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arXiv:1809.10726 · Physical review. B./Physical review. B

Disordered flat bands on the kagome lattice

Thomas Bilitewski, Roderich Moessner

Published Dec 5, 2018• 77 citations
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Abstract

In flat bands, the kinetic energy is fully quenched rendering interactions nonperturbative and resulting in complex many-body phenomena, such as the (fractional) quantum Hall effect. Here, the authors study the interplay of correlated disorder, topology, and interactions on the kagome lattice, which hosts a flat band with a quadratic-band touching point and Dirac cones. The authors find exact solutions and demonstrate how to introduce spectral gaps, thus establishing a prime platform to study topological and correlated flat-band physics.

DOI
10.1103/physrevb.98.235109

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In flat bands, the kinetic energy is fully quenched rendering interactions nonperturbative and resulting in complex many-body phenomena, such as the (fractional) quantum Hall effect. Here, the authors study the interplay of correlated disorder, topology, and interactions on the kagome lattice, which hosts a flat band with a quadratic-band touching point and Dirac cones. The authors find exact solutions and demonstrate how to introduce spectral gaps, thus establishing a prime platform to study topological and correlated flat-band physics.
Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (V1{V}_{1}V1​ and V2{V}_{2}V2​), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate V2<V1{V}_{2}<{V}_{1}V2​<V1​ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.
We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion symmetries, the energy bands consist of three doubly degenerate bands whose energy and conditions for the presence of flat bands could be obtained analytically, allowing us to tune the flat band with respect to the other two dispersive bands from the top to the middle and then to the bottom of the three bands. We further study the gapped phases of the model and show that they belong to the same phase as the band gaps only close at discrete points of the parameter space, making any two gapped phases adiabatically connected to each other without closing the band gap. Using the Pfaffian approach based on the time-reversal symmetry and parity characterization from the inversion symmetry, we calculate the bulk topological invariants and demonstrate that the unique gapped phases belong to the Z2{\mathbb{Z}}_{2}Z2​ quantum spin Hall phase, which is further confirmed by the edge state calculations.
Geometric frustration is a phenomenon where local energy constraints cannot be simultaneously satisfied because of geometric reasons. This leads to a manifold of degenerate ground states in which ordering can be highly nontrivial and exotic phases of matter could emerge. In a kagome lattice, both interaction energies of spins and kinetic energies of particles can be frustrated. In the latter case, a single-particle band structure with a flat (dispersionless) energy band results.In this dissertation, we report our experimental studies of interacting bosonic systems in kagome lattices. Such studies are performed with a quantum simulator based on ultracold atoms in optical lattices. We describe upgrades and development of the apparatus that constructs optical kagome lattices in our experiment. We briefly discuss results of an experiment studying the Bose-Hubbard model in a trimerized kagome lattice. We then report the details of an experiment investigating the interplay of kinetic frustration and interactions by probing the band structure of an optical kagome lattice with interacting ultracold bosonic atoms. Finally, we propose experimental ideas for exploring the properties of the singular band touching point in the kagome flat band.
Strange metals arise in a variety of platforms for strongly correlated electrons, ranging from the cuprates, heavy fermions to flat band systems. Motivated by recent experiments in kagome metals, we study a Hubbard model on a kagome lattice whose noninteracting limit contains flat bands. A Kondo lattice description is constructed, in which the correlation effects are captured by symmetry preserving and exponentially localized molecular orbitals. These compact molecular orbitals represent the local degrees of freedom that emerge from topological flat bands. We identify a quantum critical point at which quasiparticles are lost and strange metallicity emerges. Our theoretical work opens up a new route for realizing beyond-Landau quantum criticality, as well as the associated strange metallicity and emergent quantum phases.
Flat energy bands are suitable for observing the Fractional Quantum Hall Effect. We propose an optical setup that can be used for probing flat bands of the Kagome and dice lattice structures dressed by a gauge field. For the Kagome lattice we show that these bands are indeed topologically nontrivial. We suggest using an optical potential that generates the Kagome and dice structures simultaneously. We propose a lattice shaking-scheme to induce a gauge field that is equivalent to a magnetic field, resulting in the desired energy spectrum. Combining the shaking with resonant driving and a site-dependent phase shift, we present a construction for the Kagome lattice that generates flat bands that can be probed experimentally. Implementing interactions in this setup immediately corresponds to being in the strongly correlated regime.