Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session S56: Magic-Angle Twisted Graphene Multilayers: Correlations and SuperconductivityRecordings Available
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Sponsoring Units: DCMP Chair: Jia Li, Brown University Room: Hyatt Regency Hotel -Burnham |
Thursday, March 17, 2022 8:00AM - 8:12AM |
S56.00001: Lattice Relaxation in Magic Angle Twisted Trilayer Graphene Joshua Swann, Simon E Turkel, Ziyan Zhu, Maine Christos, Kenji Watanabe, Takashi Taniguchi, Subir Sachdev, Mathias S Scheurer, Efthimios Kaxiras, Abhay N Pasupathy, Cory R Dean Magic angle twisted trilayer graphene (MATTG) has recently emerged as a new platform to study strong correlations in flat band systems. Composed of graphene layers with an alternating twist angle of roughly 1.56 degrees, initial transport studies in these systems suggested some role for structural relaxation that may act to align the top and bottom layers reducing the twist angle disorder. However, a complete understanding of how the lattices relax in trilayer systems requires direct imaging of the lattice. Using scanning tunnelling microscopy (STM) and Piezoresponse force microscopy (PFM), we report on evidence of moiré lattice relaxation that leads to the formation of large regions of highly uniform local twist angle at the magic angle, which are bounded by regions of higher local twist angle. |
Thursday, March 17, 2022 8:12AM - 8:24AM |
S56.00002: Projected Hartree-Fock Study in Twisted Symmetric Trilayer Graphene Fang Xie, Nicolas Regnault, Dumitru Calugaru, Andrei B Bernevig, Biao Lian The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (TBG-) like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Calugaru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings \nu = −3, −2, −1, and 0 measured from charge neutrality. We study the phase diagram with w0/w1, the ratio of AA and AB interlayer hoppings, and the displacement field, which introduces an interlayer potential U and hybridizes the TBG-like bands with the Dirac bands. At small U, we find the ground states at all fillings ν are in the same phases as the tensor products of a Dirac semimetal with the filling \nu TBG insulator ground states, which are spin- valley polarized at \nu = −3, and fully (partially) intervalley coherent at \nu = −2, 0 (\nu = −1) in the flat bands. An exception is \nu = −3 with w0/w1 > 0.7, which possibly becomes a metal with competing orders at small U due to charge transfers between the Dirac and flat bands. At strong U where the bandwidths exceed interactions, all the fillings ν enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate U , semimetal or insulator phases with zero intervalley coherence may arise for \nu = −2, −1, 0. Our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states. |
Thursday, March 17, 2022 8:24AM - 8:36AM |
S56.00003: Probing Superconductivity in Magic Angle Twisted Trilayer Graphene with Josephson Junctions Part 1 Zeyu Hao, Andrew Zimmerman, Yuval Ronen, Danial Haie Najafabadi, Kenji Watanabe, Takashi Taniguchi, Philip Kim The superconductivity in magic angle twisted bilayer graphene (TBG) has been both fascinating and puzzling since its discovery. Despite intense study, its exact nature and relationship to the correlated phases remain unclear. Recently, alternating angle twisted trilayer graphene (TTG) emerged as a new system for studying moire superconductivity. TTG is more tunable as the band structure is modified by the displacement field. Multiple phenomena also point to the possibility of unconventional superconductivity in TTG, including: the superconducting phase being tightly tied with interaction driven symmetry breaking phases; Pauli limit violation; and possible evidence for nodes in the superconducting gap from STM measurements. We report our efforts to probe the nature of the superconducting state by interfacing the TTG superconductors with a conventional s-wave superconductor, niobium nitride (NbN). We have fabricated highly transparent contacts between these two materials as evidenced by conduction enhancement of the junction due to Andreev reflection when TTG is tuned to the normal state and supercurrent when TTG is superconducting. Here we will discuss the fabrication and basic properties of these new tunable junctions between 2D and 3D superconducting states. |
Thursday, March 17, 2022 8:36AM - 8:48AM |
