The violation of Wiedemann-Franz (WF) law has been widely discussed in quantum transport experiments as an indication of deviation from Fermi-liquid behavior. The conventional form of WF law is only concerned with the transmission function at the Fermi level, which, however, vanishes in many practical situations. We reinvestigate the WF law in noninteracting quantum systems with vanishing zero-energy transmission and report a universal number $21/5$ as an upper bound of the Lorenz ratio $\mathcal{R}$ in weakly energy-dependent scattering theory. We provide different experimental realizations for the observation of $\mathcal{R}=21/5$, namely, the transport setups with graphene, the multilevel quantum dot and double quantum dot. The reported universal Lorenz ratio paves an efficient way of experimentally obtaining the information about the associated quantum interferences in the system. Our work also provides enough evidence which concludes that the violation of WF law does not necessarily imply the non-Fermi-liquid nature of underlying transport processes; equally, the Fermi-liquid transport characteristics cannot be concluded by an observed validation of WF law.

中文翻译：

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韦德曼-弗朗兹定律在散射理论中的再探讨

违反维德曼-弗朗兹（WF）法则已在量子传输实验中进行了广泛讨论，以作为偏离费米液体行为的指标。WF法的常规形式仅与费米级的传递函数有关，但是，在许多实际情况下，传递函数都消失了。我们对零能量传输消失的非相互作用量子系统中的WF法进行了重新研究，并报告了一个通用数$21/5$ 作为洛伦兹比率的上限 $\mathcal{[R}$在弱能量相关的散射理论中。我们提供不同的实验实现来观察$\mathcal{[R}=21/5$即，通过石墨烯，多级量子点和双量子点进行传输。报道的通用洛伦兹比为实验获得有关系统中相关量子干扰信息的有效方法铺平了道路。我们的工作还提供了足够的证据，得出的结论是，违反世界自然基金会法律并不一定意味着潜在的运输过程具有非费米液体性质。同样，费米液体的传输特性不能通过观察到的WF法验证来得出结论。