Majorana Zero Modes in the Lieb-Kitaev Model with Tunable Quantum Metric

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Phenomena

Background:

• Band topology and Majorana zero energy modes (MZMs) are well-studied in topological superconductors.
• The influence of quantum metric on MZMs remains largely unexplored.

Purpose of the Study:

• To investigate the relationship between quantum metric and MZMs.
• To construct a tunable lattice model for studying this relationship.

Main Methods:

• Constructed a three-band Lieb-like lattice model with a tunable quantum metric and an isolated flat band.
• Introduced nearest-neighbor equal spin pairing to obtain the Lieb-Kitaev model supporting MZMs.
• Employed numerical and analytical methods to analyze MZM localization length.

Main Results:

• Demonstrated that the quantum metric length (QML), derived from the flat band's quantum metric, controls MZM localization.
• Showed that QML can significantly exceed conventional superconducting coherence length.
• Observed hybridization of MZMs and ultra-long-range crossed Andreev reflections when QML is comparable to superconductor length.

Conclusions:

• The quantum metric profoundly influences MZM properties via the QML.
• Findings are generalizable to other topological bound states.
• This work opens new avenues for controlling topological quantum phenomena.