Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session U63: Twisted 2D Heterostructures: Computational and Theoretical Studies II |
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Sponsoring Units: DCMP Chair: Nicolas Leconte Room: Mile High Ballroom 4D |
Thursday, March 5, 2020 2:30PM - 2:42PM |
U63.00001: Geometric and conventional contribution to superfluid weight in twisted bilayer graphene Xiang Hu, Timo Hyart, Dmitry I. Pikulin, Enrico Rossi We calculate the superfluid weight for twisted bilayer graphene (TBLG) taking into account both the conventional contribution and the contribution arising from the quantum geometry of the bands. We find that both contributions are larger than one would expect by treating the bands as well-isolated, that at the magic angle the geometric contribution is larger than the conventional one, and that for small deviations away from the magic angle the conventional contribution is larger than the geometric one. Our results show that, despite the flatness of the bands the superfluid weight in TBLG is finite and consistent with experimental observations. We also show how the superfluid weight can be tuned by varying the chemical potential and the twist angle opening the possibility to tune the nature of the superconducting transition between the standard BCS transition and the Berezinskii-Kosterlitz-Thouless transition. |
Thursday, March 5, 2020 2:42PM - 2:54PM |
U63.00002: Inherited and flatband-induced ordering in twisted graphene bilayers Lennart Klebl, Carsten Honerkamp The nature of the insulating and superconducting states in twisted bilayer graphene systems is intensely debated. While many works seek for explanations in the few flat bands near the Fermi level, theory and a number of experiments suggest that nontwisted bilayer graphene systems do exhibit – or are at least close to – an ordered, insulating ground state related to antiferromagnetic ordering. We investigate how this magnetic ordering scenario is affected by the slight twisting. We find that at charge neutrality the ordering tendencies of twisted systems interpolate between those of untwisted AA and AB stacked bilayers at intermediate temperatures, while at lower temperatures of the order of typical flat-band dispersion energies, the ordering tendencies are even enhanced for the twisted systems. The preferred order at charge neutrality still exhibits an antiferromagnetic spin arrangement, with ordered moments alternating on the carbon-carbon bonds, with an enveloping variation on the moiré scale (inhereted ordering). Even in the RPA analysis, the possible low-energy behaviors are quite versatile, and slight doping of one or more electrons per moiré cell can take the system into a, potentially flat-band induced, ferromagnetic phase. |
Thursday, March 5, 2020 2:54PM - 3:06PM |
U63.00003: Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene Hector Ochoa In twisted bilayer graphene, long-wavelength lattice fluctuations are dominated by phasons: acoustic collective modes resulting from coherent superpositions of optical phonons. At small twist angles, these modes describe the sliding motion of stacking domain walls separating regions of partial commensuration. The resulting soliton network is a soft elastic manifold, whose reduced rigidity arises from the competition between elastic and adhesion forces governing lattice relaxation. Shear deformations of the beating pattern dominate the electron-phason coupling. This coupling lifts the layer degeneracy of the Dirac cones at the corners of the moiré Brillouin zone, which could explain the observed fourfold (instead of eightfold) Landau level degeneracy. Electron-phason scattering gives rise to a linear-T resistivity that increases with decreasing twist angle due to the reduction of the stiffness of the soliton network. This contribution alone cannot explain the huge enhancement of the resistivity of the normal state close to the magic angle. I will discuss the connection between these soft collective modes and the widespread presence of twist angle disorder in the samples. |
Thursday, March 5, 2020 3:06PM - 3:18PM |
U63.00004: Spin-valley density wave in moiré materials Constantin Schrade, Liang Fu We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined. |
Thursday, March 5, 2020 3:18PM - 3:30PM |
U63.00005: Phonon scattering induced carrier resistivity in twisted double bilayer graphene Xiao Li, Fengcheng Wu In this work we carry out a theoretical study of the phonon-induced resistivity in twisted double bilayer graphene (TDBG), in which two Bernal-stacked bilayer graphene devices are rotated relative to each other by a small angle $\theta$. We show that at small twist angles ($\theta\sim 1^\circ$) the effective mass of the TDBG system is greatly enhanced, leading to a drastically increased phonon-induced resistivity in the high-temperature limit where phonon scattering leads to a linearly increasing resistivity with increasing temperature. We also discuss possible implications of our theory on superconductivity in such a system, and provide an order of magnitude estimation of the superconducting transition temperature. |
