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Content of SPECIAL TOPIC—Twistronics in our journal
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Projective representation of
D
6
group in twisted bilayer graphene
Noah F. Q. Yuan
Chin. Phys. B, 2021, 30 (
7
): 070311. DOI:
10.1088/1674-1056/ac00a3
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483
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Within the framework of continuum model, we study the projective representation of emergent D
6
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.
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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
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490
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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.
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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
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426
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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.
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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
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339
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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.
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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
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508
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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.
ISSN 1674-1056 CN 11-5639/O4
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