S56.00004: Probing Superconductivity in Magic Angle Twisted Trilayer Graphene with Josephson Junctions Part 2 Andrew Zimmerman, Zeyu Hao, Yuval Ronen, Danial Haie Najafabadi, Kenji Watanabe, Takashi Taniguchi, Philip Kim One of the outstanding questions in magic angle twisted graphene systems is the nature of the order parameter of the superconductivity that emerges in the flat bands. While there are hints that the superconductivity may be unconventional, further experiments are needed. One method of answering this question is to use phase sensitive measurements of the superconductivity, which provide an important probe into the nature of the superconducting order parameter. In particular, phase sensitive measurements using fabricated Josephson junctions (JJs) have been crucial in demonstrating unconventional superconductivity in materials such as high temperature cuprate superconductors and UPt3. Here we report our measurements of JJs between twisted trilayer graphene (TTG) and the conventional s-wave superconductor NbN. We observe a Fraunhofer pattern that arises from the JJ with a magnetic field period that is distinct from that of the intrinsic JJs in TTG. This period is larger than the JJ area as expected for 2D superconductors where flux penetration is controlled by the Pearl length. We will discuss how this Fraunhofer pattern is tuned by tuning the superconductivity in TTG. We will further discuss the controlled design of JJ geometry to probe the TTG superconducting order parameter. |
Thursday, March 17, 2022 8:48AM - 9:00AM |
S56.00005: Coulomb screening and thermodynamic measurements in magic-angle twisted trilayer graphene Xiaoxue Liu, Naiyuan J Zhang, Kenji Watanabi, Takashi Taniguchi, J.I.A. Li We report Coulomb screening measurements on magic-angle twisted trilayer graphene (tTLG). Utilizing a double-layer structure, we directly control the strength of Coulomb correlation between charge carriers in tTLG using proximity screening from the adjacent Bernal bilayer graphene (BLG), which is separated from tTLG by a 2 nm thick insulating barrier. By studying the influence of Coulomb screening on the stability of the superconducting phase, we argue that Coulomb repulsion competes against the underlying mechanism of Cooper pairing. This behavior is observed both at B=0 and in the presence of a large in-plane magnetic field that violates the Pauli-limit. Furthermore, we characterize the isospin properties of the moiré flat band in magic-angle tTLG using a combination of transport and thermodynamic measurements. We show that the correlated insulator at half moiré filling is spin polarized, which likely results from the extraordinarily large spin stiffness in tTLG. At the same time, a spin polarized insulator state is potentially consistent with a spin triplet superconducting order parameter. Our findings provide constraints for understanding the nature of the unique superconducting phase in magic-angle twisted trilayer graphene. |
Thursday, March 17, 2022 9:00AM - 9:12AM |
S56.00006: Renormalized Magic Angles in Twisted Asymmetric Graphene Bilayers Adam Eaton, Herb Fertig, Yantao Li, Babak Seradjeh The process of stacking graphene multilayers with a small relative twist angle between each of the layers has been found to produce flat bands at a series of “magic angles.” A number of recent studies have investigated the effects that varying the number of layers or changing the stacking arrangement (AA/AB/ABC etc.) has on the values of the magic angles. Here, by contrast, we consider how magic angles and flat bands are affected when the Fermi velocity at the Dirac points at the corners of a moire Brillouin zone are different. This can occur through differing Fermi velocity renormalizations due to differing dielectrics near the two layers. Such models are also approximately realized in 4-layer structures where the twist angles are not all the same. We model each system using a low-energy theory based on a renormalized Bistritzer-MacDonald model that involves two different renormalized Fermi velocities. We find that our renormalized BM model supports significantly larger magic angles than the magic angles that are present in TBG. |
Thursday, March 17, 2022 9:12AM - 9:24AM |
S56.00007: Theory for nodal BCS-BEC transition in twisted trilayer graphene Cyprian K Lewandowski, Alex R Thomson, Etienne Lantagne-Hurtubise, Hyunjin Kim, Youngjoon Choi, Yiran Zhang, Robert M Polski, Stevan Nadj-Perge, Jason F Alicea Recent transport [1] and scanning tunneling microscopy [2] experiments on hole-doped twisted trilayer graphene reveal two superconducting regimes, differentiated by both the measured coherence length and tunneling conductance. In this talk, we will discuss how these regimes can be understood as a gate-tuned phase transition separating gapped BEC-like and gapless BCS-like superconducting phases with a common nodal order parameter [3]. We specifically analyze the nature of the transition (including interaction effects), the behavior of the coherence length, and tunneling signatures---demonstrating consistency with experiment. |
Thursday, March 17, 2022 9:24AM - 9:36AM |
