Parsing skin effect in a non-Hermitian spinless BHZ-like model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Materials

Background:

• The non-Hermitian skin effect (NHSE) is a phenomenon where extended bulk states in non-Hermitian systems localize at the boundaries.
• NHSE is typically associated with non-reciprocal hopping amplitudes in quantum systems.
• The Bernevig-Hughes-Zhang (BHZ) model is a foundational model for topological insulators.

Purpose of the Study:

• To comprehensively investigate the non-Hermitian skin effect (NHSE) in a spinless one-dimensional Bernevig-Hughes-Zhang-like model.
• To explore the conditions under which NHSE or its variants appear or disappear, challenging the conventional understanding.
• To analyze the topological properties and bulk-boundary correspondence in the presence of NHSE.

Main Methods:

• Investigated a spinless one-dimensional Bernevig-Hughes-Zhang-like model.
• Analyzed the impact of non-reciprocity in inter-orbital hopping terms on NHSE.
• Computed complex Berry phase and spatial localization of edge modes to study topological properties and bulk-boundary correspondence.
• Compared results for PT-symmetric and non-PT-symmetric cases.

Main Results:

• Demonstrated that non-reciprocal hopping does not always lead to NHSE, revealing exceptions.
• Observed different NHSE behaviors: conventional NHSE, NHSE at both edges, and a complete absence of NHSE, depending on inter-orbital hopping.
• Identified topological phase transitions through the analysis of Berry phase and edge mode localization.
• Highlighted differences in topological properties and NHSE manifestations between PT-symmetric and non-PT-symmetric regimes.

Conclusions:

• The presence and nature of NHSE in non-Hermitian systems are more nuanced than previously thought, requiring in-depth analysis beyond simple non-reciprocity.
• Topological properties, including Berry phase and edge state localization, are crucial for understanding the bulk-boundary correspondence in these systems.
• The study provides a comprehensive framework for analyzing NHSE and topological phase transitions in non-Hermitian models.