奇偶反常支配菱方石墨烯中手性超导在 $T_c$ 之上和之下的热霍尔响应
Parity anomaly governs the thermal Hall response of chiral superconductivity in rhombohedral graphene above and below $T_c$
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中文总结 AI 辅助
本文证明奇偶反常精确决定菱方石墨烯手性超导的热霍尔响应，给出无参数公式，预测信号在配对温度出现，且符号与反常霍尔电阻一致，提供可证伪测试。
中文摘要 AI 辅助
最近，在BCS-BEC交叉附近的菱方四层和五层石墨烯中，手性超导已被证实，但没有任何理论告诉实验者应预期何种热霍尔响应，或为何任何信号应在相位相干温度 $T_c$ 之上持续存在。我们证明，$(2{+}1)$ 维场论的奇偶反常在所有温度下精确地固定了答案，且无自由参数：$\kappa_{xy}/T = (\pi^2 k_B^2/6h)\\,C_{\rm BdG}\\,\tanh[\Delta(T)/(2k_BT)]$，其中 $C_{\rm BdG}$ 是BdG陈数，$\Delta(T)$ 是费米子激发能隙。BCS-BEC双能隙关系 $\Delta^2 = \Delta_{\rm sc}^2 + \Delta_{\rm pg}^2$ 使得同一公式同时支配凝聚体和赝能隙区域，因此信号在配对形成温度 $T^{*}$ 而非 $T_c$ 处开始出现。Coleman-Hill非重整化定理和 $c_1 = 0$ 定理保护此结果免受相互作用和有限尺寸伪影的影响。三个独立的数值验证以机器精度（FHS陈数、Wilson环 $c_1 = 0$ 测试）和多体层面（对28个收敛基态的DMRG，包括实空间 $p+ip$ 特征 $\arg\mathcal{A}_y - \arg\mathcal{A}_x = -\pi/2$ 恢复至 $10^{-14}$）确认了拓扑输入。该理论提供了一个无需新实验设备的即时可证伪测试：$T_c$ 之下 $\kappa_{xy}/T$ 的符号必须等于已在 $T_c$ 之上测量的反常霍尔电阻 $R_{xy}$ 的符号，以及四个可通过稀释制冷机纳米量热法在现有器件上实现的进一步预测。
英文摘要
Chiral superconductivity has recently been confirmed in rhombohedral tetra- and pentalayer graphene near the BCS--BEC crossover, but no theory tells the experimentalist what thermal Hall response to expect, or why any signal should persist above the phase-coherence temperature $T_c$. We show that the parity anomaly of $(2{+}1)$-dimensional field theory fixes the answer exactly, at all temperatures, with no free parameters: $κ_{xy}/T = (π^2 k_B^2/6h)\,C_{\rm BdG}\,\tanh[Δ(T)/(2k_BT)]$, where $C_{\rm BdG}$ is the BdG Chern number and $Δ(T)$ is the fermionic excitation gap. The BCS--BEC two-gap relation $Δ^2 = Δ_{\rm sc}^2 + Δ_{\rm pg}^2$ makes the same formula govern both the condensate and pseudogap regimes, so the signal onsets at the pair-formation temperature $T^{*}$ rather than at $T_c$. Coleman--Hill non-renormalization and the $c_1 = 0$ theorem protect this result against interactions and finite-size artefacts. Three independent numerical validations confirm the topological input at machine precision (FHS Chern numbers, Wilson-loop $c_1 = 0$ test) and at the many-body level (DMRG on 28 converged ground states, including the real-space $p+ip$ signature $\arg\mathcal{A}_y - \arg\mathcal{A}_x = -π/2$ recovered to $10^{-14}$). The theory delivers an immediate falsifiable test that requires no new experimental apparatus: the sign of $κ_{xy}/T$ below $T_c$ must equal the sign of the anomalous Hall resistance $R_{xy}$ already measured above $T_c$, and four further predictions accessible by dilution-refrigerator nano-calorimetry on existing devices.
发表机构
- E.ON Digital Technology（E.ON数字技术）
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