Observation of interband collective excitations in twisted bilayer graphene (original) (raw)
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arXiv (Cornell University), 2021
The emergence of alternating twist multilayer graphene (ATMG) as a generalization of twisted bilayer graphene (TBG) raises the question-in what important ways do these systems differ? Here, we utilize a combination of techniques including ab-initio relaxation and single-particle theory, analytical strong coupling analysis, and Hartree-Fock to contrast ATMG with n = 3, 4, 5,. .. layers and TBG. I: We show how external fields enter in the decomposition of ATMG into twisted bilayer graphene and graphene subsystems. The parallel magnetic field is expected to have a much smaller effect when n is odd due to mirror symmetry, but surprisingly also for any n > 2 if we are are the largest magic angle. II: We compute the lattice relaxation of the multilayers leading to the effective parameters for each TBG subsystem as well as small mixing between the subsystems. We find that the second magic angle for n = 5, θ ≈ 1.14, provides the closest realization of the "chiral" model and is protected from mixing by mirror symmetry. It may be an optimal host for fractional Chern insulators. III: When there are no external fields, we integrate out the non-magic subsystems and reduce ATMG to the magic angle TBG subsystem with a screened interaction. IV: We perform an analytic strong coupling analysis of the effect of external fields and corroborate our results with numerical Hartree Fock simulations. For TBG itself, we find that an in-plane magnetic field can drive a phase transition to a valley Hall state or a gapless "magnetic semimetal" while having a weaker effect on n ≥ 3 ATMG at the first magic angle. In contrast, displacement field (V) has very little effect on TBG, but induces a gapped phase in ATMG for small V for n = 4 and above a finite critical V for n = 3. For n ≥ 3, we extract the superexchange coupling-believed to set the scale of superconductivity in the skyrmion mechanism-and show that it increases with V at angles near and below the magic angle. V: We complement our strong coupling approach with a phenomenological weak coupling theory of ATMG pair-breaking. While for n = 2 orbital effects of the in-plane magnetic field can give a critical field of the same order as the Pauli field, for n > 2 we expect the critical field to exceed the Pauli limit. Contents I. Introduction 2 II. Non-Interacting Band Structure and Symmetries 4 III. Lattice Relaxation Results 6 IV. Interacting Multilayers without external fields: magic TBG and Dirac cones decouple modulo screening 8 A. Graphene electrons screen the Coulomb interaction for TBG electrons 8 B. Insulating ground states for magic sector 9 C. Non-magic electrons remain semimetallic and decoupled 10 V. Effect of external fields on magical insulators and Dirac cones 11 A. n = 2 MATBG 11 B. n = 3 sandwiches: Mirror Superexchange and Graphene mass generation 12 C. n = 4 and beyond 14 VI. Weak coupling theory of pair-breaking 15 A. n = 2 B. n = 3 C. General n VII. Conclusions VIII. Acknowledgements References SI. Review of the mapping twisted multilayer graphene to TBG A. Trilayer n = 3 B. Tetralayer n = 4 C. n = 5 SII. Lattice relaxation A. Summary of relaxation calculation B. Effect of lattice relaxation on magic angles and the multilayer mapping SIII. Intra-TBG effects of external fields A. External fields in n = 2 MATBG 1. Electric field 2. Magnetic field B. Even n¿2
Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist
Nature Physics, 2020
Bilayer graphene was theorized to host a moiré miniband with flat dispersion if the layers are stacked at specific twist angles known as the "magic angles" 1,2. Recently, such twisted bilayer graphene (tBLG) with the first magic angle twist was reported to exhibit correlated insulating state and superconductivity 3,4 , where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Tunneling spectroscopy 5-9 and electronic compressibility measurements 10 in tBLG have revealed a van Hove singularity that is consistent with the presence of the flat miniband. However, a direct observation of the flat dispersion in the momentumspace of such moiré miniband in tBLG is still elusive. Here, we report the visualization of the flat moiré miniband by using angle-resolved photoemission spectroscopy with nanoscale resolution (nanoARPES). The high spatial resolution in nanoARPES enabled the measurement of the local electronic structure of the tBLG. We clearly demonstrate the existence of the flat moiré band near the charge neutrality for tBLG close to the magic angle at room temperature.
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using an all-band Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at some integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the correlated insulating states at ±1/2 filling and at the charge neutrality point are all valley polarized states which break C 2z and time-reversal (T) symmetries but preserve C 2z T symmetry. Such valley polarized states exhibit "moiré orbital antiferromagnetic ordering" on an emergent honeycomb lattice with compensating circulating current pattern in the moiré supercell. Within the same theoretical framework, our calculations indicate that the C = ∓1 QAH states at ±3/4 fillings of the magic-angle TBG are spin and orbital ferromagnetic states, which emerge when a staggered sublattice potential is present. We find that the nonlocalness of the exchange interactions tends to enhance the bandwidth of the low-energy bands due to the exchangehole effect, which reduces the gaps of the correlated insulator phases. The nonlocal exchange interactions also dramatically enhance the spin polarization of the system, which significantly stabilizes the orbital and spin ferromagnetic QAH state at 3/4 filling of TBG aligned with hexagonal boron nitride (hBN). We also predict that, by virtue of the orbital ferromagnetic nature, the QAH effects at electron and hole fillings of hBN-aligned TBG would exhibit hysteresis loops with opposite chiralities.
Local atomic stacking and symmetry in twisted graphene trilayers
arXiv (Cornell University), 2023
Moiré superlattices formed from twisting trilayers of graphene are an ideal model for studying electronic correlation, and offer several advantages over bilayer analogues, including more robust and tunable superconductivity and a wide range of twist angles associated with flat band formation. Atomic reconstruction, which strongly impacts the electronic structure of twisted graphene structures, has been suggested to play a major role in the relative versatility of superconductivity in trilayers. Here, we exploit an interferometric 4D-STEM approach to image a wide range of trilayer graphene structures. Our results unveil a considerably different model for moiré lattice relaxation in trilayers than that proposed from previous measurements, informing a thorough understanding of how reconstruction modulates the atomic stacking symmetries crucial for establishing superconductivity and other correlated phases in twisted graphene trilayers.
Flat band carrier confinement in magic-angle twisted bilayer graphene
Nature Communications, 2021
Magic-angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twist angle variation which has been studied elsewhere. Here, by using low temperature scanning tunneling spectroscopy and planar tunneling junction measurements, we demonstrate that flat bands in twisted bilayer graphene can amplify small doping inhomogeneity that surprisingly leads t...
Visualizing delocalized correlated electronic states in twisted double bilayer graphene
Nature Communications
The discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsi...