Session P65: 2D Materials: Twisted Bilayers

Tunable correlated insulator behavior in twisted double bilayer graphene

Recent evidence for correlated physics in moire superlattice systems has motivated numerous theoretical studies and predictions relating flat bands, interactions, topology, and the underlying dependence on twist angle. In particular, twisted structures of two Bernal-stacked graphene bilayers display transport signatures of correlated insulating states at quarter- and half-filling of the superlattice bands that appear at finite displacement fields. Here, we explore the detailed evolution of these features in the electronic structure via sensitive measurements of the electronic compressibility. By varying carrier density and displacement field in a dual-gate capacitor geometry, we tune the bands into the various incompressible regimes to shed light on the possible correlations. By applying in- and out-of-plane magnetic fields, we probe the spin character and Landau level spectrum of the moire bands and comment on the correspondence to existing theoretical predictions.   

Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene

We study ferromagnetism and its stability in twisted bilayer graphene. We show that in the perfectly flat band limit and at filling fractions $\pm 3/4$, the saturated ferromagnetic (spin and valley polarized) states are ideal ground state candidates in the large band-gap limit. By assuming a large enough substrate (hBN) induced sub-lattice potential, the same argument can be applied to filling fractions $\pm 1/4$. We estimate the regime of stability of the ferromagnetic phase around the chiral limit by studying the spectrum of one-magnon excitations. The instability of the ferromagnetic state is signaled by a negative magnon excitation energy. This approach allows us to deform the results of the idealized chiral model towards more realistic systems. Furthermore, we use the low energy part of the exact one-magnon spectrum to calculate the spin-stiffness of the Goldstone modes throughout the ferromagnetic phase. The value of spin-stiffness can determine the energy of charged skyrmions. We further calculate the spectrum of the gapped single valley-flip excitations. The valley-mode gap can be used to estimate the transition temperature of quantum anomalous Hall state.   

Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder

Stacking two graphene layers twisted by the `magic angle' generates flat energy bands, which in turn catalyzes various strongly correlated phenomena. At charge neutrality, transport measurements reveal superficially mundane semimetallicity in some samples yet robust insulation in others. We propose that the interplay between interactions and disorder admits either behavior, even when the system is strongly correlated and locally gapped. We argue that strong interactions supplemented by weak, smooth disorder stabilize a network of gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape --- even when an entirely different order is favored in the clean limit. Sufficiently small samples that realize a single domain are insulating. Conversely, multi-domain samples exhibit re-emergent massless Dirac fermions formed by gapless domain-wall modes, yielding semimetallic behavior. Our results highlight the crucial role that randomness can play in ground-state selection. We discuss experimental tests of our proposal.   

Evolution of charge modulation in twisted bilayer graphene near the magic angle

Twisting and stacking two layers of graphene with a twist-angle near "magic angle" flattens the energy band and significantly slows down the movement of charge carriers. The resulting strong electron-electron interactions favors the emergence of novel correlated phases, including a charge ordered stripe phase^[1]. Using STM on magic-angle twisted bilayer graphene with a gate tunable doping dependence, we study the evolution of the band structure with doping and its effect on the charge ordered state. When the flat band is empty or full it produces a pronounced STS spectroscopy peak which corresponds to a peak in the density of states. Bringing the Fermi level within the flat band we observe a correlation induced pseuodogap at the Fermi energy accompanied by a spatial variation of the charge distribution that breaks the C3 symmetry. We will report on the evolution of the charge ordered phase with temperature, magnetic field and on its relation to the pseudogap.

[1] Y. Jiang, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, J. Mao, E.Y. Andrei, Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene, Nature, 573 (2019) 91-95.   

