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arXiv 2109.02098cond-mat.mes-hallcond-mat.other
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具有库仑相互作用的关联二阶Dirac半金属

Correlated second-order Dirac semimetals with Coulomb interactions

Yu-Wen Lee, Yu-Li Lee

摘要:

利用重整化群研究了长程库仑相互作用对二阶狄拉克半金属低温性质的影响。与一阶Dirac半金属相比,在连续极限下,全旋转对称性也被破坏,低能物理过程由两个无量纲参数控制:无量纲耦合常数和各向异性参数之比.我们表明,前者流到零,后者流到一个固定的值在低能量。因此,人们可以根据重整化微扰理论计算物理量。作为应用,我们通过求解重整化群方程确定了比热随温度的变化关系。在完全旋转对称性破缺之后,存在交叉温度标度$T_c$(和长度标度$L_c$)。只有当温度远小于$T_c$时,物理量才接近一阶狄拉克半金属的值。同样,当距离小于$L_c$时,屏蔽库仑势将变为各向异性,而在其尾部恢复为未屏蔽形式。

英文摘要:

We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation symmetry is broken even in the continuum limit, and thus the low-energy physics is controlled by two dimensionless parameters: the dimensionless coupling constant and the ratio of the anisotropy parameters. We show that the former flows to zero and the latter flows to a fixed value at low energies. Thus, one may calculate physical quantities in terms of the renormalized perturbation theory. As an application, we determine the temperature dependence of the specific heat by solving the renormalization-group equations. Following from the breaking of the full rotation symmetry, there exists a crossover temperature scale $T_c$ (and a length scale $L_c$). Physical quantities approach the values for the first-order Dirac semimetal only when the temperature is much smaller than $T_c$. Similarly, the screened Coulomb potential will become anisotropic when the distance is smaller than $L_c$, while the unscreened form is recovered at its tail.

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