Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
Yuan Cao, Daniel Rodan-Legrain, Jeong Min Park, Fanqi Noah Yuan, Kenji Watanabe, Takashi Taniguchi, Rafael M. Fernandes, Liang Fu, Pablo Jarillo-Herrero
Strongly interacting electrons in solid-state systems often display tendency towards multiple broken symmetries in the ground state. The complex interplay between different order parameters can give rise to a rich phase diagram. Here, we report on the identification of intertwined phases with broken rotational symmetry in magic-angle twisted bilayer graphene (TBG). Using transverse resistance measurements, we find a strongly anisotropic phase located in a 'wedge' above the underdoped region of the superconducting dome. Upon crossing the superconducting dome, a reduction of the critical temperature is observed, similar to the behavior of certain cuprate superconductors. Furthermore, the superconducting state exhibits a anisotropic response to an directional-dependent in-plane magnetic field, revealing a nematic pairing state across the entire superconducting dome. These results indicate that nematic fluctuations might play an important role in the low-temperature phases of magic-angle TBG, and pave the way for using highly-tunable moiré superlattices to investigate intertwined phases in quantum materials.
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena magic-angle twisted bilayer graphene hosts superconductivity, interaction induced insulating states, magnetism, electronic nematicity, linear-in-T low-temperature resistivity, and quantized anomalous Hall states. We highlight some key research results …
Due to its potential connection with nematicity, electronic anisotropy has been the subject of intense research effort on a wide variety of material platforms. The emergence of spatial anisotropy not only offers a characterization of material properties of metallic phases, which cannot be accessed via conventional transport techniques, but it also provides a unique window into the interplay between Coulomb interaction and broken symmetry underlying the electronic order. In this work, we utilize a new scheme of angle-resolved transport measurement (ARTM) to characterize electron anisotropy in m…
Strongly correlated quantum matter exhibits a rich variety of remarkable properties, but the organizing principles that underlie the behavior remain to be established. Graphene heterostructures, which can host narrow moire electron bands that amplify the correlation effect, represent a new setting to make progress on this overarching issue. In such correlated moire systems, an insulating state is a prominent feature of the phase diagram and may hold the key to understanding the basic physics. Here we advance the notion of a fragile insulator, a correlation-driven insulating state that is on th…
We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry breaking patterns, having therefore complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half-filling…
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…
In crystalline solids the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in 'magic-angle' bilayer graphene. Much less explored is rhombohedral graphite (RG), perhaps the simplest and structurally most perfect condensed matter system to host a flat band protected by symmetry. By scanning tunneling microscopy we map the flat band charge density of 8, 10 and 17 layers and identify a domain structure emerging from a competition between a sublattice antiferromagnetic insulator…
The discovery of magic angle twisted bilayer graphene (MATBG) has unveiled a rich variety of superconducting, magnetic and topologically nontrivial phases. The existence of all these phases in one material, and their tunability, has opened new pathways for the creation of unusual gate tunable junctions. However, the required conditions for their creation - gate induced transitions between phases in zero magnetic field - have so far not been achieved. Here, we report on the first experimental demonstration of a device that is both a zero-field Chern insulator and a superconductor. The Chern ins…
Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($ν=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($ν=2$) owing to competing intervalley coherent states, as well as spin-polarized and …
The dominance of Coulomb interactions over kinetic energy of electrons in narrow, non-trivial moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases such as correlated insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most of these phases occur at or near an integer number of carriers per moiré unit cell. Experimental demonstration of ordered states at fractional moiré band-fillings at zero applied magnetic field $B$, is a challenging pursuit. In this letter, we report the observation of states near half-inte…
Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
We study theoretically a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows to switch on/off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field $D_0$, and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with $D_0$; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase t…
We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and s…
Contribution of remote bands to orbital magnetization in twisted bilayer graphene
ShanghaiTech University（上海科技大学）；State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（量子功能材料国家重点实验室，上海科技大学物理科学与技术学院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（凝聚态物理北京国家实验室和中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, Boston College（波士顿学院物理系）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Department of Physics and Institute for Quantum Science and Technology, Shanghai University（上海大学物理系和量子科学技术研究院）；Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University（上海高温超导重点实验室，上海大学）
The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a TBG-like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Călugăru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings $ν=-3, -2, -1$ and $0$ measured from charge neutrality. We study the phase diagram with $w_0/w_1$, the ratio of $AA$ and $AB$ interlayer hoppings, and the displacement field, which introduces an interlayer potential $U$ and hybridize…
