatment of the finite Kitaev chain for arbitrary chemical potential and chain length. By means of an exact analytical diagonalization in the real space, we derive the momentum quantization conditions and present exact analytical formulas for the resulting energy spectrum and eigenstate wave functions, encompassing boundary and bulk states. In accordance with an analysis based on the winding number topological invariant, and as expected from the bulk-edge correspondence, the boundary states are topological in nature. They can have zero, exponentially small or even finite energy. Further, for a fixed value of the chemical potential, their properties are ruled by the ratio of the decay length to the chain length. A numerical analysis confirms the robustness of the topological states against disorder.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MAJORANA FERMIONS; STATES; Kitaev chain; Majorana zero modes; topological phase; Fibonacci polynomials; electronic band structure; exact diagonalization |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Grifoni > Group Milena Grifoni |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Mar 2021 14:11 |
| Last Modified: | 08 Mar 2021 14:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43540 |
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