Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model

Lin, Xiyue; Chen, Bin-Bin; Li, Wei; Meng, Zi Yang; Shi, Tao

doi:10.1103/physrevlett.128.157201

Cited by 22 publications

(17 citation statements)

References 79 publications

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“…Twisted bilayer graphene (TBG) system around the magic angle is an ideal platform to realize various intriguing quantum phases , such as the correlated insulators, − quantum anomalous Hall states, and ,,− unconventional superconductivity. ,− ,,− Around magic angle 1.05°, there are two topologically nontrivial flat bands contributed by each valley and spin degrees of freedom. − A lot of the unusual phenomena, including correlated insulators and quantum anomalous Hall effects, can be attributed to the presence of such topologically nontrivial flat bands in the electronic degrees of freedom. The electron–electron (e–e) Coulomb interactions dominates over the kinetic energy near magic angle, and the interplay between the strong Coulomb correlations and the nontrivial topology of the flat bands give rise to diverse correlated insulator states and topological states, which have been extensively studied from the theoretical point of view over the past few years. − …”

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Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

et al. 2022

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Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some lowfrequency C 2z -breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.

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Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

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“…Discussion -In this study, we show that at 3/4 filling and 𝑇 = 0, a QAH-TMI state emerges in magic angle TBGs, due to the interplay between flat band quantum wavefunctions and Coulomb interactions. In analogy to its real-space-model cousin [41], this QAH-TMI phase melts at a very low temperature, much lower than the zero-temperature gap Δ. We identify that low-energy excitonic states are the origin of this low transition temperature.…”

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“…Because of the proliferation of excitons -particle-hole bound states -this phase transition takes place at a significantly reduced temperature (at the scale of a few meV) than the mean-field estimation of the topological band gap (at the scale of a few tens of meV). Between these two energy scales, an exciton-proliferated phase is observed, which acquires distinctive experimental signatures in charge compressibility and optical conductivities close to the transition [41].…”

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“…Introduction -Quantum moiré systems, bestowed with the quantum geometry of wavefunctions -manifested in the distribution of Berry curvature in the flat bands -and strong long-range Coulomb electron interactions, exhibit a rich quantum phase diagram including correlated insulating, unconventional metallic and superconducting phases, thanks to the high tunability by twisting angles, gating and tailored design of the dielectric environment . In addition to this complex ground-state phase diagram with possibly different pairing mechanism and symmetry breaking patterns [9,[36][37][38][39], recent theoretical studies [14,32,[40][41][42] indicates that correlated flat bands also exhibit unique thermodynamic and quantum dynamic responses, fundamentally different from conventional correlated electron lattice model systems, such as the Hubbard-type model.…”

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“…Previous results [40] based on a real-space effective model [43][44][45] for twisted bilayer graphene (TBG) at 3/4 filling, via density matrix renormalization group computation, successfully identify a quantum anomalous Hall (QAH) state as the long-sought-after topological Mott insulator (TMI) [46][47][48], as the ground state of the interaction-only system spontaneously breaks the time-reversal symmetry and acquires a finite Chern number. Then by means of thermal tensor network and the perturbative field-theoretical approaches [41], the finite-𝑇 phase diagram and the dynamical properties of the real-space TBG model have been revealed, which contains the QAH and charge density wave insulators at low-𝑇, and an Ising transition separating them from the high-𝑇 symmetric phases. Because of the proliferation of excitons -particle-hole bound states -this phase transition takes place at a significantly reduced temperature (at the scale of a few meV) than the mean-field estimation of the topological band gap (at the scale of a few tens of meV).…”

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Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Pan¹,

Lu²,

Li³

et al. 2022

Preprint

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While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene and transition metal dichalcogenides. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, there exists a unique thermodynamic characteristic for the correlated flat-band models with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which "quantum teleport" the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and give rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.

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Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Yan

Meng

2023

Nat Commun

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Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane’s conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

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Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model

Cited by 22 publications

References 79 publications

Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

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