One-dimensional Majorana modes in electronic circuits
Final Report Abstract
This project explored the rapidly evolving and expanding field of one-dimensional Majorana modes in various condensed-matter settings. These modes emerge, e.g., at the edges of twodimensional topological superconductors, in long topological Josephson junctions and spin systems. Characterization of a Majorana fermion as one half of a regular Dirac fermion receives here a particularly clear justification. Indeed, certain networks of edge states containing the Dirac-to-Majorana and Majorana-to-Dirac converters (scattering junctions) show the quantized conductance halved as compared to the usual value in circuits with only Dirac modes. In this project we studied the properties of 1D Majorana modes in electronic circuits, taking into account effects of interactions, disorder, and quantum interference. Specifically, we investigated transport in interferometers with 1D Majorana modes. Further, we explored Josephson physics in 1D Majorana wires as well as well as emergence of zero Majorana modes in perpendicular magnetic fields. We also investigated related spin chains under influence of disorder and interactions. Finally, we explored emergence of Majoranas in topological spin textures. The work on the project was very successful resulting in numerous publications. While the experimental realization of 0D and 1D Majorana modes has turned out to be very challenging, the very recent experimental progress makes us optimistic that our theoretical predictions can be experimentally verified in near future.
Publications
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Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids. Physical Review B, 102(22).
Rex, Stefan; Gornyi, Igor V. & Mirlin, Alexander D.
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Current-phase relation in a topological Josephson junction: Andreev bands versus scattering states. Physical Review B, 103(11).
Backens, Stefan & Shnirman, Alexander
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Dynamics of many-body delocalization in the time-dependent Hartree–Fock approximation. Annals of Physics, 435, 168486.
Pöpperl, Paul; Doggen, Elmer V.H.; Karcher, Jonas F.; Mirlin, Alexander D. & Tikhonov, Konstantin S.
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Eigenstate correlations around the many-body localization transition. Physical Review B, 103(6).
Tikhonov, K. S. & Mirlin, A. D.
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Microwave response of a chiral Majorana interferometer. Physical Review B, 104(3).
Shapiro, Dmitriy S.; Mirlin, Alexander D. & Shnirman, Alexander
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A topological flux trap: Majorana bound states at screw dislocations. New Journal of Physics, 24(5), 053057.
Rex, Stefan & Willa, Roland
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Topological Josephson Junction in Transverse Magnetic Field. JETP Letters, 116(12), 891-895.
Backens, S.; Shnirman, A. & Makhlin, Yu.
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Coulomb blockade of chiral Majorana and complex fermions far from equilibrium. Physical Review B, 107(12).
Shapiro, Dmitriy S.; Mirlin, Alexander D. & Shnirman, Alexander
