Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity
Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity
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DOI：
10.1103/physrevb.101.165112
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发表时间：
2019-12
影响因子：
3.7
通讯作者：
Yuval Vinkler-Aviv;D. May;F. Anders
中科院分区：
文献类型：
--
作者：
Yuval Vinkler-Aviv;D. May;F. Anders
本文采用解析和数值方法研究了时间反转对称螺旋电子边与磁性杂质反铁磁耦合的电导。杂质可以通过产生反向散射电流来降低非相互作用螺旋边的完美电导G_0。对于时间反转对称装置，后向散射稳态电流在近藤温度T_K以下趋于消失。我们证明了维持完美电导的核心作用是由全局$U(1)$对称性起作用的。这种对称性可以通过螺旋模式与局部杂质的各向异性交换耦合而被打破。这种各向异性通常在重正化群（RG）流动到低温强耦合极限时动态消失。利用时间相关数值重整化群（TD-NRG）方法进一步研究了各向异性交换耦合的作用，该方法特别适用于计算强相关装置的非平衡观测值。我们研究了在各向同性强耦合固定点到达之前，有限偏置电压和温度在切断RG流中的作用，提取了相关的能量尺度，以及从弱相互作用区到强耦合无背散射屏蔽区交叉的表现方式。最值得注意的是，我们发现在低温下，后向散射电流的电导遵循幂律行为$G\sim (T/T_K)^2$，我们将其理解为由于有限偏置导致的时间反转对称性破坏而产生的强烈非线性效应。
We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the conductance of the backscattering current follows a power-law behavior $G\sim (T/T_K)^2$, which we understand as a strong nonlinear effect due to time-reversal symmetry breaking by the finite-bias.