Analytical model of the energy spectrum and Landau levels of a twisted double bilayer graphene

Abstract

Motivated by recent experiments Adak et al. (2020) and Szentpéter et al. (2021), in this work we have considered a twisted double bilayer graphene system. Within the low energy effective theory, the bandwidth expression of the moire flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • In this work, in this work we have considered a twisted double bilayer graphene system. • Within the low energy effective theory, the bandwidth expression of the moiré flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. • We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. • Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. • We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • The results presented in this work will be useful for the experimental investigation of the tDBG system.