Thursday, March 5, 2020 3:30PM - 3:42PM |
U63.00006: Functional renormalization group analysis of many-body states in a large moiré unit cell systems Lennart Klebl, Dante M. Kennes, Carsten Honerkamp Layers of two-dimensional materials arranged at a twist angle with respect each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states. For the exploration of these, renormalization group methods are an appropriate, flexible tool that takes into account the mutual influence of competing tendencies. We we show how the functional renormalization group known from simpler two-dimensional systems can be employed for the large-unit cell moiré superlattices, providing a description on the atomic scale and absorbing available ab-initio information on the model parameters. For the case of twisted bilayer graphene models, we explore the leading ordering tendencies depending on the band filling and the range of interactions. The results indicate a delicate balance between distinct magnetically ordered ground states. |
Thursday, March 5, 2020 3:42PM - 3:54PM |
U63.00007: Three-Dimensional Topological Twistronics Fengcheng Wu, Ruixing Zhang We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle θ between successive layers. Our theory employs a nonsymmorphic symmetry that enables a precise definition of an effective out-of-plane crystal momentum, and also captures the in-plane moire pattern formed between neighboring twisted layers. To demonstrate the novel topological physics that can be achieved through 3D twistronics, we present two examples. In the first example of chiral twisted graphite, Weyl nodes arise because of inversion-symmetry breaking, with θ-tuned transitions between type-I and type-II Weyl fermions, as well as magic angles at which the in-plane velocity vanishes. In the second example of twisted Weyl semimetal, the twist in the lattice structure induces a chiral gauge field A that has a vortex-antivortex lattice configuration. Line modes bound to the vortex cores of the A field give rise to 3D Weyl physics in the moire scale. We also discuss possible experimental realizations of 3D twistronics. |
Thursday, March 5, 2020 3:54PM - 4:06PM |
U63.00008: Ferromagnetic Mott state in twisted graphene bilayers at the magic angle Kagnjun Seo, Valeri Kotov, Bruno Uchoa We address the effective tight-binding Hamiltonian that describes the insulating Mott state of twisted graphene bilayers at a magic angle [1]. In that configuration, twisted bilayers form a honeycomb superlattice of localized states, characterized by the appearance of flat bands with fourfold degeneracy. After calculating the maximally localized superlattice Wannier wave functions, we derive the effective spin model that describes the Mott state at quarter filling, which has an emergent SU(4) symmetry that is reminiscent of spin and valley quantum numbers. We suggest that the system is an exotic ferromagnetic Mott insulator, with well-defined experimental signatures. |
Thursday, March 5, 2020 4:06PM - 4:18PM |
U63.00009: Theory of generalized Wigner crystals in moire superlattices. Bikash Padhi, Chitra Ramasubramanian, Philip Phillips Recent developments in moire materials (twisted layers of graphene or transition metal compounds) has opened up a new avenue to realize quasi-flat bands in condensed matter systems in which the interactions dominate. Our previous calculations suggested that the correlations in such systems could be strong enough to realize electronic solids called Wigner crystals (WC). Such states have been observed before in (continuum) 2D electron gas and recently it was also claimed to be observed in a (moire lattice of) twisted bilayer of WS/WSe2. Despite the experimental advances, a clear understanding of the physics of WC coupled to an underlying lattice is completely lacking. In this talk we present some preliminary results based on a model we construct to address this problem. In such a scenario, melting of a WC (coupled to lattice) can be understood in terms of an interplay of coulomb interaction and the tendency for forming solitons. |
Thursday, March 5, 2020 4:18PM - 4:30PM |
U63.00010: Floquet flat-band engineering of twisted bilayer graphene Or Katz, Gil Refael, Netanel Lindner Twisted Bilayer Graphene at the magic twist angle features flat energy bands, which lead to superconducitvity and strong correlation physics. These unique properties are typically limited to an extremely narrow range of twist angles around the magic angle. Here we demonstrate that coherent optical irradiation could lead to emergence of flat isolated Floquet-Bloch bands at a wide range of small twist angles. At small twist angles larger than 1°, these bands exhibit non-trivial topology and a non-zero chern number. We show that the effect can potentially be realized with relatively weak optical beams at the visible-infrared range, potentially allowing for realization of optically tuned flat bands. |
