# Dirac Electrons in One, Two and Three Dimensions

# Dirac Electrons in One, Two and Three Dimensions

Dirac materials, with their characteristic linear energy dispersion and high electron mobility, provide a unique playground for exploring upcoming ideas in condensed matter physics, such as the interplay of symmetry, geometry and topology, with electrical transport measurements. I will describe ongoing experiments in my lab at the University of Utah studying such materials in one, two and three dimensions. With 3D topological insulators (TIs)(materials which are insulating in the bulk but conducting on surfaces), we report five-layer van der Waals heterostructures with boron nitride dielectrics and graphite gates for individually controlling charge densities of top and bottom surfaces. Using such structures and tuning thickness of the 3D TI down to the few-nm-thin limit, we report an array of effects as a function of TI thickness: (i) In the thick (~100 nm) TI limit, we observe individually tunable half-integer quantum Hall effects (in units of e2/h) of uncoupled TI surfaces, which are signatures of Dirac fermions due to their geometric Berry’s phase; (ii) For intermediate thickness, we observe strong capacitive coupling in the quantum Hall regime, including gap opening at charge neutrality, possibly due to interaction effects; (iii) For ultra-thin (<5 nm) TIs, we obtain gap opening and massive Dirac fermions due to strong inter-surface tunneling. I will also discuss our recent work with 2D ABC trilayer graphene boron nitride moire superlattices studying topological flat bands in these systems. Finally, I will talk about our recent results in 1D carbon nanotubes, together with the Minot group, where we study a quantum interference between electrons circling the nanotube in the CW versus CCW direction, due to deviations from a Dirac bandstructure, which we use to obtain structural information of our system.