Magic continuum in twisted bilayer WSe2: Mott state and superconductivity

Emergent quantum phases driven by electronic interactions can manifest in materials with narrowly dispersing, i.e. “flat", energy bands. Recently, flat bands have been realized in a variety of graphene-based heterostructures using the tuning parameters of twist angle, layer stacking and pressure, and resulting in correlated insulator and superconducting states. Here we report the experimental observation of similar correlated phenomena in twisted bilayer tungsten diselenide (tWSe₂), a semiconducting transition metal dichalcogenide (TMD). Unlike twisted bilayer graphene where the flat band appears only within a narrow range around a “magic angle", we observe correlated states over a continuum of angles, spanning 4° to 5.1°. Hall measurements supported by ab initio calculations suggest that the strength of the insulator is driven by the density of states at half filling, consistent with a 2D Hubbard model in a regime of moderate interactions. At 5.1° twist, we observe evidence of superconductivity upon doping away from half filling, reaching zero resistivity around 3 K. Our results establish twisted bilayer TMDs as a model system to study interaction-driven phenomena in flat bands with dynamically tunable interactions.
Reference: arXiV: 1910.12147   

Magic continuum in twisted bilayer WSe2: Correlated states under high magnetic field

Emergent quantum phases driven by electronic interactions can manifest in materials with
narrowly dispersing, i.e. “flat”, energy bands. Recently, flat bands have been realized in a variety
of graphene-based heterostructures using the tuning parameters of twist angle, layer stacking and
pressure, and resulting in correlated insulator and superconducting states. Here we report the
experimental observation of similar correlated phenomena in twisted bilayer tungsten diselenide
(tWSe2), a semiconducting transition metal dichalcogenide (TMD). We observed that a Mott-
like insulator appears at half band filling that can be sensitively tuned with displacement field
over a continuum of angles, spanning 4° to 5.1°. We further study the system under high
magnetic field. The interleaved Landau fans coming from band edge and full-filling of Moiré
cell show the first observed Hofstadter butterfly pattern in TMD. The strength of correlated
insulating state is modulated by magnetic field in an unusual way and the extra Landau fan
coming from half-filling shows complex patterns. These exotic features allow us to study the
interplay between topology, electronic correlations and magnetism in the flat band platform.   

Magic continuum in twisted bilayer WSe2: critical phenomena and phase transitions

Emergent quantum phases driven by electronic interactions can manifest in materials with narrowly dispersing, i.e. “flat", energy bands. Recently, flat bands have been realized in a variety of graphene-based heterostructures using the tuning parameters of twist angle, layer stacking and pressure, and resulting in correlated insulator and superconducting states. Here we report the experimental observation of similar correlated phenomena in twisted bilayer tungsten diselenide (tWSe2), a semiconducting transition metal dichalcogenide (TMD). Unlike twisted bilayer graphene where the flat band appears only within a narrow range around a “magic angle", we observe correlated states over a continuum of angles, spanning 4° to 5.1°. Hall measurements supported by ab initio calculations suggest that the strength of the insulator is driven by the density of states at half filling, consistent with a 2D Hubbard model in a regime of moderate interactions. At 5.1° twist, we observe evidence of superconductivity upon doping away from half filling, reaching zero resistivity around 3 K. This talk will focus on the critical phenomena and phase transitions in this system in an attempt to convey the uniqueness of its quantum phases.

Reference: arXiV: 1910.12147   

Designing quantum geometry and nonlinear responses in van der Waals homostackings

The recent discovery of magic-angle twisted bilayer graphene has attracted tremendous interest. Despite the excitement, an important open question is that whether layer stacking can enable other new dimensionalities that can be utilized to discover fundamentally new physics and functionalities. In this talk, I will show that van der Waals (vdW) homostackings can be used to very effectively design the quantum geometry and nonlinear or nonreciprocal responses of many vdW materials. Specifically, carefully designed homostackings can generate strong Berry curvature in the electronic structures of 2D materials. As a result, exotic nonlinear responses such as nonlinear Hall and circular photogalvanic effects are enabled in materials. Moreover, homostackings can turn many vdW materials, even graphene and transition metal dichalchogenides, into being ferroelectric, paving the way for realizing nonvolatile memory devices. The results are applicable to a wide range of vdW materials and therefore provide a new means to discover, control and harness emergent quantum phenomena in 2D devices.   

Moire Physics of Twisted Bilayers from the Fourier Transforms of Two-Center Amplitudes

The number of experimentally realized twisted bilayer systems has diversified over the last decade as exfoliation techniques have improved and novel phenomena have been observed. The theoretical progress in modeling these systems has been focused on a narrow subset of materials that have band structures or band edges near special points in momentum space, allowing an expansion of the Hamiltonian.

