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    SPECIAL TOPIC — Twistronics

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    Twistronics in graphene-based van der Waals structures
    Ya-Ning Ren(任雅宁), Yu Zhang(张钰), Yi-Wen Liu(刘亦文), and Lin He(何林)
    Chin. Phys. B, 2020, 29 (11): 117303.   DOI: 10.1088/1674-1056/abbbe2
    Abstract365)   HTML    PDF (2345KB)(349)      

    The electronic properties of van der Waals (vdW) structures can be substantially modified by the moiré superlattice potential, which strongly depends on the twist angle among the compounds. In twisted bilayer graphene (TBG), two low-energy Van Hove singularities (VHSs) move closer with decreasing twist angles and finally become highly non-dispersive flat bands at the magic angle (∼ 1.1°). When the Fermi level lies within the flat bands of the TBG near the magic angle, Coulomb interaction is supposed to exceed the kinetic energy of the electrons, which can drive the system into various strongly correlated phases. Moreover, the strongly correlated states of flat bands are also realized in other graphene-based vdW structures with an interlayer twist. In this article, we mainly review the recent scanning tunneling microscopy (STM) advances on the strongly correlated physics of the magic-angle TBG (MATBG) and the small-angle twisted multilayer graphene. Lastly we will give out a perspective of this field.

    Superconductivity in twisted multilayer graphene: A smoking gun in recent condensed matter physics
    Yonghuan Chu(楚永唤), Fangduo Zhu(朱方铎), Lingzhi Wen(温凌志), Wanying Chen(陈婉莹), Qiaoni Chen(陈巧妮), and Tianxing Ma(马天星)
    Chin. Phys. B, 2020, 29 (11): 117401.   DOI: 10.1088/1674-1056/abbbea
    Abstract208)   HTML    PDF (998KB)(203)      

    We review the recent discoveries of exotic phenomena in graphene, especially superconductivity. It has been theoretically suggested for more than one decade that superconductivity may emerge in doped graphene-based materials. For single-layer pristine graphene, there are theoretical predictions that spin-singlet d + id pairing superconductivity is present when the filling is around the Dirac point. If the Fermi level is doped to the Van Hove singularity where the density of states diverges, then unconventional superconductivity with other pairing symmetry would appear. However, the experimental perspective was a bit disappointing. Despite extensive experimental efforts, superconductivity was not found in monolayer graphene. Recently, unconventional superconductivity was found in magic-angle twisted bilayer graphene. Superconductivity was also found in ABC stacked trilayer graphene and other systems. In this article, we review the unique properties of superconducting states in graphene, experimentally controlling the superconductivity in twisted bilayer graphene, as well as a gate-tunable Mott insulator, and the superconductivity in trilayer graphene. These discoveries have attracted the attention of a large number of physicists. The study of the electronic correlated states in twisted multilayer graphene serves as a smoking gun in recent condensed matter physics.

