Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours - such as spin or valley - that the electrons can undergo and the excitation spectrum of the broken symmetry states that they form. These properties cannot be probed directly with electrical transport measurements.

Following a crossover

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene.

Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands.

Reducing the energy bandwidth of electrons in a lattice below the long-range Coulomb interaction energy promotes correlation effects. Moiré superlattices—which are created by stacking van der Waals heterostructures with a controlled twist angle^1,2,3—enable the engineering of electron band structure. Exotic quantum phases can emerge in an engineered moiré flat band.

When a strong magnetic field is applied to a two-dimensional electron system, interactions between the electrons can cause fractional quantum Hall (FQH) effects^1,2.

Coulomb interaction between two closely spaced parallel layers of conductors can generate the frictional drag effect by interlayer Coulomb scattering. Employing graphene double layers separated by few‐layer hexagonal boron nitride, we investigate density tunable magneto- and Hall drag under strong magnetic fields. The observed large magnetodrag and Hall-drag signals can be related with Laudau level filling status of the drive and drag layers.

An exciton condensate is a Bose–Einstein condensate of electron and hole pairs bound by the Coulomb interaction^1,2.