Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session K56: Twisted Bilayer Graphene: Structure and Emergent PhasesRecordings Available

Hide Abstracts 
Sponsoring Units: DCMP Chair: Eslam Khalaf, Harvard University Room: Hyatt Regency Hotel Burnham 
Tuesday, March 15, 2022 3:00PM  3:12PM 
K56.00001: Anomalous electronphonon coupling in magicangle twisted bilayer graphene. Andreij Gadelha We investigate the electronphonon coupling properties of magicangle twisted bilayer graphene (MATBG) using gatedependent Raman spectroscopy. We use illumination from the bellow and iongate to dope MATBG highly. Thus, we monitor the electronphonon coupling through the CC stretching mode (G band) linewidth as a function of gate voltage. We then compare the MATBG results with largeangle twisted bilayer graphene and Bernal bilayer. We support our results with an atomistic model that reveals a unique MATBG electronphonon coupling signature influenced by its singular electronic and solitonic structures. Our results point to a relationship between electronphonon 
Tuesday, March 15, 2022 3:12PM  3:24PM 
K56.00002: Torsional Periodic Lattice Distortion in Twisted Bilayer Graphene Suk Hyun Sung, Yin Min Goh, Hyobin Yoo, Rebecca Engelke, Philip Kim, Robert Hovden Periodic lattice distortions (PLD) are at the heart of correlated electronic behavior such as superconductivity, metalinsulator transitions, and charge density waves. PLDs are typically intrinsic to a crystal, Fermisurface driven, accompanied by a CDW, and have periodicity spanning a few unit cells (~1–2nm). Recently, extrinsic van der Waals driven superlattices with tunable periodicity (up to a few 100nm) was discovered in twisted bilayer graphene (tBLG). tBLG has been spotlighted for extraordinary correlated electron behaviors at the socalled "magic" angle (1.1°). The structure of tBLG is a complex moiré material where relaxation between layers acts to minimize high energy AA regions and maximize low energy AB. Here, we provide an atomic description of tBLG superlattices at and near the magic angle using a torsional PLD and report the torsional PLD amplitude of 7.8 ± 0.6 pm and 6.1 ± 0.4 pm for twist angle of 1.1° and 1.2°. The PLD amplitude was quantified by matching experimental and simulated diffraction intensities. The atomic rearrangement is remarkably well described with a single coefficient in a single harmonic torsional PLD that can be extracted from a single experimental diffraction pattern. 
Tuesday, March 15, 2022 3:24PM  3:36PM 
K56.00003: Wigner crystallization at large fine structure constant Sandeep Joy, Brian Skinner At low electron density, massive Dirac electrons can form a Wigner crystal phase if the ratio of interaction energy to Fermi energy is very large. The strength of Coulomb interactions in Dirac systems is characterized by the effective fine structure constant, α=e^{2}/∈_{r}hv, where h is the reduced Planck’s constant, v is the Dirac velocity, and ∈_{r} is the dielectric constant. We discuss the fate of the Wigner crystal, including its quantum and thermal melting, as α is increased. We show that in the limit of large α, the critical density and critical temperature associated with melting approaches a constant universal value due to the renormalization of the electron charge by the interband dielectric response. Our results have implications for twisted bilayer graphene, where α becomes very large near the magic angle. 
Tuesday, March 15, 2022 3:36PM  3:48PM 
K56.00004: Stackingdependent binding energy of bilayer graphene from diffusion Monte Carlo Kittithat Krongchon, Tawfiqur Rakib, Elif Ertekin, Harley T Johnson, Lucas K Wagner The phase diagram of twisted bilayer graphene as described by the electronic properties is sensitive to geometry relaxations, the determination of which requires an accurate description of the van der Waals interaction between bilayers. However, there does not exist enough accurate data to fully parameterize the registry dependence between the bilayers. We use the accurate [PRL 115 115501 (2015)] diffusion Monte Carlo (DMC) to parameterize the interaction between layers of graphene. The large DMC data set of 36 energy evaluations as a function of registry is used to refit the Kolmogorov–Crespi potential [PRB 71 235415 (2005)]. The new parameterization results in larger grain boundaries between regions of AB stacked graphene in the moiré lattice. We will discuss the effects of this difference in atomic structure on the electronic structure of bilayer graphene. 
