Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session S14: 2D Materials (Metals, Superconductors, and Correlated Materials)  Twisted Graphene IIFocus

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Sponsoring Units: DMP DCOMP Chair: Roland Koch Room: BCEC 153C 
Thursday, March 7, 2019 11:15AM  11:27AM 
S14.00001: Electronic compressibility of magicangle graphene superlattices Spencer Tomarken, Yuan Cao, Ahmet Demir, Kenji Watanabe, Takashi Taniguchi, Pablo JarilloHerrero, Raymond Ashoori Recent calculations and measurements have revealed that the superlattice formed by twisting and stacking two monolayers of graphene at particular small twist angles (dubbed 'magic angles') relative to their crystallographic axes can form an electronic system with substantially reduced Fermi velocity compared to monolayer graphene. Moreover, exotic insulating [1] and superconducting phases [2] near fractional filling of the moiré miniband have been observed in initial transport and capacitance measurements, drawing comparisons to the highTc cuprates and other superconducting platforms with analogous phase diagrams. Here we report the first thermodynamic compressibility measurements of magic angle twisted bilayer graphene in the low frequency limit. We find strongly incompressible features at quarter and halffilling of the electrondoped regime, whereas we find substantially weaker features at the equivalent holedoped densities. We extract the thermodynamic gaps at fractional filling and compare our results to recent transport studies. 
Thursday, March 7, 2019 11:27AM  11:39AM 
S14.00002: Multicomponent Superfluidity and Screening in Biased ElectronHole Double Bilayer Graphene with Realistic Bands. Sara Conti, David Neilson, Francois M Peeters, Andrea Perali Superfluidity has recently been reported in double electronhole bilayer graphene. The multiband nature of the bilayers is expected to be very important because the band gaps between conduction and valence bands are small. Here we report on a detailed meanfield study that takes into account the effects of multichannel electronhole pairing, including Josephsonlike pair transfer between bands; screening from both intraband and interband excitations; and effects of the nonparabolic band dispersion that accompanies the variable band gaps in bilayer graphene. From the selfconsistent calculation based on the random phase approximation in superfluid state, we obtain a density range for superfluidity consistent with the density range reported in the recent experiments. We find for nonzero gaps, that the boost of the density of states from the flattening of the bands strengthens the superfluidity. We also find that the superfluidity modifies the intraband screening in a fundamentally different way from the interband screening. Surprisingly, the net effect of the screening is to restrict the superfluid pairing entirely to the conduction band  even for very small band gaps. This makes the system behave almost analogously to a oneband superfluid. 
Thursday, March 7, 2019 11:39AM  11:51AM 
S14.00003: Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands Jian Kang, Oskar Vafek We build symmetry adapted maximally localized Wannier states, and construct the low energy tight binding model for the four narrow bands of the twisted bilayer graphene. We do so when the twist angle is commensurate, near the "magic" value, and the narrow bands are separated from the rest of the bands by energy gaps. On each layer and sublattice, every Wannier state has three peaks near the triangular Moire lattice sites. However, each Wannier state is localized and centered around a site of the honeycomb lattice that is dual to the triangular Moire lattice. Space group and the time reversal symmetries are realized locally. The corresponding tight binding model provides a starting point for studying the correlated manybody phases. 
Thursday, March 7, 2019 11:51AM  12:03PM 
S14.00004: Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene Mikito Koshino, Fanqui Yuan, Takashi Koretsune, Masayuki Ochi, Kazuhiko Kuroki, Liang Fu We develop an effective extended Hubbard model to describe the lowenergy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tightbinding model on the emergent honeycomb lattice. We find that the Wannier state takes a peculiar threepeak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per supercell, we find an unexpected coincidence in the direct Coulomb energy between a chargeordered state and a homogeneous state, which could possibly lead to an unconventional manybody state. 