Thursday, March 5, 2020 4:30PM - 4:42PM |
U63.00011: Mirror symmetry breaking and the stacking-shift effect in twisted trilayer graphene Chao Lei, Lukas Linhart, Wei Qin, Allan MacDonald A continuum model of twisted trilayer graphene devices was constructed using ab initio first principles theory to assess the dependence of electronic structure on local stacking. We have applied the model to study electronic structure and transport properties as a function of band filling. When the middle layer of Bernal stacking trilayer graphene is twisted a mirror symmetry exists which is absent in the case of twisted top layers and twisted bilayer graphene.The mirror symmetry decouples band with even and odd parity, but is lost when the top layer is shifted relative to the bottom layer or an electric field is applied.We study the consequences of mirror and C3v symmetry broking by this top layer lateral stacking shift effect or electric field, focusing on the electronic structure and transport properties such as the longitudinal and Hall conductivities of this system.Whereas a lateral shift has no effect for either top layer twisted trilayers or bilayers, large changes in electronic structure occur for middle-layer twisted trilayers. |
Thursday, March 5, 2020 4:42PM - 4:54PM |
U63.00012: Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach Stephen Carr, Shiang Fang, Hoi Chun Po, Ashvin Vishwanath, Efthimios Kaxiras The complexity of the atomic-scale structures in twisted bilayer graphene (TBG) has made even the study of single-particle physics at low energies around the Fermi level challenging. We provide a convenient and physically motivated picture of single-particle physics in TBG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of ab initio tight-binding models, including the effects of atomic relaxations. We obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between 1.3° and 0.6°. |
Thursday, March 5, 2020 4:54PM - 5:06PM |
U63.00013: Collective Modes in Magic-Angle Twisted Bilayer Graphene Ajesh Kumar, Ming Xie, Allan MacDonald We study the collective modes of the correlated insulating states in magic-angle twisted bilayer graphene (MATBG) within the framework of the generalized random phase approximation (GRPA), also known as the time-dependent Hartree-Fock approximation (TDHFA), using a continuum model and assuming insulating states that break spin/valley flavor but not translational symmetries. The calculations confirm the stability of the translationally invariant states and provide values for key energy scales associated with low-energy collective fluctuations, including spin-stiffnesses and gaps for valley-wave modes. We find that zone-boundary collective mode energies are an order of magnitude smaller than the charge gaps. By fitting to the calculated collective excitation spectra, we derive generalized spin models that fully capture the low-energy physics. Finally, we discuss how these collective mode energies vary with moiré band filling factor and the possible role of their coupling to Fermi surface quasiparticles in superconductivity and non-Fermi liquid behavior. |
Thursday, March 5, 2020 5:06PM - 5:18PM |
U63.00014: Periodic Strain-Induced Moire Patterns in Graphene. Md Tareq Mahmud, Nancy Sandler Lattice mismatch between graphene and a substrate produces local variations in the density of states (LDOS) as observed in STM images. These are known as moire patterns, in analogy with classical interference produced by two overlapping periodic arrays. These have been observed in twisted bilayer graphene[1], a system that can be thought of as monolayer graphene deposited on a substrate with misaligned crystalline orientations. In this regime, the resulting charge density distribution is related to superconductor and Mott insulator phases observed in experiments. It is natural to wonder if similar features could be obtained by depositing graphene on engineered substrates inducing modulated strain fields. Starting from the simplest case of two overlapping deformations, we obtain the LDOS profile for a one-dimensional array, and show the emergence of a different periodicity, a feature associated with moire patterns. We identify conditions for discrete and continuous charged regions, and extend our results to a 2D close-packed structure, demonstrating that periodic deformations can be used to generate moire patterns. |
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