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Register a new userLarge-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene
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A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report the first definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moire patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic field can be fine-tuned by both the rotation angle and heterostrain applied to the system. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.
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We present a systematic study of the low-energy collective modes for different insulating states at integer fillings in twisted bilayer graphene. In particular, we provide a simple counting rule for the total number of soft modes, and analyze their energies and symmetry quantum numbers in detail. To study the soft mode spectra, we employ time dependent Hartree-Fock whose results are reproduced analytically via an effective sigma model description. We find two different types of low-energy modes - (i) approximate Goldstone modes associated with breaking an enlarged U(4)$times$U(4) symmetry and, surprisingly, a set of (ii) nematic modes with non-zero angular momentum under three-fold rotation. The modes of type (i) include true gapless Goldstone modes associated with exact symmetries in addition to gapped pseudo-Goldstone modes associated with approximate symmetries. While the modes of type (ii) are always gapped, we show that their gap decreases as the Berry curvature grows more concentrated. For realistic parameter values, the gapped soft modes of both types have comparable gaps of only a few meV, and lie completely inside the mean-field bandgap. The entire set of soft modes emerge as Goldstone modes of a different idealized model in which Berry flux is limited to a solenoid, which enjoys an enlarged U(8) symmetry. Furthermore, we discuss the number of Goldstone modes for each symmetry-broken state, distinguishing the linearly vs quadratically dispersing modes. Finally, we present a general symmetry analysis of the soft modes for all possible insulating Slater determinant states at integer fillings that preserve translation symmetry, independent of the energetic details. The resulting soft mode degeneracies and symmetry quantum numbers provide a fingerprint of the different insulting states enabling their experimental identification from a measurement of their soft modes.
We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a parallel field by forming a quadratic band crossing point (QBCP) at the Moire Brillouin zone center. Over a large range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible ramifications of our study to the interacting ground states of twisted bilayer graphene systems.
The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great deal of interest, sparked by the discovery of correlated insulating and superconducting states, for twist angle $theta$ close to a so-called magic angle $approx 1.1{deg}$. In this work, we unveil, via near-field optical microscopy, a collective plasmon mode in charge-neutral TBG near the magic angle, which is dramatically different from the ordinary single-layer graphene intraband plasmon. In selected regions of our samples, we find a gapped collective mode with linear dispersion, akin to the bulk magnetoplasmons of a two-dimensional (2D) electron gas. We interpret these as interband plasmons and associate those with the optical transitions between quasi-localized states originating from the moire superlattice. Surprisingly, we find a higher plasmon group velocity than expected, which implies an enhanced strength of the corresponding optical transition. This points to a weaker interlayer coupling in the AA regions. These intriguing optical properties offer new insights, complementary to other techniques, on the carrier dynamics in this novel quantum electron system.
Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when $ pm 1, pm 2, pm 3$ electrons occupy each moir e unit cell and lead to the formation of correlated insulating, superconducting and ferromagnetic phases. While some phases have been shown to carry a non-zero Chern number, the local microscopic properties and topological character of many other phases remain elusive. Here we introduce a set of novel techniques hinging on scanning tunneling microscopy (STM) to map out topological phases in MATBG that emerge in finite magnetic field. By following the evolution of the local density of states (LDOS) at the Fermi level with electrostatic doping and magnetic field, we visualize a local Landau fan diagram that enables us to directly assign Chern numbers to all observed phases. We uncover the existence of six topological phases emanating from integer fillings in finite fields and whose origin relates to a cascade of symmetry-breaking transitions driven by correlations. The spatially resolved and electron-density-tuned LDOS maps further reveal that these topological phases can form only in a small range of twist angles around the magic-angle value. Both the microscopic origin and extreme sensitivity to twist angle differentiate these topological phases from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions and exhibits an unexpected splitting between zero Landau levels that can be as large as ${sim },3-5$ meV. Our results show how strong electronic interactions affect the band structure of MATBG and lead to the formation of correlation-enabled topological phases.
Graphene-based moir{e} systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moir{e} unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moir{e} superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data [arXiv:2009.11645] to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moir{e} scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moire degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. We compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moir{e} systems.
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