Local Theory of the Insulating State

Area of Science:

• Condensed matter physics
• Materials science
• Quantum mechanics

Background:

• Insulators and metals exhibit distinct electron ground state organizations.
• The quantum metric tensor probes electronic properties but requires homogenous samples.
• Distinguishing metallic from insulating regions is crucial in materials science.

Purpose of the Study:

• To introduce a novel localization marker for differentiating metallic and insulating material characteristics.
• To develop a method applicable to localized electron distributions, including Anderson localization.
• To enable discrimination between bulk and boundary properties in topological insulators.

Main Methods:

• Utilizing the ground state electron distribution as the sole input.
• Developing a localization marker analogous to the quantum metric tensor.
• Applying the marker to systems with and without spectral gaps, including those with nonzero Chern invariants.

Main Results:

• The proposed marker successfully detects the metallic versus insulating character of sample regions.
• The method functions even in the Anderson localization regime (gapless spectrum).
• The marker differentiates the insulating bulk from the conducting boundary in Chern insulators.

Conclusions:

• The new localization marker offers a versatile tool for analyzing electronic properties at a local level.
• This approach overcomes limitations of previous methods requiring macroscopic homogeneity.
• The findings have implications for understanding and characterizing diverse electronic materials.