2024/01/11 by Simon Becker, Becker, Simon, Mengxuan Yang +1
Chemistry · Materials Science · #2D Materials and Applications #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fullerene Chemistry and Applications #Graphene research and applications #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Spectral Theory (math.SP) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2401.06078
openalex publication_date 2024/01/11 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe2 [C23,Z23] and WSe2 [MD23]. In this article, we study the MacDonald Hamiltonian for twisted transition metal dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we show that TMDs do not exhibit flat bands. The flatness in TMDs for small twisting angles is due to spatial confinement by a matrix-valued potential. We show that by generalizing semiclassical techniques developed by Simon [Si83] and Helffer-Sjöstrand [HS84] to matrix-valued potentials, there exists a wide range of model parameters such that the low-lying bands are of exponentially small width in the twisting angle, topologically trivial, and obey a harmonic oscillator-type spacing with explicit parameters.