Quantum Critical Dynamics Induced by Topological Zero Modes.

Area of Science:

• Condensed matter physics
• Topological materials
• Disordered quantum systems

Background:

• The Su-Schrieffer-Heeger (SSH) model describes topological insulators with unique edge states.
• Chiral disorder introduces complexities in the transport properties of these systems.
• Understanding transport near topological transitions is crucial for novel electronic applications.

Purpose of the Study:

• Investigate low-frequency AC transport in SSH chains with chiral disorder.
• Analyze the impact of topological domain wall zero modes on conductivity scaling.
• Determine the relationship between wave function decay and conductivity at criticality.

Main Methods:

• Real-space renormalization group analysis.
• Hybridization arguments for zero modes.
• Theoretical investigation of AC conductivity scaling.

Main Results:

• Observed anomalous logarithmic scaling of AC conductivity (σ(ω)∼logω) at the topological delocalization transition.
• Found conductivity scaling of σ(ω)∼ω^{2|δ|}log^{2}ω away from criticality.
• Linked critical conductivity scaling to the stretched-exponential spatial decay of zero-mode wave functions (ψ(x)∼e^{-√x}).

Conclusions:

• Hybridized topological domain wall zero modes are responsible for the anomalous AC conductivity scaling.
• The spatial decay of zero-mode wave functions dictates the conductivity behavior at criticality.
• Provides insights into transport phenomena in disordered topological systems near phase transitions.