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arXiv:2104.09528 · Physical Review Letters

Gapping Fragile Topological Bands by Interactions

Ari M. Turner, Erez Berg, Ady Stern

Published Feb 3, 2022• 8 citations
arXivHTMLPDF

Abstract

We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole known as "trions." The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality.

DOI
10.1103/physrevlett.128.056801

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We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole known as "trions." The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality.
Determining the nature of charge carriers is a fundamental goal in the study of strongly correlated electron systems. Here, we employ the continuous-field momentum-space quantum Monte Carlo method to reveal exotic "Dirac trion" excitations in the finite-temperature normal state of twisted bilayer graphene. While the ground state is a symmetry-breaking insulator with gapped (∼\sim∼ 20 meV) electron-like excitations, we show that a small temperature (∼\sim∼ 3 meV), well below the interaction scale, drives the system into a strongly fluctuating symmetric normal state. We demonstrate that this normal state hosts gapless excitations consisting of three-particle bound states, two electrons and one hole, that are exactly orthogonal to the higher-energy electrons at the zero-momentum gapless point. These Dirac trions have the remarkable property of being arbitrarily light despite being composed of heavy constituents, and their spectra can be easily tuned by varying the twist angle and interlayer hopping strength. Our unbiased quantum many-body computation sheds light on the Dirac trions in a projected correlated flat-band setting and opens the door for further investigation of many-body excitations in strongly correlated topological bands beyond Landau levels.
Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order 10−3ER10^{-3}E_R10−3ER​, corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbor nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed ``fragile topological phases.'' In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a U(1)\mathrm{U}(1)U(1) charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g., electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.
Two-dimensional topological insulators protected by nonlocal symmetries or with fragile topology usually do not admit robust in-gap edge modes due to the incompatibility between the symmetry and the boundary. Here, we show that in a parity-time (PT) symmetric system robust in-gap topological edge modes can be stably induced by non-Hermitian couplings that spontaneously break the PT symmetry of the eigenstates. The topological edge modes traverse the imaginary spectral gap between a pair of fragile topological bands, which is opened by the presence of the non-Hermitian perturbation. We demonstrate that the net number of resulting in-gap modes is protected by an operator version of anomaly cancellation that extends beyond the Hermitian limit. The results imply that loss and gain can in principle drive fragile topological phenomena to stable topological phenomena.
Fragile topological phases become trivial upon the addition of suitable trivial bands, distinguishing them from stable topological phases. Nevertheless, various response phenomena and material realizations have been proposed for fragile phases. At the same time, many of these phenomena can also occur in atomic insulators, leaving open the question of what properties are specific to fragile phases. Enlarging the unit cell offers a natural perspective on this question. Band folding increases the number of bands in a manner analogous to adding trivial bands. In this work, we establish a systematic framework for determining the stability of fragile topology under unit-cell enlargement. We first establish a systematic criterion for trivialization under enlargements compatible with space-group symmetry, grounded in a physical electron-positron picture and formulated through a Hilbert-basis analysis of momentum-space symmetry data. We then show that, for all two-dimensional wallpaper groups, with or without spin-orbit coupling and/or time-reversal symmetry, every symmetry-indicated fragile phase is adiabatically connected to an atomic insulator in a suitable finite supercell and can therefore be trivialized by an arbitrarily small symmetry-preserving perturbation. Our results reveal that fragile topology has only finite stability under translation-symmetry refinement. This highlights that the fate of a fragile phase can depend on translation-symmetry-breaking perturbations, such as charge-density-wave ordering, and suggests that physical signatures insensitive to translation refinement are unlikely to uniquely characterize fragile topology.