    Density wave and topological superconductivity in the magic-angle-twisted bilayer-graphene
    Ming Zhang(张铭), Yu Zhang(张渝), Chen Lu(卢晨), Wei-Qiang Chen(陈伟强), and Fan Yang(杨帆)
    Chin. Phys. B, 2020, 29 (12): 127102.   DOI: 10.1088/1674-1056/abc7b5
    Abstract193)   HTML    PDF (2690KB)(194)      
    The model dependence in the study of the magic-angle twisted bilayer-graphene (MA-TBG) is an important issue in the research area. It has been argued previously that the two-band tight-binding (TB) model (per spin and valley) cannot serve as a start point for succeeding studies as it cannot correctly describe the topological aspect of the continuum-theory model near the Dirac nodes in the mini Brillouin zone (MBZ). For this purpose, we adopt the faithful TB model [Phys. Rev. B 99 195455 (2019)] with five bands (per spin and valley) as our start point, which is further equipped with extended Hubbard interactions. Then after systematic random-phase-approximation (RPA) based calculations, we study the electron instabilities of this model, including the density wave (DW) and superconductivity (SC), near the van Hove singularity (VHS). Our results are as follows. In the case neglecting the tiny inter-valley exchange interaction, the exact $SU(2)_K\times SU(2)_K'$ symmetry leads to the degeneracy between the inter-valley charge DW (CDW) and the spin DW (SDW) (which would be mixed then), and that between the singlet $d+id$-wave and triplet $p+ip$-wave topological SCs. When a realistic tiny inter-valley exchange interaction is turned on with nonzero coefficient (J H≠ 0), the SDW or CDW is favored respectively at the critical point, determined by $J_\rm H\to 0^-$ or $J_\rm H\to 0^+$. In the mean time, the degeneracy between the singlet $d+id$-wave and triplet $p+ip$-wave topological SCs is also lifted up by the tiny J H. These results are highly similar to the results of our previous study [arXiv:2003.09513] adopting the two-band TB model, with the reason lying in that both models share the same symmetry and Fermi-surface (FS) nesting character near the VHS. Such a similarity suggests that the low-energy physics of the doped MA-TBG is mainly determined by the symmetry and the shape of the FS of the doped system, and is insensitive to other details of the band structure, including the topological aspects near the Dirac nodes in the MBZ.
    Progress on band structure engineering of twisted bilayer and two-dimensional moirè heterostructures
    Wei Yao(姚维), Martin Aeschlimann, and Shuyun Zhou(周树云)
    Chin. Phys. B, 2020, 29 (12): 127304.   DOI: 10.1088/1674-1056/abc7b6
    Abstract263)   HTML    PDF (3653KB)(283)      
    Artificially constructed van der Waals heterostructures (vdWHs) provide an ideal platform for realizing emerging quantum phenomena in condensed matter physics. Two methods for building vdWHs have been developed: stacking two-dimensional (2D) materials into a bilayer structure with different lattice constants, or with different orientations. The interlayer coupling stemming from commensurate or incommensurate superlattice pattern plays an important role in vdWHs for modulating the band structures and generating new electronic states. In this article, we review a series of novel quantum states discovered in two model vdWH systems -graphene/hexagonal boron nitride (hBN) hetero-bilayer and twisted bilayer graphene (tBLG), and discuss how the electronic structures are modified by such stacking and twisting. We also provide perspectives for future studies on hetero-bilayer materials, from which an expansion of 2D material phase library is expected.
    A review of experimental advances in twisted graphene moirè superlattice
    Yanbang Chu(褚衍邦), Le Liu(刘乐), Yalong Yuan(袁亚龙), Cheng Shen(沈成), Rong Yang(杨蓉), Dongxia Shi(时东霞), Wei Yang(杨威), and Guangyu Zhang(张广宇)
    Chin. Phys. B, 2020, 29 (12): 128104.   DOI: 10.1088/1674-1056/abb221
    Abstract305)   HTML    PDF (1441KB)(284)      
    Twisted moirè superlattice receives tremendous interests since the discovery of correlated insulating states and superconductivity in magic angle twist bilayer graphene (MA-TBG) [Nature 556 80 (2018), Nature 556 43 (2018)], even gives arise to a new field "twistronics" [Science 361 690 (2018)]. It is a new platform hosting strong electron correlations, providing an alternative for understanding unconventional superconductivity. In this article, we provide a review of recent experimental advances in the twisted moirè superlattice, from MA-TBG to twisted double bilayer graphene and other two-dimensional materials based moirè superlattice, covering correlated insulating states, superconductivity, magnetism, et al.
    Correlated insulating phases in the twisted bilayer graphene