Thursday, March 7, 2019 12:03PM  12:15PM 
S14.00005: Collisionless transport close to a fermionic quantum critical point in Dirac materials Vladimir Juricic, Bitan Roy Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. In this talk, we discuss the scaling of optical conductivity (OC) in the collisionless regime (ω»T) in the vicinity of a relativistic GrossNeveuYukawa quantum critical point, separating twodimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. In particular, we show that close to such a critical point a universal suppression of both the interband OC and the Drude peak (while maintaining its delta function profile) inside the critical regime occurs due to strongly coupled gapless fermionic and bosonic excitations [1]. We carry out the computation to the leading order in 1/N_{f} and εexpansions, where N_{f} counts fermion flavor number and ε=3d. Correction to the OC at such a nonGaussian critical point due to the longrange Coulomb interaction and generalizations of these scenarios to a strongly interacting threedimensional Dirac or Weyl liquid are also presented. 
Thursday, March 7, 2019 12:15PM  12:27PM 
S14.00006: Upper bounds on the superconducting critical temperature: Applications to TwistedBilayer Graphene Nishchhal Verma, Tamaghna Hazra, Mohit Randeria Understanding the material parameters that control the superconducting (SC) transition temperature T_{c} is a problem of fundamental importance. In many novel superconductors of interest, fluctuations of the phase of the SC order parameter determines T_{c}, rather than the BCS collapse of the amplitude due to pair breaking. We derive rigorous upper bounds on the superfluid density or phase stiffness D_{s} valid in any dimension, essentially controlled by the noninteracting band structure. This in turn leads to rigorous upper bounds on T_{c} in 2D, which holds irrespective of the form or strength of the pairing interactions, mechanism or orderparameter symmetry. Although these bounds are of completely general validity, they are most illuminating for narrowband, strongly interacting systems. Our results lead to strong restrictions for magicangle twisted bilayer graphene (MATBG), where we show that the maximum possible T_{c} is quite close to the experimental observations. This shows that MATBG must be a strongly interacting system where phase stiffness rather than pair breaking is responsible for T_{c}. We also discuss the question of deriving rigorous upper bounds on T_{c} in 3D. 
Thursday, March 7, 2019 12:27PM  12:39PM 
S14.00007: Strong coupling phases of partially filled twisted bilayer graphene narrow bands Oskar Vafek, Jian Kang We identify the manybody insulating states favored by the Coulomb interactions projected onto the microscopically constructed Wannier basis of the four narrow bands of the twisted bilayer graphene near the ``magic angle''. The nonlocal interaction terms are novel and their form can be traced to the topologically nontrivial nature of the narrow bands. In the strong coupling limit and at the filling of two elecrons/holes per moire unit cell, the ground state can be found exactly; it is SU(4) ferromagnetic with exactly one electron/hole on each honeycomb lattice site. The kinetic terms break the SU(4) symmetry and select the ground state in which the two valleys with opposite spins are equally mixed. Although such an insulating state is not quite a spin singlet, the magnetic moment per particle vanishes in the thermodynamic limit and therefore its Zeeman coupling to an external magnetic field also vanishes at linear order. We also find gapped extended excited states with a gap that decreases in an external magnetic field. Finally, we propose that an insulating stripe ferromagnetic phase could be the ground state for the filling of one electron/hole per unit cell, with a gap that does not decrease in an external magnetic field. 
Thursday, March 7, 2019 12:39PM  12:51PM 
S14.00008: GateTunable Mott Insulator in Trilayer GrapheneBoron Nitride Moiré Superlattice Guorui Chen, Lili Jiang, Shuang Wu, Bosai Lv, Hongyuan Li, Kenji Watanabe, Takashi Taniguchi, Zhiwen Shi, Yuanbo Zhang, Feng Wang Mott insulator plays a central role in strongly correlated physics, where the repulsive Coulomb interaction dominates over the electron kinetic energy and leads to insulating states with one electron occupying each unit cell. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott physics. Here we report the realization of such a tunable Mott insulator in the ABC trilayer graphene (TLG) and hexagonal boron nitride (hBN) heterostructure with a Moiré superlattice. The Moiré superlattice in TLG/hBN heterostructures leads to narrow electronic minibands that are gatetunable. The Mott insulator states emerge at 1/4 and 1/2 fillings, corresponding to one electron and two electrons per site, respectively. Moreover, the Mott states in the ABC TLG/hBN heterostructure exhibit unprecedented tunability: the Mott gap can be modulated in situ by a vertical electrical field, and at the meantime the electron doping can be gatetuned to fill the band from one Mott insulating state to another. Our observation opens up tremendous opportunities to explore novel strongly correlated phenomena in twodimensional Moiré superlattice heterostructures. 
