Tuning the topology of $p$-wave superconductivity in an analytically
solvable two-band model
- URL: http://arxiv.org/abs/2010.00164v1
- Date: Thu, 1 Oct 2020 01:20:46 GMT
- Title: Tuning the topology of $p$-wave superconductivity in an analytically
solvable two-band model
- Authors: Haiping Hu, Erhai Zhao and Indubala I. Satija
- Abstract summary: We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice.
We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce and solve a two-band model of spinless fermions with $p_x$-wave
pairing on a square lattice. The model reduces to the well-known extended
Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled
Kitaev chains in two respective limits. We show that its phase diagram contains
a topologically nontrivial weak pairing phase as well as a trivial strong
pairing phase as the ratio of the pairing amplitude and hopping is tuned.
Introducing periodic driving to the model, we observe a cascade of Floquet
phases with well defined quasienergy gaps and featuring chiral Majorana edge
modes at the zero- or $\pi$-gap, or both. Dynamical topological invariants are
obtained to characterize each phase and to explain the emergence of edge modes
in the anomalous phase where all the quasienergy bands have zero Chern number.
Analytical solution is achieved by exploiting a generalized mirror symmetry of
the model, so that the effective Hamiltonian is decomposed into that of
spin-$1/2$ in magnetic field, and the loop unitary operator becomes spin
rotations. We further show the dynamical invariants manifest as the Hopf
linking numbers.
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