Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene (2007.06115v3)

Abstract: In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by the interplay of the moire superlattice with the B, which endow the flat bands with a substructure of topologically nontrivial subbands characteristic of the Hofstadter butterfly. The new phases can be accounted for in a Stoner picture in which exchange interactions favor polarization into one or more spin- and valley-isospin flavors; in contrast to conventional quantum Hall ferromagnets, however, electrons polarize into between one and four copies of a single Hofstadter subband with Chern number C=-1. In the case of the C=\pm3 insulators in particular, B catalyzes a first order phase transition from the spin- and valley-unpolarized B=0 state into the ferromagnetic state. Distinct from other moire heterostructures, tBLG realizes the strong-lattice limit of the Hofstadter problem and hosts Coulomb interactions that are comparable to the full bandwidth W and are consequently much stronger than the width of the individual Hofstadter subbands. In our experimental data, the dominance of Coulomb interactions manifests through the appearance of Chern insulating states with spontaneously broken superlattice symmetry at half filling of a C=-2 subband. Our experiments show that that tBLG may be an ideal venue to explore the strong interaction limit within partially filled Hofstadter bands.

• The paper demonstrates that moderate magnetic fields in tBLG induce Hofstadter subband ferromagnetism and symmetry-broken Chern insulators with distinct Chern numbers.
• It employs a Stoner-like exchange mechanism, where a first-order phase transition at Chern numbers ±3 shifts states from non-magnetic to ferromagnetic.
• The findings deepen our understanding of correlated electron states and suggest promising applications in spintronics and quantum computing.

Hofstadter Subband Ferromagnetism and Symmetry Broken Chern Insulators in Twisted Bilayer Graphene

The paper explores the novel electronic properties of twisted bilayer graphene (tBLG) under moderate external magnetic fields. Specifically, the authors present evidence for the emergence of Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in this unique material system. The findings expand on the understanding of tBLG's complex phase diagram by identifying new magnetic phenomena not readily observable at zero external magnetic field.

At a twist angle of approximately 1.1 degrees, twisted bilayer graphene is known to host a pair of low-energy flat bands, which have previously been associated with a plethora of quantum phenomena, including insulating, superconducting, and magnetic states. These phenomena are observed at partial fillings of the flat bands. The current paper shifts attention from prior investigations predominantly focused on zero-field properties and introduces magnetic fields to explicate the emergence of new electronic phases.

In moderate magnetic fields, the authors report a sequence of ferromagnetic Chern insulators characterized by different Chern numbers, specifically $|C| = 1, 2$, and $3$. The interplay between the magnetic field and the moiré superlattice transforms the flat bands into a series of topologically nontrivial subbands, tracing the familiar fractal pattern known as the Hofstadter butterfly. This fractal structure, once theorized by Hofstadter in 1976, is marked by the intricate behavior of electron wave functions under the combined influence of a magnetic field and a periodic potential.

The ferroelectricity present in Chern insulators results from a Stoner-like mechanism, wherein the exchange interactions energetically favor aligning spins in particular subbands. Notably, at Chern numbers $C = \pm 3$, the application of a magnetic field prompts a first-order phase transition from a non-magnetic to a ferromagnetic state, indicating the field's role as a critical variable controlling the degree of polarization across the subbands.

Distinct from previously studied moiré heterostructures, tBLG under the influence of these medium-strength fields probes the strong-lattice limit of the Hofstadter problem. The experimental data show this system's superior capability to sustain strong correlation effects, as evidenced by the appearance of Chern insulating states at half-filling of a $C=-2$ subband, accompanied by spontaneous symmetry breaking.

The implications for such findings in twisted bilayer graphene are multifaceted. Theoretically, they contribute to the understanding of correlated electron states and topological phases in low-dimensional systems. Practically, the results suggest potential pathways for utilizing tBLG's unique band structure for application in spintronic devices and quantum computing, in which control over nontrivial topology could play a critical role.

Looking ahead, these insights open avenues for exploring the phases of matter that arise at fractional fillings of Chern bands and their dependencies on external perturbations like magnetic fields and interlayer twist angle. The field could steer toward further visualizing the impact of these variables on Hofstadter landscape scenarios using advanced spectroscopic techniques, possibly leading to realizations of more exotic quantum states critical for next-generation technology.