# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1904.06902