Universality of Boundary Charge Fluctuations

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Insulators exhibit phase transitions where their electronic band gap closes and reopens.
• Topological insulators possess unique properties due to their electronic band structure.
• Characterizing these transitions is crucial for understanding material properties and developing new electronic devices.

Purpose of the Study:

• To introduce quantum fluctuations of boundary charge (ΔQ_{B}^{2}) as a universal tool for characterizing insulator phase transitions.
• To demonstrate the applicability of this method across various insulator types, including topological, band, Anderson, and Mott insulators.
• To investigate the universal scaling behavior of ΔQ_{B}^{2} with the gap size (E_{g}) near phase transitions in different dimensions.

Main Methods:

• Theoretical analysis of quantum fluctuations of boundary charge.
• Investigation of phase transitions involving the closing and reopening of the direct band gap.
• Derivation of universal scaling relations for ΔQ_{B}^{2}(E_{g}) in one and two dimensions.

Main Results:

• Quantum fluctuations of boundary charge (ΔQ_{B}^{2}) serve as a powerful, unified tool for characterizing insulator phase transitions.
• The method is applicable to diverse insulator types, including topological, nontopological band, Anderson, and Mott insulators.
• A universal scaling law ΔQ_{B}^{2}(E_{g}) is identified near phase transitions, with specific forms derived for different dimensions (e.g., inverse gap in 1D, logarithmic in 2D for Dirac-like spectra).

Conclusions:

• Quantum charge fluctuations at the boundary provide a robust method for probing insulator phase transitions.
• The universality of the scaling behavior highlights fundamental physics governing these transitions.
• This approach offers new insights into the nature of topological and other correlated insulating states.