scholarly journals Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Jong Yeon Lee ◽  
Eslam Khalaf ◽  
Shang Liu ◽  
Xiaomeng Liu ◽  
Zeyu Hao ◽  
...  
Keyword(s):  
Displacement Field ◽  
Twist Angle ◽  
Vertical Displacement ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Hartree Fock ◽  
Flat Bands ◽  
Half Filling ◽  
Spin Triplet ◽  
Experimental Findings

AbstractTwo graphene monolayers twisted by a small magic angle exhibit nearly flat bands, leading to correlated electronic states. Here we study a related but different system with reduced symmetry - twisted double bilayer graphene (TDBG), consisting of two Bernal stacked bilayer graphenes, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field. We construct a phase diagram as a function of twist angle and displacement field, incorporating interactions via a Hartree-Fock approximation. At half-filling, ferromagnetic insulators are stabilized with valley Chern number $${C}_{{\rm{v}}}=\pm 2$$Cv=±2. Upon doping, ferromagnetic fluctuations are argued to lead to spin-triplet superconductivity from pairing between opposite valleys. We highlight a novel orbital effect arising from in-plane fields plays an important role in interpreting experiments. Combined with recent experimental findings, our results establish TDBG as a tunable platform to realize rare phases in conventional solids.

scholarly journals Magnetism of magic-angle twisted bilayer graphene

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Javad Vahedi ◽  
Robert Peters ◽  
Ahmed Missaoui ◽  
Andreas Honecker ◽  
Guy Trambly de Laissardière
Keyword(s):  
Mean Field ◽  
Bilayer Graphene ◽  
Real Space ◽  
Localized States ◽  
Magic Angle ◽  
Experimental Realization ◽  
Hartree Fock ◽  
Large Size ◽  
Twisted Bilayer Graphene ◽  
Magnetic States

We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called ``magic angles’’ using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction UU that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effect is overestimated in the rescaled system, hinting at a complex interplay of flatness of the minibands close to the Fermi level and the spatial extent of the corresponding localized states. Our findings shed new light on perspectives for experimental realization of magnetic states in charge-neutral twisted bilayer graphene.

scholarly journals Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene

Science ◽  
2021 ◽  
Vol 371 (6534) ◽  
pp. 1133-1138 ◽  
Author(s):  
Zeyu Hao ◽  
A. M. Zimmerman ◽  
Patrick Ledwith ◽  
Eslam Khalaf ◽  
Danial Haie Najafabadi ◽  
...  
Keyword(s):  
Displacement Field ◽  
Weak Coupling ◽  
Twist Angle ◽  
Magic Angle ◽  
Van Hove Singularity ◽  
Displacement Fields ◽  
Graphene Layers ◽  
Vdw Heterostructure ◽  
Quantum Phenomena ◽  
Trilayer Graphene

Engineering moiré superlattices by twisting layers in van der Waals (vdW) heterostructures has uncovered a wide array of quantum phenomena. We constructed a vdW heterostructure that consists of three graphene layers stacked with alternating twist angles ±θ. At the average twist angle θ ~ 1.56°, a theoretically predicted “magic angle” for the formation of flat electron bands, we observed displacement field–tunable superconductivity with a maximum critical temperature of 2.1 kelvin. By tuning the doping level and displacement field, we found that superconducting regimes occur in conjunction with flavor polarization of moiré bands and are bounded by a van Hove singularity (vHS) at high displacement fields. Our findings display inconsistencies with a weak coupling description, suggesting that the observed moiré superconductivity has an unconventional nature.

scholarly journals Carrier transport theory for twisted bilayer graphene in the metallic regime

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Girish Sharma ◽  
Indra Yudhistira ◽  
Nilotpal Chakraborty ◽  
Derek Y. H. Ho ◽  
M. M. Al Ezzi ◽  
...  
Keyword(s):  
Experimental Data ◽  
Carrier Transport ◽  
Transport Theory ◽  
Phonon Scattering ◽  
Twist Angle ◽  
Quantitative Agreement ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Accurate Treatment ◽  
Twisted Bilayer Graphene

AbstractUnderstanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments.

scholarly journals Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle

2019 ◽  
Vol 5 (9) ◽  
pp. eaaw9770 ◽  
Author(s):  
Emilio Codecido ◽  
Qiyue Wang ◽  
Ryan Koester ◽  
Shi Che ◽  
Haidong Tian ◽  
...  
Keyword(s):  
Energy Gap ◽  
Twist Angle ◽  
High Energy ◽  
Bilayer Graphene ◽  
Unit Cell ◽  
Flat Band ◽  
Magic Angle ◽  
Strongly Correlated ◽  
New Information ◽  
Twisted Bilayer Graphene

The emergence of flat bands and correlated behaviors in “magic angle” twisted bilayer graphene (tBLG) has sparked tremendous interest, though its many aspects are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of ~0.93°, which is smaller than the magic angle by 15%. At an electron concentration of ±5 electrons/moiré unit cell, we observe a narrow resistance peak with an activation energy gap ~0.1 meV. This indicates additional correlated insulating state, and is consistent with theory predicting a high-energy flat band. At doping of ±12 electrons/moiré unit cell we observe resistance peaks arising from the Dirac points in the spectrum. Our results reveal that the “magic” range of tBLG is in fact larger than what is previously expected, and provide a wealth of new information to help decipher the strongly correlated phenomena observed in tBLG.

