We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (
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Abstract J ), for several stackings and moiré superlattices. For AA stacking, a gapped quantum spin liquid phase emerges at a finite$${{\mathbb{Z}}}_{2}$$ J c. We show that this phase survives in the well-controlled large-J limit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite-q inter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively ‘untwisting’ the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev materials. -
Abstract The surface states of 3D topological insulators in general have negligible quantum oscillations (QOs) when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators (TKIs) can support surface states with an arbitrarily large Fermi surface (FS) when the chemical potential is pinned to the Dirac point. We illustrate that these FSs give rise to finite-frequency QOs, which can become comparable to the extremal area of the unhybridized bulk bands. We show that this occurs when the crystal symmetry is lowered from cubic to tetragonal in a minimal two-orbital model. We label such surface modes as ‘shadow surface states’. Moreover, we show that the sufficient next-nearest neighbor out-of-plane hybridization leading to shadow surface states can be self-consistently stabilized for tetragonal TKIs. Consequently, shadow surface states provide an important example of high-frequency QOs beyond the context of cubic TKIs.
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Abstract Excitons are spin integer particles that are predicted to condense into a coherent quantum state at sufficiently low temperature. Here by using photocurrent imaging we report experimental evidence of formation and efficient transport of non-equilibrium excitons in Bi2-xSbxSe3nanoribbons. The photocurrent distributions are independent of electric field, indicating that photoexcited electrons and holes form excitons. Remarkably, these excitons can transport over hundreds of micrometers along the topological insulator (TI) nanoribbons before recombination at up to 40 K. The macroscopic transport distance, combined with short carrier lifetime obtained from transient photocurrent measurements, indicates an exciton diffusion coefficient at least 36 m2 s−1, which corresponds to a mobility of 6 × 104 m2 V−1 s−1at 7 K and is four order of magnitude higher than the value reported for free carriers in TIs. The observation of highly dissipationless exciton transport implies the formation of superfluid-like exciton condensate at the surface of TIs.