Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Kwan, Yves H.; Wagner, Glenn; Chakraborty, Nilotpal; Simon, Steven H.; Parameswaran, S. A.

doi:10.1103/physrevb.104.115404

Cited by 22 publications

(6 citation statements)

References 46 publications

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“…When the system is valley polarized into QAH domains, adjacent domains carry opposite Chern numbers, thus realizing a network of gapless chiral edge modes. Alternatively, adjacent domains may have opposite valley polarizations; the competition between these possibilities depends on detailed domain wall energetics ( 84 ) and may be probed by an out-of-plane magnetic field. This situation is similar to the Chern mosaic in hBN-aligned magic-angle TBG ( 38 , 85 ).…”

Section: Discussionmentioning

confidence: 99%

Magic-angle helical trilayer graphene

Devakul,

Ledwith,

Xia

et al. 2023

Sci. Adv.

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We propose magic-angle helical trilayer graphene (HTG), a helical structure featuring identical rotation angles between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure realizing flat topological bands carrying nontrivial valley Chern number. These bands feature near-ideal quantum geometry and are isolated from remote bands by a very large energy gap, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states.

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Section: Discussionmentioning

confidence: 99%

Magic-angle helical trilayer graphene

Devakul,

Ledwith,

Xia

et al. 2023

Sci. Adv.

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“…There is no topological obstruction to the construction of hybrid Wannier states, making them an attractive basis for the flat bands of magic angle graphene, as was also recognized by the authors of Refs. [25,[44][45][46]. Geometrically, this defines a model on a cylinder, with real space in the x direction and k space around the circumference [47].…”

Section: D Wanniermentioning

confidence: 99%

Efficient simulation of moiré materials using the density matrix renormalization group

et al. 2020

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We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques-even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley, and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moiré materials in future work.

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“…There is at present no theory to fit the IKS state into this Pomeranchuk scenario. For the uniform QHFM states, several groups have recently calculated the collective mode spectrum [122][123][124][125]. In this work, we have not attempted to do this for the IKS states, although it would be helpful to obtain a more complete picture of the low-energy physics at the different integer fillings.…”

Section: Discussionmentioning

confidence: 99%

“…Alignment of the TBG sample with the hBN substrate leads to a staggered sublattice potential on one or both of the graphene layers. This can be incorporated into our model by projecting the σ z operator onto the active bands of interest [122], with a coefficient ∆ of order 10 meV.…”

Section: Lattice Vectorsmentioning

confidence: 99%

Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

Kwan,

Wagner,

Soejima

et al. 2021

Preprint

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We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekulé spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries, but preserves a modified translation symmetry T -which simultaneously shifts the spatial coordinates and rotates the U (1) angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

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Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Cited by 22 publications

References 46 publications

Magic-angle helical trilayer graphene

Magic-angle helical trilayer graphene

Efficient simulation of moiré materials using the density matrix renormalization group

Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

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