Anderson's Theorem for Correlated Insulating States in Twisted Bilayer Graphene

Area of Science:

• Condensed matter physics
• Materials science
• Quantum mechanics

Background:

• Correlated insulating phases in magic-angle twisted bilayer graphene show significant sample dependence.
• The Kramers intervalley coherent (K-IVC) state is a leading candidate for these insulating phases at even fillings.
• Understanding the stability of these states against disorder is crucial for experimental realization.

Purpose of the Study:

• To derive an Anderson theorem for the K-IVC state in twisted bilayer graphene.
• To investigate the robustness of the K-IVC state against various perturbations.
• To classify the stability of the K-IVC state against experimentally relevant conditions.

Main Methods:

• Theoretical derivation of an Anderson theorem.
• Analysis of the K-IVC state's response to PT-odd and PT-even perturbations.
• Classification of stability based on perturbation types.

Main Results:

• An Anderson theorem governing the K-IVC state's robustness against disorder was derived.
• The K-IVC gap is robust against PT-odd local perturbations.
• PT-even perturbations can induce subgap states, reducing or eliminating the gap.

Conclusions:

• The K-IVC state's stability is characterized by its distinct response to PT-odd and PT-even perturbations.
• The derived Anderson theorem provides a framework for understanding sample dependence in twisted bilayer graphene.
• This theoretical insight helps distinguish the K-IVC state from other potential insulating ground states.