Tuesday, March 15, 2022 3:48PM  4:00PM 
K56.00005: An accurate tight binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation Shivesh Pathak, Tawfiqur Rakib, Run Hou, Andriy H Nevidomskyy, Elif Ertekin, Harley T Johnson, Lucas K Wagner A major hurdle in understanding the phase diagram of twisted bilayer graphene (TBLG) are the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an accurate local environment tight binding model (LETB) fit to tight binding parameters computed from ab initio density functional theory (DFT) calculations across many atomic configurations. With the accurate parameterization, it is found that the magic angle shifts to slightly lower angles than often quoted, from around 1.05 degrees to around 0.99 degrees, and that isolated flat bands appear for rigidly rotated graphene layers, with enhancement of the flat bands when the layers are allowed to distort. Study of the orbital localization supports the emergence of fragile topology in the isolated flat bands without the need for lattice relaxation. 
Tuesday, March 15, 2022 4:00PM  4:12PM 
K56.00006: Fractional Chern Insulators and Hofstadter Band Geometry in MagicAngle Graphene Daniel E Parker, Patrick J Ledwith, Eslam Khalaf, Tomohiro Soejima, Johannes Hauschild, Ashvin Vishwanath Fractional Chern Insulators (FCIs) generalize the celebrated fractional quantum hall effect to the lattice setting. A number of theoretical proposals have suggested (hBNaligned) magicangle graphene (MATBG) is a prime candidate for realizing FCIs, as its bandstructure and quantum geometry are relatively close to that of the lowest Landau level. Indeed, this was borne out in a recent experiment, which observed 8 FCIs in hBNMATBG at magnetic fields as low as 5 Tesla. This talk will examine a constellation of questions surrounding this experiment. Can we understand the appearance of these FCIs? What quantum geometric conditions are necessary to favor FCIs in the minibands of the Hofstadter butterfly? Can MATBG support FCIs without an external field? 
Tuesday, March 15, 2022 4:12PM  4:24PM 
K56.00007: Fractons in moir\'e materials Dan Mao, Kevin Zhang, Zhen Bi, EunAh Kim As a unique opportunity hosted by the magic angle twisted bilayer graphene (MATBG), the emergence of a novel fractional correlated insulating (FCI) state dictated by the geometry of the threepeak structure of Wannier orbitals has been proposed [1]. While Ref.[1] established the novel FCI state with extensive groundstate landscape at the filling of $n\pm1/3$ from rigorous considerations in the strong coupling limit, little is known about the nature of excitations. At the same time, novel correlated ground states often host unusual excitations. In this talk, I will discuss the nature of two distinct fractionalized excitations in the FCI phase. : (1) fractonlike vortices and (2) solitonlike domain wall edge states. Although both types of excitations carry fractional electric charges, their topological charges are distinct. Moreover, both defects' movements are restricted to emergent lowdimensional subspace embedded in the twodimensional (2D) space of MATBG and hence ``fractonic''. Specifically, fractonic vortices are immobile while the domain wall edge states' motion is restricted along one direction, behaving much like a 2D version of solitons in a SuSchrifferHeeger chain. We discuss implications of these fractonic excitations on the bandwidth tuned and doping tuned phase transition from the fractional correlated insulator phase to the Fermi liquid phase. We also discuss how magnetism can intertwine with dynamics of the fractons. We propose experiments to pursue these fractons in the partially filled (n\pm1/3) magic angle twisted bilayer graphene is tantalizing. 
