Additional levels between Landau bands due to vacancies in graphene: Towards defect engineering

Abstract

We describe the effects of vacancies on the electronic properties of a graphene sheet in the presence of a perpendicular magnetic field: from a single defect to an organized vacancy lattice. An isolated vacancy is the minimal possible inner edge, showing an antidotlike behavior, which results in an extra level between consecutive Landau levels. Two close vacancies may couple to each other, forming a vacancy molecule tuned by the magnetic field. We show that a vacancy lattice introduce an extra band in between Landau levels with localization properties that could lead to extra Hall resistance plateaus.

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

“…2 /h steps at higher energies (in contrast with the two 2e 2 /h steps in LL0) are rationalized by the fact that, even for the fully periodic case where random disorder broadening is absent, the two new states within each higher-energy LL are very close in energy [44]. Thus, unrealistically small broadening and a complete absence of disorder would be required to resolve the energy lifting of extended states for LLs different than LL0.…”

“…2), while the conductivity clearly resolves it. The different position of the peaks for SVs and DVs is reminiscent of their behavior when arranged in periodic arrays [44].…”

“…In this article, by using efficient computational methods, we provide tangible numerical insight into the rich physics of the QHE in disordered graphene, backing up the single-particle scenarios [38][39][40][41][42]44] in which dense distributions of defects can explain the formation of a zero-energy plateau in disordered graphene [29,30] and the presence of sets of extended states in Hall measurements [28,31]. In the presence of single vacancies (SVs) and double vacancies (DVs), critical states are found to preclude the formation of the usual graphene LLs.…”

Quantum transport in graphene Hall bars: Effects of vacancy disorder

“…However, the lowest field considered in that reference (beside B = 0 T) was around 300 T, therefore our results can be understood as a low field limit of those presented in Ref. 25.…”

“…For example, Ref. 25 showed that vacancy coupling does not depend on their type, however, we showed that these states have a certain symmetry, therefore the coupling strength will also depend on direction, and not only on distance. Divacancies also cause localization, but for fields that we consider, their localization energies are much closer to those of the relativistic LLs, which makes them harder to observe experimentally.…”