We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behaviour of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behaviour at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a $T^2$ coefficient of conductance becomes zero at quarter-filling whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU($4$) scaling behaviour at $_{B}B

中文翻译：

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半填充纳米管点中场诱导的SU（4）到SU（2）近藤交叉：光谱和有限温度特性

我们使用威尔逊数值重归一化组（NRG）研究碳纳米管（CNT）量子点中近藤效应的有限温度特性。在没有磁场的情况下，由自旋和轨道自由度组成的CNT的四个简并能级引起SU（4）Kondo效应。我们重新审查了SU（4）电导率的通用缩放行为，以便在较宽的温度范围内进行四分之一和一半的填充。我们发现低温下普遍结垢行为的填充依赖性$Ť$可以用扩展的费米液体理论清楚地解释。该理论阐明了${Ť}^2$在四分之一填充时电导系数变为零，而在半填充时电导系数是有限的。我们还研究了在半填充的CNT点观察到的从SU（4）到SU（2）近藤状态的场致交叉。交叉是由自旋和轨道塞曼分裂的匹配引起的，即使在磁场中，塞曼分裂也将四层中的两层锁定在费米能级$乙$。我们发现电导显示SU（$4$）在$ _ {B} B的缩放行为