Tuesday, March 15, 2022 4:24PM  4:36PM 
K56.00008: Fractional correlated insulating states at n±1/3 filled magic angle twisted bilayer graphene Kevin Zhang, Yang Zhang, Liang Fu, EunAh Kim Although much progress has been made on the physics of magic angle twisted bilayer graphene at integer fillings, little attention has been given to fractional fillings. Here we show that the threepeak structure of Wannier orbitals, dictated by the symmetry and topology of flat bands, facilitates the emergence of a novel state at commensurate fractional filling of ν=n±1/3. We dub this state a ``fractional correlated insulator'' [1]. Specifically for the filling of 1/3 electrons per moiré unit cell, we show that shortrange interactions alone imply an approximate extensive entropy due to the ``breathing" degree of freedom of an irregular honeycomb lattice that emerges through defect lines. The leading furtherrange interaction lifts this degeneracy and selects a novel ferromagnetic nematic state that breaks AB/BA sublattice symmetry. The proposed fractional correlated insulating state might underlie the suppression of superconductivity at ν=21/3 filling observed in Ref. [2]. Further investigation of the proposed state would open doors to new regimes of correlation effects in MATBG. 
Tuesday, March 15, 2022 4:36PM  4:48PM 
K56.00009: Landau level degeneracy lifting by the emergence of massive quasiparticles in magicangle twisted bilayer graphene Shuang Wu, Zhenyuan Zhang, Kenji Watanabe, Takashi Taniguchi, Eva Y Andrei In twisted bilayer graphene, when reducing the twist angle towards the magic angle, ~1.1°, a transition from 8fold to 4fold band degeneracy is observed by quantum oscillations in perpendicular magnetic fields exceeding several Tesla. Lowfield quantum oscillations can provide direct insights into the origin of the lifted degeneracy. Here we report on magnetotransport measurements of a multiterminal twisted bilayer graphene device with a twist angle of 1.17°±0.02° .^{1} We find that even at very low magnetic fields, B=0.4T, the Landau sequence already exhibits 4fold degeneracy. Furthermore, Shubnikovde Haas oscillation on the Landau fan emanating from the charge neutrality point (CNP), reveal a zero Berry phase, contrary to the π/2 phase expected for massless Dirac fermions. This shows that the reduced degeneracy is a consequence of emergent interactioninduced massive quasiparticles, in contrast to noninteracting band structure calculations that find Dirac cones at the CNP. Thus, a correct description of the system must include correlations effects even at the lowest fields. 
Tuesday, March 15, 2022 4:48PM  5:00PM 
K56.00010: Twist induced ferromagnetism in a bilayer graphene nanoflex Dharmendra Pant, Sandip Aryal, Subhasish Mandal, Ranjit Pati Twisted bilayer graphene shows various interesting phenomena like superconductivity, anomalous Hall effect, and ferromagnetism at a magic angle close to 1.1º. In this talk, we will discuss the observed ferromagnetism in a twisted bilayer graphene nanoflex (TBLGNF) using a firstprinciples approach. Our results demonstrate that when the energy gap of a TBLGNF approaches zero, electronic instability induced spontaneous reorganization of electrons leads to the emergence of a stable ferromagnetic gap state with porbitals at the boundary contributing to ferromagnetism [1]. We notice the ferromagnetic gap state appearing aperiodically between 0 and 30^{o}. A spin pairing mechanism is found to be responsible for the reappearance of the stable nonmagnetic phase when a ferromagnetic TBLGNF approaches an unstable metallic phase. 
