The interaction between electrons produces a new quantum multi body quantum phase of matter, whose wave function reflects electron correlation effects, symmetry breaking, and collective excitation. In the magic twisted bilayer graphene (MATBG), many quantum phases have been discovered, including related insulating phases, unconventional superconducting phases, and magnetic topological phases. However, the microscopic information of symmetry breaking is still insufficient to understand these quantum phases. Today, Kevin P. Nuckolls, Ryan L. Lee, Myungchul Oh, Dillon Wong, Tomohiro Soejima, Ali Yazdani, and others from Princeton University in the United States, used high-resolution scanning tunneling microscopy to study the wave functions of related phases in magic angle graphene MATBG.
The square of the wave function of the bandgap phase, including the related insulation phase, pseudogap phase, and superconducting phase, exhibits a clear breaking symmetry pattern on the graphene atomic lattice, with a √ 3 ×√ 3 hyperperiodicity, which has complex spatial dependence on the Mohr scale. Based on a set of complex local order parameters and the introduction of symmetry based analysis, these parameters display complex texture patterns that distinguish various related phases.
Compare the observed quantum texture of the relevant insulator filled with ± 2 electrons per mole cell with the expected theoretical ground state. In typical magic angle graphene MATBG devices, these textures match well with the proposed asymmetric Kekul é helix order textures, while in ultra-low strain samples, the data exhibits local symmetry, such as time reversal symmetry interval coherent phase.
In addition, the superconducting state of magic angle graphene MATBG exhibits strong interval coherence characteristics, and only phase-sensitive measurements can distinguish between superconducting and insulator signals.

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