Spectral characterization of magic angles in twisted bilayer graphene

• Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this Letter we show that in the approximation of vanishing AA coupling, the magic angles (at which there exist entirely flat bands) are given as the eigenvalues of a non-Hermitian operator, and that all bands start squeezing exponentially fast as the angle θ tends to 0. In particular, as the interaction potential changes, the dynamics of magic angles involves the nonphysical complex eigenvalues. Using our new spectral characterization, we show that the equidistant scaling of inverse magic angles is special for the choice of tunneling potentials in the continuum model, and is not protected by symmetries. While we also show that the protection of zero-energy states holds in the continuum model as long as particle-hole symmetry is preserved, we observe that the existence of flat bands and the exponential squeezing are special properties of the chiral model.

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NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

NATURVETENSKAP  -- Fysik -- Den kondenserade materiens fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Condensed Matter Physics (hsv//eng)

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