STM Study of Quantum Hall Isospin Ferromagnetic States of Zero Landau Level in Graphene Monolayer

TL;DR

This study uses atomic-scale imaging to explore quantum Hall isospin ferromagnetic states in graphene's zero Landau level, revealing spin and valley splitting behaviors and an interaction-driven density wave at charge neutrality.

Contribution

It provides the first atomic-scale imaging of QHIFM states in graphene, demonstrating direct visualization of wavefunctions and density waves associated with these states.

Findings

Valley splitting scales linearly with magnetic field.

Spin degeneracy is lifted by magnetic fields at all fillings.

Density wave with Kekule distortion observed at charge neutrality.

Abstract

A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the relativistic zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor v = 0 of charge-neutral graphene, have been extensively explored in experiment. To date, identification of these high-field broken-symmetry states has mostly relied on macroscopic transport techniques. Here, we study splitting of the zero LL of graphene at partial filling and demonstrate a direct approach by imaging the QHIFM states at atomic scale with a scanning tunneling microscope. At half filling of the zero LL (v = 0), the system is in a spin unpolarized state and we observe a linear magnetic-field-scaling of valley splitting. Simultaneously, the spin degeneracy in the two valleys is also lifted by the magnetic fields. When the Fermi level lies inside the spin-polarized states (at v = 1 or -1), the spin splitting is dramatically enhanced because of the strong many-body effects. At v = 0, we direct image the wavefunctions of the QHIFM states at atomic scale and observe an interaction-driven density wave featuring a Kekule distortion, which is responsible for the large gap at charge neutrality point in high magnetic fields.