Complex band structure eigenvalue method adapted to Floquet systems: topological superconducting wires as a case...

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• The eigenvalue method and complex band structure are established for static lattice systems.
• Superlattices extend these methods to systems with multi-layer periodicity.
• Analyzing time-dependent quantum systems with periodic driving presents unique challenges.

Purpose of the Study:

• To adapt the superlattice scheme for analyzing time-dependent quantum systems under periodic driving.
• To develop a method for obtaining Floquet states and quasienergy spectra.
• To demonstrate the method's applicability to complex, anharmonic driving protocols.

Main Methods:

• An adapted superlattice scheme is proposed, treating time periodicity as an additional spatial dimension.
• The method solves for Floquet states and quasienergy spectra by analyzing an enlarged artificial system at a single energy.
• The approach is validated on systems with spin-orbit interaction and driven quantum dots.

Main Results:

• The adapted superlattice scheme successfully obtains Floquet states and quasienergy spectra for time-dependent systems.
• The method handles arbitrary periodic excitations, including strong and anharmonic drivings.
• Applications include topological superconductors in quantum wires and driven quantum dots.

Conclusions:

• The presented superlattice scheme offers a powerful tool for studying Floquet topological phases in periodically driven quantum systems.
• This method provides a unified approach for both time-independent and time-dependent lattice models.
• The technique is versatile and applicable to a range of quantum phenomena.