Majorana Basics

1. Basic knowledga of topology and quantum computing

• Review paper from Roman, weblink, PDF
• Online course on topology in condensed matter: From Kitaev chain to a nanowire, weblink
• GSppt: Topology Matters: From Transport to Quantum Computing, by T. Zhou

1.1 Nanowire system

Computational methods:

• Infinite system with translational symmetry: Topological conditions, Topological invariants, weblink

  • code: Nanowire_1D_inifinite_workshop.ipynb
  • code: Nanowire_1D_finite_workshop.ipynb

• Finite system: Majorana zero modes

  • Codes in New J. Phys. 16 (2014) 063065
  • code: Nanowire_1D_finite_paperexample.ipynb

1.2 Planar Josephson junctions

Warm-up Publications

• Theory: PRX 7, 021032 (2017); PRL 118, 107701 (2017)
• Experiments: Nature 569, 89 (2019)PDF; Nature 569, 93 (2019) PDF; PRL 126, 036802 (2021) PDF;
• T. Zhou’s Work: PRL 124, 137001 (2020) PDF; Nature Communications 13 (1), 1738-1747 (2022) PDF

Computational methods

• Infinite system with translation symmetry: Topological conditions, Topological invariants

  • GScode: SNS-1D-infinite_xdirection.ipynb

• Finite system: Majorana zero modes

  • GScode: SNS_2D_finite.ipynb