Thursday, March 7, 2019 12:51PM  1:03PM 
S14.00009: KohnLuttinger Superconductivity in Twisted Bilayer Graphene Jose Gonzalez, Stauber Tobias We propose that the superconductivity observed in twisted bilayer graphene can be explained as the consequence of a KohnLuttinger instability, which leads to an effective attraction between electrons with originally repulsive interaction. As the first magic angle is approached, we find two consecutive transitions between different topologies in the highest valence band of the twisted bilayers, driven by the doubling and subsequent strong coupling of van Hove singularities in the electronic spectrum. This leads to extended saddle points and energy contours with almost perfect nesting between states belonging to different K valleys. The highly anisotropic screening of the Coulomb interaction induces an effective attraction in a channel with odd parity under the exchange of the two mirror patches of the Fermi line, which develop a universal shape close to the magic angle. We also consider the competition with charge and spindensitywave instabilities, adjacent to the superconducting phase, and whose onset typically takes place for a Hubbard repulsion below the bandwidth of the highest valence band, thus reinforcing our microscopic approach to the superconductivity of twisted bilayer graphene. 
Thursday, March 7, 2019 1:03PM  1:15PM 
S14.00010: Magnetotransport properties in twisted bilayer graphene at magic angle Evan Laksono, Alexander Reaves, Manraaj Singh, Xingyu Gu, Jia Ning Leaw, Nimisha Raghuvanshi, Shaffique Adam Recent experimental works on magicangle twisted bilayer graphene have pointed to the existence of insulating and superconducting phases when the flat bands are halffilled. Among the mysteries in the experiments is the observed Landau fan diagram which shows a reduction in degeneracy close to the charge neutrality point compared to that at larger twist angle. These features are a remarkable departure from theoretical expectations. In this work, we use our recently developed theory for the noninteracting band structures [1, 2] to understand the behaviors of twisted bilayer graphene under the influence of magnetic field, and offer the possible scenarios that lead to the unconventional features in the magnetotransport at charge neutrality and at halffilling. 
Thursday, March 7, 2019 1:15PM  1:27PM 
S14.00011: Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene Johannes Lischner, Dante Kennes, Christoph Karrasch We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electronelectron interactions and thus unleashes stronglycorrelated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near halffilling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased manybody renormalization group techniques combined with a meanfield analysis of the effective couplings. 
Thursday, March 7, 2019 1:27PM  1:39PM 
S14.00012: Topological and strong correlation physics in orbitalactive honeycomb lattice materials  applications to twisted bilayer graphene, bismuthene, transitionmetal oxide film, etc Congjun Wu, Shenglong Xu We apply the symmetry principle to analyze the physical properties of orbitalactive honeycomb systems which include a large class of mateirals (e.g. the twistedbilayer graphene, transitionmetaloxide layer, bismuthene, stanene, metalorganic framework, and quantum dot array). Their orbital degree of freedom transforms as a twodimensional irreducible representation of the lattice symmetry group, which results in band structures consisting of both the dispersionless flat bands and orbitalactive Dirac bands. The flat bands amplify strong correlation effect to yield Wigner crystal and flatband ferromagnetism. The activeorbital degree of freedom boosts the topological gap of the Dirac bands to the order of atomic scale spinorbit coupling, i.e. at the scale of 1eV, as observed experimentally in bismuthene. In the Mottinsulating states, the orbital exchange becomes heavily frustrated as described by a novel 120 degree model whose classic ground states are mapped to all possible loop configurations covering the lattice, and quantum fluctuations select the closest packed loop configuration. The orbital degree of freedom also facilitate an fwave superconductivity in which the gap nodal lines are determined by the orbital symmetry independent of the concrete pairing interactions. 
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