Instanton-Induced Supersymmetry Breaking in Topological Semimetals

Area of Science:

• Condensed Matter Physics
• High-Energy Physics
• Quantum Mechanics

Background:

• Supersymmetry (SUSY) is a proposed symmetry beyond the standard model with applications in various physics fields.
• Topological semimetals exhibit unique electronic properties influenced by broken symmetries, such as those induced by magnetic fields.

Purpose of the Study:

• To systematically implement supersymmetric quantum mechanics in topological semimetals.
• To elucidate the mechanism behind the gap opening in topological semimetallic phases.
• To establish a simple criterion for predicting gap opening.

Main Methods:

• Implementing supersymmetric quantum mechanics in topological semimetals.
• Analyzing the role of dynamical SUSY breaking via instanton effects.
• Relating the instanton effect magnitude to the energy gap.

Main Results:

• Dynamical SUSY breaking via instantons is the mechanism for gap opening in topological semimetals.
• The energy gap magnitude is proportional to the instanton effect.
• A finite energy gap opens if and only if the SUSY potential has an even number of zeros.
• Even infinitesimal magnetic fields can open gaps in topological semimetals due to SUSY breaking.

Conclusions:

• The connection between SUSY quantum mechanics and topological semimetals explains previously ambiguous phenomena.
• This framework provides guidance for future research in topological materials.
• It opens new avenues for exploring topological semimetals and their properties.