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arXiv:2308.02292 · Physical review. B./Physical review. B

Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions

Krystian Jabłonowski, Jan Skolimowski, Wojciech Brzezicki, Krzysztof Byczuk, Marcin M. Wysokiński

Published Nov 27, 2023• 17 citations
arXivHTMLPDF

Abstract

Recently, a quantum anomalous Hall state at odd-integer filling in moir\'e stacked ${\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}$ was convincingly interpreted as a topological Mott insulator state appearing due to strong interactions in band basis [P. Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, Nat. Commun. 14, 5999 (2023)]. In this work, we aim to analyze the formation of a topological Mott insulator due to interactions in orbital basis instead, being more natural for systems where interactions originate from the character of $f$ or $d$ orbitals rather than band flatness. For that reason, we study an odd-integer filled Anderson lattice model incorporating odd-parity hybridization between orbitals with different degrees of correlations introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological Mott insulating state can be realized in a considered model only when weak intra- and interorbital correlations involving dispersive states are taken into account. Interestingly, we find that all topological transitions between trivial and topological Mott insulating phases are not accompanied by a spectral gap closing, consistent with a phenomenon called first-order topological transition. Instead, they are signaled by a kink developed in spectral function at one of the time reversal invariant momenta. We believe that our approach can provide insightful phenomenology of topological Mott insulators in spin-orbit coupled $f$ or $d$ electron systems.

DOI
10.1103/physrevb.108.195145

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Recently, a quantum anomalous Hall state at odd-integer filling in moir'e stacked MoTe2/WSe2{\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}MoTe2​/WSe2​ was convincingly interpreted as a topological Mott insulator state appearing due to strong interactions in band basis [P. Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, Nat. Commun. 14, 5999 (2023)]. In this work, we aim to analyze the formation of a topological Mott insulator due to interactions in orbital basis instead, being more natural for systems where interactions originate from the character of fff or ddd orbitals rather than band flatness. For that reason, we study an odd-integer filled Anderson lattice model incorporating odd-parity hybridization between orbitals with different degrees of correlations introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological Mott insulating state can be realized in a considered model only when weak intra- and interorbital correlations involving dispersive states are taken into account. Interestingly, we find that all topological transitions between trivial and topological Mott insulating phases are not accompanied by a spectral gap closing, consistent with a phenomenon called first-order topological transition. Instead, they are signaled by a kink developed in spectral function at one of the time reversal invariant momenta. We believe that our approach can provide insightful phenomenology of topological Mott insulators in spin-orbit coupled fff or ddd electron systems.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder-/interaction-induced edge excitations and charge pumping in optical lattices.
We investigate properties of a topological Mott insulator in one dimension by examining the bulk topological invariant and the entanglement spectrum of a correlated electron model. We clarify how gapless edge states in a noninteracting topological band insulator evolve into spinon edge states in a topological Mott insulator. Furthermore, we propose a topological Mott transition, which is a new type of topological phase transition which has never been observed in free fermion systems. This unconventional transition occurs in spin liquid phases in the Mott insulator and is accompanied by zeros of the single-electron Green's function and a gap closing in the spin excitation spectrum.
The Lieb lattice possesses three bands and with intrinsic spin orbit coupling λ\lambdaλ, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction UUU on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength (UcritU_{crit}Ucrit​), creating a correlated flat band insulator. Beyond UcritU_{crit}Ucrit​, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of UUU introduced only on one sublattice where λ=0\lambda=0λ=0, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.