Tuesday, March 15, 2022 5:00PM  5:12PM 
K56.00011: Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition Cecile Repellin, Senthil Todadri When one of the graphene layers of Magic Angle Twisted Bilayer Graphene is nearly aligned with its hexagonal boron nitride substrate (a configuration dubbed TBG/hBN), the active electronic bands are nearly flat, and have a Chern number C=±1. Recent experiments demonstrated a quantum anomalous Hall effect and spontaneous valley polarization at integer filling υ_{T}=3 of the conduction band in this system. Motivated by this discovery, we ask whether fractional quantum anomalous Hall states (FQAH) could also emerge in TBG/hBN. We focus on the range of filling fractions where valley ferromagnetism was observed experimentally. Using exact diagonalization, we find that the ground states at υ_{T}=10/3 and υ_{T}=17/5 are fractional Chern insulator states in the flat band limit (in the hole picture, these are the fractional quantum Hall fractions 2/3 and 3/5). The ground state is either spin polarized or a spin singlet depending sensitively on band parameters. For nominally realistic band parameters, spin polarization is favored. Flattening the Berry curvature by changing a band parameter gives way to the spin singlet phase. Our estimation of the charge gap in the flat band limit shows that the FQAH state may be seen at accessible temperatures in experiments. We also study the effect of a nonzero bandwidth and show that there is a reasonable range of parameters in which the FQAH state is the ground state. 
Tuesday, March 15, 2022 5:12PM  5:24PM 
K56.00012: Moiré Superlattices at Fractional Band Fillings: Emergent Fermi Liquids, Charge Density Waves and Fractional Chern Insulators Ahmed Abouelkomsan, Zhao Liu, Kang Yang, Emil J Bergholtz 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 nontrivial holedispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. We find that the singlehole 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. Moreover, we investigate the possible instabilites to the emergent Fermi surfaces and find competing charge density wave states at different commensurate fillings in the Moiré system ABC stacked trilayer graphene aligned with boron nitride. In addition, we predict both twisted bilayer graphene aligned with boron nitride and gatetunable twisted double bilayer graphene to be versatile platforms for the realization of fractional Chern insulator states like spinsinglet Halperin states and spin polarized states in bands with Chern number C =1 and C = 2 at zero external magnetic fields. 
Tuesday, March 15, 2022 5:24PM  5:36PM 
K56.00013: Band structure of the rippled twisted bilayer graphene Xu Han, Jianpeng Liu, Junwei Liu, Ding Pan The twisted bilayer graphene has attracted great interest due to its ability to manipulate new and rich electronic properties. It is known that 2D crystals may have some outofplane deformations to stabilize their atomic structures. Here, we studied how ripples may affect the electronic band structure of the twisted bilayer graphene using classical force fields and tightbinding models validated by density functional theory. We generated ripples by applying strain and found that the ripples may induce electric dipole moments perpendicular to the 2D plane, which may significantly affect the band structure of the twisted bilayer graphene close to the first magic angle. Our study suggests that small ripples may not obviously affect electronic properties of monolayer graphene, whereas they cannot be ignored when studying electronic properties of the twisted bilayer graphene. 
Tuesday, March 15, 2022 5:36PM  5:48PM 
K56.00014: Structural relaxation of twisted bilayer graphene approaching the magic angle by firstprinciples studies Martin Callsen, MeiYin Chou, ChiRuei Pan Twisted bilayer graphene has attracted a great amount of attention due to its various and peculiar electronic phases as the twisting angle becomes very small. As an example, alternating superconducting and correlated insulating phases depending on the band filling can be observed at the socalled magic angle around 1°. While the crucial role of structural relaxation in determining the electronic properties and the occurrence of flat bands in the electronic structure has already been pointed out, the involved system sizes have limited early theoretical studies to the outofplane deformation [1] or phenomenological models [2]. More recently, plane wavebased density functional theory (DFT) calculations [3, 4] showed oscillating relaxation patterns at low twisting angles, which is at odds with the earlier studies. Therefore, further investigation is required. 
Tuesday, March 15, 2022 5:48PM  6:00PM 
K56.00015: The moiré distortion effect on the flat band in twisted bilayer graphene. Naoto Nakatsuji, Mikito Koshino We theoretically investigated the effect of nonuniform distortion on the electronic structure of twisted bilayer graphene (TBG). Usually, the flat bands of TBG can be understood by the moiré band theory based on a regular periodicity of the moiré superlattice. 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2022 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
1 Research Road, Ridge, NY 119612701
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700