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 magnetic field affects the Bloch band structure in a couple of ways. First it breaks the Bloch band into magnetic subbands or the Landau levels are broadened into magnetic Bloch bands. The resulting group of subbands in the central portion of the energy scale is associated with the integer quantum Hall effect (IQHE). Then at high fields it changes the integrated density of states of the remaining lowest and topmost subband, respectively, which can be associated with fractional quantum Hall effect (FQHE). Here, we employ the Maxwell Chern-Simons gauge theory to formulate the subband-gap map…
The nontrivial band topology can influence the Hofstadter spectrum. We investigate the Hofstadter spectrum for various models of Chern insulators under a rational flux $\frac{ϕ_{0}}{q}$, here $ϕ_{0}=\frac{h}{e}$ and $q$ being an integer. We find two major features. First, the number of splitting subbands is $|q-C|$ with Chern number $C$. Second, the anomalous open-orbit subbands with Chern numbers $q-1$ and $-q-1$ emerge, which are beyond the parameter window $(-q/2,q/2)$ of the Diophantine equation studied by Thouless-Kohmoto-Nightingale-den Nijs [Phys. Rev. Lett. \textbf{49}, 405 (1982)]. Th…
Applying a unified approach, we study integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) in the Hofstadter model with short range interaction between fermions. An effective field, that takes into account the interaction, is determined by both the amplitude and phase. Its amplitude is proportional to the interaction strength, the phase corresponds to the minimum energy. In fact the problem is reduced to the Harper equation with two different scales: the first is a magnetic scale (cell size corresponding to a unit quantum magnetic flux), the second scale (determines the…
Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model …
In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanni…
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected $2\times 2$ effective Hamiltonian including interlayer effective mass, interlayer coupling…
From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Collège de France（法兰西学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Sorbonne Université（索邦大学）