Twist-angle two-dimensional superlattices and their application in (opto)electronics

2022 ◽  
Vol 43 (1) ◽  
pp. 011001
Author(s):  
Kaiyao Xin ◽  
Xingang Wang ◽  
Kasper Grove-Rasmussen ◽  
Zhongming Wei
Keyword(s):  
Twist Angle ◽  
Transition Metal Dichalcogenides ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Two Dimensional ◽  
Experimental Realization ◽  
Theoretical Simulation ◽  
Band Engineering ◽  
Theoretical Predictions ◽  
Metal Dichalcogenides

Abstract Twist-angle two-dimensional systems, such as twisted bilayer graphene, twisted bilayer transition metal dichalcogenides, twisted bilayer phosphorene and their multilayer van der Waals heterostructures, exhibit novel and tunable properties due to the formation of Moiré superlattice and modulated Moiré bands. The review presents a brief venation on the development of “twistronics” and subsequent applications based on band engineering by twisting. Theoretical predictions followed by experimental realization of magic-angle bilayer graphene ignited the flame of investigation on the new freedom degree, twist-angle, to adjust (opto)electrical behaviors. Then, the merging of Dirac cones and the presence of flat bands gave rise to enhanced light-matter interaction and gate-dependent electrical phases, respectively, leading to applications in photodetectors and superconductor electronic devices. At the same time, the increasing amount of theoretical simulation on extended twisted 2D materials like TMDs and BPs called for further experimental verification. Finally, recently discovered properties in twisted bilayer h-BN evidenced h-BN could be an ideal candidate for dielectric and ferroelectric devices. Hence, both the predictions and confirmed properties imply twist-angle two-dimensional superlattice is a group of promising candidates for next-generation (opto)electronics.

scholarly journals Phonons and Quantum Criticality Revealed by Temperature Linear Resistivity in Twisted Double Bilayer Graphene

2021 ◽  
Author(s):  
Yanbang Chu ◽  
Le Liu ◽  
Cheng Shen ◽  
Jinpeng Tian ◽  
Jian Tang ◽  
...  
Keyword(s):  
Displacement Field ◽  
Single Particle ◽  
Carrier Density ◽  
Phonon Scattering ◽  
Twist Angle ◽  
Bilayer Graphene ◽  
Quantum Criticality ◽  
Van Hove Singularity ◽  
Scattering Model ◽  
Wide Range

Abstract Twisted double bilayer graphene (TDBG) is an electric-field-tunable moiré system, exhibiting electron correlated states and related temperature linear (T-linear) resistivity. The displacement field provides a new knob to in-situ tune the relative strength of electron interactions in TDBG, yielding not only a rich phase diagram but also the ability to investigate each phase individually. Here, we report a study of carrier density (n), displacement field (D) and twist angle (θ) dependence of T-linear resistivity in TDBG. For a large twist angle (θ > 1.5°) where correlated insulating states are absent, we observe a T-linear resistivity (order of 10Ω/K) over a wide range of carrier density and its slope decreases with increasing of n before reaching the van Hove singularity, in agreement with acoustic phonon scattering model. The slope of T-linear resistivity is non-monotonically dependent on displacement field, with a single peak structure closely connected to single-particle van Hove Singularity (vHS) in TDBG. For an optimal twist angle of ~ 1.23° in the presence of correlated states, the slope of T-linear resistivity is found maximum at the boundary of the correlated halo regime (order of 100Ω/K), resulting a ‘M’ shape displacement field dependence. The observation is beyond the phonon scattering model from single particle picture, and instead it suggests a strange metal behavior. We interpret the observation as a result of symmetry-breaking instability developed at quantum critical points where electron degeneracy changes. Our results demonstrate that TDBG is an ideal system to study the interplay between phonon and quantum criticality, and might help to map out the evolution of the order parameters for the ground states.

scholarly journals Visualizing delocalized correlated electronic states in twisted double bilayer graphene

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Canxun Zhang ◽  
Tiancong Zhu ◽  
Salman Kahn ◽  
Shaowei Li ◽  
Birui Yang ◽  
...  
Keyword(s):  
Local Density ◽  
Coulomb Repulsion ◽  
Bilayer Graphene ◽  
Differential Conductance ◽  
Scanning Tunneling ◽  
Flat Band ◽  
Tunneling Microscopy ◽  
Hartree Fock ◽  
Half Filling ◽  
Graphene Devices

AbstractThe discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moiré systems.

scholarly journals Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle

2021 ◽  
Vol 118 (30) ◽  
pp. e2100006118
Author(s):  
Xiaobo Lu ◽  
Biao Lian ◽  
Gaurav Chaudhary ◽  
Benjamin A. Piot ◽  
Giulio Romagnoli ◽  
...  
Keyword(s):  
Condensed Matter ◽  
Bilayer Graphene ◽  
Band Gaps ◽  
Magic Angle ◽  
Two Dimensional ◽  
Quantum Phases ◽  
Electron Band ◽  
Flat Bands ◽  
Twisted Bilayer Graphene ◽  
Hofstadter Butterfly

Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θm2 ∼ 0.5°, which cannot be explained without considering electron–election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

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