S56.00008: Symmetry-breaking Transitions and Superconductivity in Magic-Angle Graphene Multilayers Yiran Zhang, Robert M Polski, Cyprian K Lewandowski, Alex R Thomson, Yang Peng, Youngjoon Choi, Hyunjin Kim, Kenji Watanabe, Takashi Taniguchi, Jason F Alicea, Felix von Oppen, Gil Refael, Stevan Nadj-Perge Graphene moiré superlattice systems have emerged as a platform hosting an abundance of correlated insulating, topological, and superconducting phases. However, so far, only alternating twisted stacking geometries of bilayer and trilayer graphene are found to exhibit robust superconductivity exhibiting Fraunhofer patterns and zero resistance. Here we investigate strongly correlated phases and superconductivity in magic-angle twisted graphene tri-, quadri-, and pentalayers placed in proximity to a tungsten diselenide (WSe2) monolayer. All three multilayer structures exhibit flavor symmetry-breaking cascade of electronic transitions, superconductivity, and, surprisingly, insulating states in the trilayer and quadrilayer. Moreover, we identify universal and layer-specific features in this family of moiré structures arising from the intricate relations between superconducting states, symmetry-breaking transitions, and van Hove singularities. Unexpectedly, as the number of layers is increased, superconductivity is observed in an increasingly larger range of filling factors. Our results highlight the non-trivial role of dispersive bands in defining properties of highly tunable graphene moiré superconductors. |
Thursday, March 17, 2022 9:36AM - 9:48AM |
S56.00009: Electrical Transport in Multilayer Twisted Graphene Homojunctions Isabelle Y Phinney, Andrew Zimmerman, Zeyu Hao, Philip Kim In recent years, two-dimensional moire systems have emerged as a highly tunable playground for studying correlated physics. Superconductivity, correlated insulators and metals and ferromagnetism, among other phases, were first observed in twisted bilayer graphene (TBG). However, this characteristic abundance of interesting phases is not limited only to TBG but has also been shown in other graphene systems, including twisted double bilayer graphene, twisted trilayer graphene, and ABC-trilayer graphene. Here, we will report on our experimental work on multilayer twisted graphene homojunctions. We construct alternative-angle twisted stacks of graphene up to 4 layers. To untangle the relationship between these strongly correlated phases and the symmetries and properties of moire flat bands, we use the available experimental knobs of doping, displacement field, electric and magnetic fields, and temperature. We identify superconductivity and flavour ferromagnetism in these multilayer twisted graphene structures tuned by displacement fields as well as carrier densities. We will discuss our efforts to extend the family of moire materials by tuning the number of layers and stacking order in search of new strongly correlated physics. |
Thursday, March 17, 2022 9:48AM - 10:00AM |
S56.00010: Spectroscopic Signatures of Strong Correlations and Unconventional Superconductivity in Twisted Trilayer Graphene – Part 1 Youngjoon Choi, Hyunjin Kim, Cyprian K Lewandowski, Alex R Thomson, Jason F Alicea, Stevan Nadj-Perge Among the moire material family, magic-angle twisted bilayer and trilayer graphene have shown robust superconductivity. However, the microscopic mechanisms leading to superconductivity in these systems are still elusive. We utilized scanning tunneling microscopy to study correlated phases and superconductivity in twisted trilayer graphene. After establishing correlation effects on the band structure such as flavor polarizing phase transitions and doping-dependent band deformations, we identified superconducting gaps around the half-filling for hole doping by observing pronounced coherence peaks that disappear at around the reported critical temperatures and fields. Moreover, the gap survives well above the critical temperatures and fields, reminiscent of pseudogap phase in other unconventional superconductors. Our results highlight the unconventional nature of superconductivity in magic angle twisted trilayer graphene. |
Thursday, March 17, 2022 10:00AM - 10:12AM |
S56.00011: Spectroscopic signatures of unconventional superconductivity in twisted trilayer graphene - Part 2 Hyunjin Kim, Youngjoon Choi, Cyprian K Lewandowski, Alex R Thomson, Jason F Alicea, Stevan Nadj-Perge Magic-angle twisted trilayer graphene (MATTG) has emerged as a novel moiré material that exhibits strong electronic correlations and unconventional superconductivity. We performed high-resolution scanning tunneling microscopy/spectroscopy measurements on MATTG which establish symmetry-breaking cascade and doping-dependent band deformations analogous to magic angle bilayers. Strikingly, upon doping two to three holes per moiré site we observed a pronounced gap accompanied with coherence peak that disappears with increased temperature and magnetic field, indicative of unconventional superconductivity in this system. The observed evolution of tunneling spectrum with doping shows the transition from the U- to V-shaped gap, which is theoretically compatible with a sharp transition from a Bardeen-Cooper-Schrieffer (BCS) to a Bose-Einstein-condensation (BEC) superconductor with a nodal order parameter. We also observed dip-hump structure signaling strongly coupled bosonic mode to the superconductor. Our results pave the way to a deeper understanding of what drives superconductivity in moiré materials. |