    Yuan-Da Liao(廖元达), Xiao-Yan Xu(许霄琰), Zi-Yang Meng(孟子杨), and Jian Kang(康健)
    Chin. Phys. B, 2021, 30 (1): 017305.   DOI: 10.1088/1674-1056/abcfa3
    Abstract325)   HTML7)    PDF (1150KB)(333)      
    We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is SU(4) symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the SU(4) manifold with degeneracy. The kinetic terms, treated as perturbation, break this large SU(4) symmetry and propel the appearance of intervalley coherent state, quantum topological insulators, and other symmetry-breaking insulating states. We first present the theoretical analysis of moir\'e lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.
    Projective representation of D6 group in twisted bilayer graphene
    Noah F. Q. Yuan
    Chin. Phys. B, 2021, 30 (7): 070311.   DOI: 10.1088/1674-1056/ac00a3
    Abstract70)      PDF (935KB)(46)      
    Within the framework of continuum model, we study the projective representation of emergent D6 point group in twisted bilayer graphene. We then construct tight-binding models of the lowest bands without and with external electromagnetic fields, based on the projective representation.
    Bilayer twisting as a mean to isolate connected flat bands in a kagome lattice through Wigner crystallization
    Jing Wu(吴静), Yue-E Xie(谢月娥), Ming-Xing Chen(陈明星), Jia-Ren Yuan(袁加仁), Xiao-Hong Yan(颜晓红), Sheng-Bai Zhang(张绳百), and Yuan-Ping Chen(陈元平)
    Chin. Phys. B, 2021, 30 (7): 077104.   DOI: 10.1088/1674-1056/abd7d6
    Abstract77)      PDF (4557KB)(75)      
    The physics of flat band is novel and rich but difficult to access. In this regard, recently twisting of bilayer van der Waals (vdW)-bounded two-dimensional (2D) materials has attracted much attention, because the reduction of Brillouin zone will eventually lead to a diminishing kinetic energy. Alternatively, one may start with a 2D kagome lattice, which already possesses flat bands at the Fermi level, but unfortunately these bands connect quadratically to other (dispersive) bands, leading to undesirable effects. Here, we propose, by first-principles calculation and tight-binding modeling, that the same bilayer twisting approach can be used to isolate the kagome flat bands. As the starting kinetic energy is already vanishingly small, the interlayer vdW potential is always sufficiently large irrespective of the twisting angle. As such the electronic states in the (connected) flat bands become unstable against a spontaneous Wigner crystallization, which is expected to have interesting interplays with other flat-band phenomena such as novel superconductivity and anomalous quantum Hall effect.
    Magnon bands in twisted bilayer honeycomb quantum magnets
    Xingchuan Zhu(朱兴川), Huaiming Guo(郭怀明), and Shiping Feng(冯世平)
    Chin. Phys. B, 2021, 30 (7): 077505.   DOI: 10.1088/1674-1056/abeee5
    Abstract72)      PDF (1804KB)(51)      
    We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave theory. Although the interlayer coupling can be ferromagnetic or antiferromagnetic, we keep the intralayer one ferromagnetic to avoid possible frustration. For the interlayer ferromagnetic case, we find the magnon bands have similar features with the corresponding electronic energy spectrums. Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets, their slopes are reduced with the decrease of the twist angles. On the other hand, the interlayer antiferromagnetic couplings generate quite different magnon spectra. The two single-layered magnon spectra are usually decoupled due to the opposite orientations of the spins in the two layers. We also develop a low-energy continuous theory for very small twist angles, which has been verified to fit well with the exact tight-binding calculations. Our results may be experimentally observed due to the rapid progress in two-dimensional magnetic materials.
    Faraday rotations, ellipticity, and circular dichroism in magneto-optical spectrum of moiré superlattices
    J A Crosse and Pilkyung Moon
    Chin. Phys. B, 2021, 30 (7): 077803.   DOI: 10.1088/1674-1056/ac051f
    Abstract57)      PDF (12244KB)(27)      
    We study the magneto-optical conductivity of a number of van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As the magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, the other four structures display strong circular dichroism with monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride being particularly pronounced owing to strong inversion symmetry breaking properties of the hexagonal boron nitride layer. As the left and right circularly polarized light interact with these structures differently, plane-polarized incident light undergoes a Faraday rotation and gains an ellipticity when transmitted. The size of the respective angles is on the order of a degree.