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arXiv:2308.10935 · Physical review. B./Physical review. B

Superconductivity in a topological lattice model with strong repulsion

Rahul Sahay, Stefan Divic, Daniel E. Parker, Tomohiro Soejima, Sajant Anand, Johannes Hauschild, Monika Aidelsburger, Ashvin Vishwanath, Shubhayu Chatterjee, Norman Y. Yao, Michael P. Zaletel

Published Nov 12, 2024• 8 citations
arXivHTMLPDF

Abstract

Can superconductivity arise from strong repulsive interactions between electrons in a lattice model with topological bands? Here, the authors answer this question in the affirmative via DMRG numerical simulations of an interacting spinful bilayer Hofstadter model featuring low-lying bands of opposite Chern number. Furthermore, by developing a new technique to probe the pairing symmetry in number-conserving DMRG, the authors demonstrate that superconductivity is $p$-wave, tantalizingly reminiscent of nodal pairing recently observed in twisted bilayer graphene, which shares many structural similarities with their model. This work thus showcases the possibility of an all-electronic pairing mechanism in the strong coupling limit in two dimensions, which can be tested directly with cold fermions in an optical lattice.

DOI
10.1103/physrevb.110.195126

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Can superconductivity arise from strong repulsive interactions between electrons in a lattice model with topological bands? Here, the authors answer this question in the affirmative via DMRG numerical simulations of an interacting spinful bilayer Hofstadter model featuring low-lying bands of opposite Chern number. Furthermore, by developing a new technique to probe the pairing symmetry in number-conserving DMRG, the authors demonstrate that superconductivity is ppp-wave, tantalizingly reminiscent of nodal pairing recently observed in twisted bilayer graphene, which shares many structural similarities with their model. This work thus showcases the possibility of an all-electronic pairing mechanism in the strong coupling limit in two dimensions, which can be tested directly with cold fermions in an optical lattice.
DMRG study of strongly interacting Z2\mathbb{Z}_2Z2​ flatbands: a toy model inspired by twisted bilayer graphene
Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern =\pm1 = ± 1 ), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry ( \mathbb{Z}_2 ℤ 2 ). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle | + + ⋯ + ⟩ or all negative |{--\cdots-}\rangle | − − ⋯ − ⟩ . If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1 ν = 1 spin- \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.
An important question about unconventional superconductors is how attractions can emerge in a purely repulsive electronic system. Here, the authors study comprehensively one such electronic mechanism, where pairing is induced by a third electron undergoing a virtual interband transition. Their exact solution of an illustrative Hubbard model establishes superconductivity due to interband polarization in both the weak and strong coupling regimes. Relevance of this pairing mechanism for twisted bilayer graphene is also discussed.
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Motivated by the recent novel electronic features extracted from the magic-angle graphene superlattices, we studied the ground state superconducting pairing correlations within the Hubbard model on a twisted bilayer honeycomb lattice. Using Constrained-Path Quantum Monte Carlo method, we found that the [Formula: see text] pairing correlation dominates over other pairing patterns among various electron fillings and interaction strengths, and the effective pairing interaction was enhanced as the on-site Coulomb interaction increased. We further examined the effect of the nearest neighbor interaction [Formula: see text], and the effective pairing interaction with [Formula: see text] pairing symmetry was also enhanced by either a repulsive or attractive interaction. Our intensive numerical results confirm the interaction driven superconductivity with a dominant [Formula: see text] pairing symmetry in twisted bilayer graphene.
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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.