Topological crystalline superconductors in two dimensions.

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Superconductivity

Background:

• Topological crystalline superconductors host exotic edge states protected by crystalline symmetries.
• Classifying these edge modes is crucial for understanding their properties and potential applications.
• Time-reversal symmetry plays a key role in the emergence of these topological phases.

Purpose of the Study:

• To propose a general framework for classifying topological edge modes in 2D topological crystalline superconductors.
• To investigate the realization of topological crystalline phases.
• To distinguish topological phases based on mirror and mirror-inversion symmetries.

Main Methods:

• Development of a theoretical framework for classifying topological edge modes.
• Analysis of superconductors with time-reversal and crystalline symmetries (mirror and mirror-inversion).
• Identification of criteria for distinguishing topological phases.

Main Results:

• A framework is established to classify topological edge modes protected by crystalline symmetries.
• Majorana edge modes are identified along mirror invariant lines in specific topological phases.
• AIII class topological edge modes are found along mirror-inversion invariant lines and in mirror-inversion parity subspaces.

Conclusions:

• The proposed framework successfully classifies topological edge modes in 2D topological crystalline superconductors.
• Distinctive topological edge modes, including Majorana and AIII class, are characterized by their symmetry protection.
• The study provides a criterion for distinguishing topological phases in crystalline superconductors with combined symmetries.