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arXiv 1002.1404cond-mat.mes-hall
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反演对称相互作用模型量子电导的普适标度

Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model

Axel Freyn, Jean-Louis Pichard

摘要:

我们考虑了无自旋费米子在一维晶格中的量子输运,晶格中嵌入了相互作用区域(两个位置具有位置间排斥U和位置间跳跃td,通过跳跃项tc耦合到引线)。利用粒子-空穴对称情况下的数值重整化群,我们研究了量子电导g与格点间跳跃td的关系。当td -> 0或td ->无穷大时完全反射的相互作用区域,如果td取定义该相互作用模型的特征能量的中间值τ(U,tc),则变为完全透射。当td < tc sqrt(U)时,g由无量纲比X=td/τ的普适函数给出。这种普适性表征了非相互作用区(τ= tc ^2)、微扰区(U <tc ^2)和非微扰区(U > tc ^2),微扰区的τ可以用哈特里-福克理论得到,非微扰区的τ是由反演对称性引起的轨道近藤效应的特征温度TK的两倍。当td < τ时,表达式g(X)=4/(X+1/X)^2在没有相互作用的情况下成立,也描述了存在相互作用时的电导。为了得到这些结果,我们将这个无自旋模型映射到一个有自旋的安德森模型上,其中量子杂质位于半无限一维导线的端点,td扮演磁场h的角色。这使我们能够使用在零温度下安德森模型的磁化强度m(h)获得的精确结果来描述g(td)。我们期望这种通用缩放在具有2D引线的模型中也是有效的,并且使用2D半导体异质结构和由具有强电容性点间耦合的两个相同量子点制成的相互作用区域以及通过可调谐量子点接触连接的相互作用区域来观察。

英文摘要:

We consider quantum transport of spinless fermions in a 1D lattice embedding an interacting region (two sites with inter-site repulsion U and inter-site hopping td, coupled to leads by hopping terms tc). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the inter-site hopping td. The interacting region, which is perfectly reflecting when td -> 0 or td -> infinity, becomes perfectly transmitting if td takes an intermediate value τ(U,tc) which defines the characteristic energy of this interacting model. When td < tc sqrt(U), g is given by a universal function of the dimensionless ratio X=td/τ. This universality characterizes the non-interacting regime where τ=tc^2, the perturbative regime (U < tc^2) where τcan be obtained using Hartree-Fock theory, and the non-perturbative regime (U > tc^2) where τis twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When td < τ, the expression g(X)=4/(X+1/X)^2 valid without interaction describes also the conductance in the presence of the interaction. To obtain those results, we map this spinless model onto an Anderson model with spins, where the quantum impurity is at the end point of a semi-infinite 1D lead and where td plays the role of a magnetic field h. This allows us to describe g(td) using exact results obtained for the magnetization m(h) of the Anderson model at zero temperature. We expect this universal scaling to be valid also in models with 2D leads, and observable using 2D semi-conductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive inter-dot coupling and connected via a tunable quantum point contact.

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