Tuning the bands in ABA trilayer graphene

Abstract: The fractional Quantum Hall effect is a paradigmatic phenomenon arising from a confluence of electron-electron interaction, disorder, and topology. Bernal-stacked trilayer graphene (TLG) offers a versatile platform to explore the tunability of such electron-electron interactions with the help of an out-of-plane electric field. In this talk, I will discuss the various properties of the odd denominator fractional quantum Hall state formed within the monolayer-like band of TLG. Specifically, I demonstrate the universality of the scaling exponent, which governs the localization to delocalization phase transitions in the quantum Hall regime. Surprisingly, we observe this scaling exponent to be identical to that for the integer quantum Hall transitions. Moreover, we observe the sequence of FQHE at filling factor ν = 7/3 ,12/5 ,10/3,17/5 and their particle-hole conjugates 1 − ν = 8/3 ,13/5 ,11/3,18/5 formed within monolayer-like the band to have very similar energy gaps, manifesting particle-hole symmetry at low perpendicular displacement fields, D. This symmetry breaks down at high D. Specifically, as D increases, the particle-hole conjugate states become more unstable. This is directly linked to Landau level mixing, a consequence that can be controlled by tuning with the electric field. Further, we explore the effect of high perpendicular biasing on monolayer-like and bilayer-like bands. We experimentally demonstrate the enhancement of the Lande-g factor between Nm =0+  and Nm =0+ under high electric fields within the ML-Like band. This enhancement is attributed to the intricate interplay of electron-electron interactions, which is probed directly through the LL Fan diagram.  Focusing on the impact within the BL-like band at very high electric fields, our study reveals the evolution of LLs from a gully coherent state with strong C3 symmetry resulting from the formation of three Dirac cones at low magnetic fields regime to a magnetic breakdown regime at high B. This transition leads to a rich pattern of LL crossings and multiple phase transitions between spin, valley, and orbital degree of freedom as the magnetic field is gradually increased, which were theoretically predicted but experimentally unexplored.