Thursday, March 17, 2022 10:12AM - 10:24AM |
S56.00012: Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene Maine Christos, Subir Sachdev, Mathias S Scheurer Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions ν of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of ν and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene. |
Thursday, March 17, 2022 10:24AM - 10:36AM |
S56.00013: Highero-order Van Hove singularity and Moire' of Moire' periodicity in Twisted Trilayer Graphene Daniele Guerci, Pascal Simon, Christophe Mora, Yuncheng Mao Moiré potentials obtained in twisted graphene multi-layer structures have proven remarkably fruitful for tuning the single-particle spectrum and thereby achieving exotic phases driven by the combined effects of correlation and topology. A new appealing direction has been recently opened with experiments on mirror-symmetric twisted trilayer graphene (mTTG) where only the intercalated layer is rotated by a small angle. Convincing signatures of correlated phases and superconductivity have been observed [1,2], tunable with a perpendicular electrical (displacement) field. In the first part of this talk we will argue that the single particle spectrum of mTTG shows an higher-order VHS [3] upon tuning the displacement field and rotation angle. The strong singularity is protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry. Our findings include an interesting topological Lifshitz transition when varying a third parameter, separating regions of locally open and closed semiclassical orbits. In the second part we will present a novel theory [4] for treating a different configuration of trilayer graphene, where the layers are twisted with two consecutive and independent angles. The superposition of the two different Moiré patterns gives rise to a new Moiré of Moiré periodicity on a length scale much larger than the Moiré one. Thanks to the separation between the two length scales we derive a low-energy continuum model in the Moiré of Moiré superlattice. Further, we will show that the spectrum exhibits VHS singularities at low-energy which are likely to be the precursor of strongly correlated phases [5]. |
Thursday, March 17, 2022 10:36AM - 10:48AM |
S56.00014: Interaction induced velocity renormalization in magic-angle twisted trilayer graphene Elio J König, Laura Classen, Jed Pixley Twistronics heterostructures allow to reduce the electronic single particle velocity and thereby to engineer strong effective interactions. Here we show that the reverse may also hold, i.e. that these interactions strongly renormalize the band structure. We demonstrate this mechanism for mirror-symmetric magic-angle twisted trilayer graphene at charge neutrality and in the vicinity of an Ising Gross-Neveu critical point corresponding to the onset of valley Hall or Hall order. While the non-interacting model displays fermionic modes with strongly different velocities, the infrared physics is determined by a fixed point with equal velocities. However, the RG flow of the relative velocities and of the relative coupling to the critical bosonic mode is strongly non-monotonous and dominated by the vicinity of a repulsive fixed point. We predict experimental consequences of this theory for tunneling and transport experiments and discuss the expected behavior at other quantum critical points, including those corresponding to intervalley coherent ordering. |
Thursday, March 17, 2022 10:48AM - 11:00AM |
S56.00015: Alternating Twisted Multilayer Graphene: the generic partition rules, double flat bands and orbital magnetoelectric effect Bo Xie, Shihao Zhang, Jianpeng Liu Twisted graphene systems have drawn significant attention due to the discoveries of various intriguing phases. The alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, motivating us to study the electronic structures and physical properties of this class of alternating twisted graphene systems. We consider generic alternating twisted multilayer graphene (ATMG) systems with M-L-N stacking configurations. The M (L) graphene layers and the L (N) layers are twisted by an angle θ(-θ). Based on an analytic analysis from a simplified k.p model approach, we derive generic partition rules for the low-energy electronic structures, which exhibit intriguing band dispersions at magic angle, including one pair of flat bands (per spin per valley), one pair of flat bands co-existing with E(k)~kJ dispersions (J is positive integer), and two pairs of flat bands (per spin per valley). Such unusual non-interacting electronic structures may have unconventional correlation effects. For a mirror symmetric ATMG with two pairs of flat bands (per spin per valley), we find that the system may exhibit a magnetoelectric phenomenon in the sense that the orbital magnetization of a correlated insulator state can be linearly tuned by a vertical displacement field. |
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