Imaging tunable quantum Hall broken-symmetry orders in graphene

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Strongly Correlated Electron Systems

Background:

• Electrons in flat bands exhibit negligible kinetic energy, leading to exotic many-body states driven by Coulomb interactions.
• The zeroth Landau level in graphene is a prime example of a strongly interacting flat band, theoretically predicted to host diverse broken-symmetry states.

Purpose of the Study:

• To directly visualize and characterize the lattice-scale orders of broken-symmetry phases in graphene.
• To explore the tunability of these phases by manipulating Coulomb interaction screening and magnetic fields.

Main Methods:

• Utilized scanning tunnelling spectroscopy to image distinct broken-symmetry phases in graphene.
• Investigated the phase diagram by varying the dielectric environment (low/high dielectric constant) and magnetic field strength.

Main Results:

• Identified a Kekulé bond order in unscreened graphene, aligning with Kosterlitz-Thouless transition observations.
• Observed a sublattice-unpolarized ground state under dielectric screening at low magnetic fields, transitioning to a charge-density-wave order with partial sublattice polarization at higher fields.
• Discovered secondary lattice-scale orders coexisting with Kekulé and charge-density-wave orders, expanding beyond theoretical predictions.

Conclusions:

• Direct visualization confirms multiple broken-symmetry phases in graphene, tunable via dielectric screening.
• The findings reveal a richer phase diagram than predicted, highlighting the importance of Coulomb interaction screening.
• This work provides a valuable platform for exploring correlated phases in other quantum materials.