Kitaev chain and topological superconductivity
A simple one-dimensional p-wave superconducting model can host unpaired Majorana end modes.
$$H=\sum_j[-\mu c_j^\dagger c_j-t(c_j^\dagger c_{j+1}+h.c.)+\Delta c_jc_{j+1}+h.c.]$$
What this means
A simple one-dimensional p-wave superconducting model can host unpaired Majorana end modes.
Deep dive: mathematical and physical mechanism
For real nonzero $t,\Delta$ and an infinite homogeneous chain, the standard topological regime is $|\mu|<2|t|$; the gap closes at $|\mu|=2|t|$. Open boundaries in the topological regime support exponentially localized zero modes in the ideal long-chain limit.
How it appears in quantum phenomena
Proximitized one-dimensional systems are engineered to approximate Kitaev physics.
Assumptions, caveats and limitations
Finite wire length splits modes; disorder, interactions, and additional bands complicate experiments.
Connect the ideas
For context, see the Interacting Topological Phases topic guide and the reading references.