Correlated Electronic Phenomena in Twisted Bilayer Graphene

Twisted bilayer graphene consists of two atomically thin sheets of graphene overlaid with a small rotational misalignment, producing a long-wavelength moiré pattern. At a critical “magic” twist angle of approximately 1.1°, the system develops nearly flat electronic bands in which the kinetic energy of electrons is quenched and electron–electron interactions dominate. In this regime, a rich tapestry of correlated phases emerges, including Mott-like insulating states at commensurate fillings and unconventional superconductivity upon slight doping. Experimental studies have also revealed cascade-like resets of spectral weight, anomalies in electronic compressibility, sensitivity to in-plane and out-of-plane electric and magnetic fields, and signs of fragile topology linked to band geometry. The interplay of local moment formation, heavy quasiparticles and momentum-selective incoherent states points to a hierarchy of electronic phenomena that bridges weak-coupling instabilities and strong-coupling lattice models. This platform has not only deepened our understanding of two-dimensional quantum matter but also opened avenues for tunable quantum devices operating at the interface of topology, magnetism and superconductivity.

Research from Nature Portfolio

Recent studies have elucidated the emergence of heavy quasiparticles and cascade phenomena in the magic-angle regime without invoking conventional symmetry-breaking orders. By combining dynamical mean-field theory with self-consistent Hartree calculations, researchers have shown that the redistribution of spectral weight and oscillations of remote bands can be understood in terms of local moment formation and momentum-differentiated quasiparticle coherence. This approach accounts for asymmetric jumps in the inverse compressibility and predicts a sharp momentum dependence of incoherent weight that is tied to the fragile topological character of the flat bands.

Complementary work on a related moiré platform—twisted double bilayer graphene—has demonstrated how a vertical displacement field can isolate flat bands and stabilise correlated insulating and spin-triplet superconducting phases. A detailed phase diagram as a function of twist angle and displacement field reveals ferromagnetic insulators with non-trivial valley Chern numbers at half-filling, and superconductivity mediated by inter-valley pairing upon doping. This study highlights the potential of electrostatic control to tune correlation strength and to unveil novel orbital effects under in-plane fields.

Correlated Electronic Phenomena in Twisted Bilayer Graphene publication trend

The graph below shows the total number of articles in correlated electronic phenomena in twisted bilayer graphene across all publications each year (not limited to Nature Index journals).

Technical terms

Moiré pattern: A large-scale interference pattern formed by overlaying two periodic lattices with a small twist or lattice mismatch.

Magic angle: The specific twist angle (~1.1°) at which flat electronic bands appear in twisted bilayer graphene.

Flat bands: Energy bands with minimal dispersion, leading to low electron velocity and enhanced interaction effects.

Mott insulator: A state in which strong electron–electron repulsion localises charges, preventing conduction despite partially filled bands.

Wannier orbital: A spatially localised function constructed from Bloch states, useful for mapping continuum models onto lattice Hamiltonians.

Extended Hubbard model: A lattice model including on-site and further-neighbour interactions to describe correlated electrons in narrow bands.

Van Hove singularity: A divergence in the electronic density of states at energies where the band dispersion has saddle points.

Hartree–Fock approximation: A mean-field method that treats electron interactions by self-consistent fields, capturing exchange and direct Coulomb effects.

References

1. Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene. Nature Communications (2023).
2. Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene. Nature Communications (2019).
3. Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene. Physical Review X (2018).
4. Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene. Physical Review X (2018).
5. Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene. npj Quantum Materials (2019).
6. Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle. Physical Review X (2019).