临界拓扑平带中无能隙的拓扑横向输运

中文摘要 AI 辅助

量子化的霍尔输运传统上依赖于体态谱隙，该谱隙将占据子空间隔离并指数级抑制热涨落。最近发现的临界拓扑平带（CTFBs）挑战了这一范式：一条完全平坦的能带与色散连续谱相接触，同时保持明确定义的整数陈数。然而，其有限温度下的横向输运性质完全未被探索。在此，我们发展了CTFBs中本征电、热电和热霍尔响应的低温理论。在固定粒子数下，宏观平带简并迫使化学势产生奇异的Lambert-$W$漂移，生成低温修正的代数-对数层级：电霍尔为$T\ln(1/T)$，热电霍尔为$T[\ln(1/T)]^2$，热霍尔电导率为$T[\ln(1/T)]^3$，取代了有隙陈绝缘体的激活式热保护。相反，将化学势外部钉扎在平带能量上会使平带在任何非零温度下锁定在半占据状态，阻碍了当$T\to0^+$时完全填充拓扑基态的恢复。我们的结果表明，体态谱隙对于零温霍尔量子化并非必要，但对于其指数级热保护则是不可或缺的。

英文摘要

Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-$W$ drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: $T\ln(1/T)$ for electrical Hall, $T[\ln(1/T)]^2$ for thermoelectric Hall, and $T[\ln(1/T)]^3$ for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as $T\to0^+$. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.

发表机构

• The University of Tokyo（东京大学）
• Tohoku University（东北大学）
• RIKEN（理化学研究所）
• Ajou University（亚洲大学）

机构由 AI 辅助整理，请以论文原文为准。

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7 pages, 3 figures