In twisted bilayer systems, the breaking of the mono-layer Bravais lattice translation symmetry induces off-diagonal couplings between monolayer Bloch States. In an effort to model the coarse-grained couplings we establish new integral results for the two dimensional Fourier Transforms of generalized Slater-Koster hopping amplitudes, for various radial scaling functions, in the form of a series which rapidly converges over the entire parameter space.

Applied with a first-order gradient expansion of the strain fields, we evaluate this continuum model approach in relation to commensurate band structure calculations for a variety of appropriate Van-der Waals bilayer structures.   

Phonons in Twisted Transition Metal Dichalcogenide Bilayers (“Twistnonics”): Ultra-soft Phasons, and a transition from Superlubric to Pinned Phase

The tunability of the interlayer coupling by twisting one layer with respect to another layer of two-dimensional materials provide a unique way to manipulate phonons and related properties. We refer to this engineering of phononic properties as "Twistnonics". We study the effects of twisting on low-frequency shear (SM) and layer breathing (LBM) modes in transition metal dichalcogenide (TMD) bilayer using atomistic classical simulations. We show that these low-frequency modes are extremely sensitive to twist and can be used to infer the twist angle. We find unique “ultra-soft” phason modes (frequency ≤ 1 cm⁻¹) for any non-zero twist, corresponding to an effective translation of the moiré lattice by relative displacement of the constituent layers in a non-trivial way. Unlike the acoustic modes, the velocity of the phason modes is quite sensitive to twist angle. As twist angle decreases, (θ ≤ 3^° , & ≥ 57^°) the ultra-soft modes represent the acoustic modes of the “emergent” soft moiré scale lattice. Also, new high-frequency SMs appear, identical to those in stable bilayer TMD (θ = 0^°/60^°). Our study reveals the possibility of an intriguing θ dependent superlubric to pinning behavior and of the existence of ultra-soft modes in all two-dimensional materials.   

Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands

We consider the core problem of Coulomb interactions within fractionally filled Moiré flat bands and demonstrate that the dual description in terms of holes, which acquire a non-trivial hole-dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. We find that the single-hole dispersion has a profound impact on the phase diagram: in experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent Fermi liquid states at band filling fractions down to 1/3 and 2/3 respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behaviour. We also show that fractional Chern insulators can form in twisted bilayer graphene aligned with boron nitride at band filling 1/3.   

Valley Jahn-Teller effect in Twisted Bilayer Graphene

The surprising insulating and superconducting states of narrow-band graphene twisted bilayers have been mostly discussed so far in terms of strong electron correlation, with little or no attention to phonons and electron-phonon effects. We found that, among the 33492 phonons of a fully relaxed θ=1.08° twisted bilayer, there are few special, hard, and nearly dispersionless modes that resemble global vibrations of the moiré supercell ('moiré phonons'). One of them, doubly degenerate at Γ, couples very strongly with the valley degrees of freedom, also doubly degenerate, realizing a so-called Exe Jahn-Teller (JT) coupling. The JT coupling lifts very efficiently all degeneracies which arise from the valley symmetry, and may lead, for an average atomic displacement as small as 0.5 mÅ, to an insulating state at charge neutrality. In addition, freezing the same phonon at a zone boundary point brings about insulating states at most integer occupancies of the four ultraflat electronic bands.

Ref:
M. Angeli, E. Tosatti and M. Fabrizio, Phys. Rev. X 9, 041010 (2019)   

Electron pairing instability in magic angle twisted bilayer graphene

Superconductivity is one of the most intriguing properties observed recently in magic angle twisted bilayer graphene. Its origin is evidently closely tied to the nearly flat low energy bands at magic angle, which possess both spin/valley flavor symmetries and unique topological properties. The precise mechanism of pairing remains unclear however. Here we make an unbiased assessment of different pairing models, taking both Coulomb interactions and effective interactions induced by electron-phonon coupling into account. We find that It is essential to account for the screening of Coulomb interactions by remote metallic gates which increase the momentum dependence of Coulomb interactions and open the door to unconventional pairing channels. I will also comment on orbital suppression of superconductivity by an in-plane magnetic field, and on the possibility of using the magnetic-field dependence of superconductivity to identify the pairing mechanism.