绝缘态颗粒膜导电特性的广义解释：临界路径理论的新观点

     由于真空镀磨技术的飞跃进步与普及，绝缘体-导体复合物（insulator-conductor composites）颗粒膜的物性研究一直是一个兼具基础与应用双重意义的课题。其中，处于绝缘态的颗粒膜的导电行为已经被研究了半个多世纪。几十年来，实验上发现在一个很大的温度区间（约1–100 K），许多颗粒膜的电导都呈现的温度变化关系，与组成样品的纳米尺度导体（金属）材料无关。这是一个广泛出现的物理现象，称为“颗粒跃迁导电”（granular hopping conduction）过程。

    吊诡的地方在于，上述这个导电温度变化行为，与著名俄国科学家A. L. Efros和B. L. Shklovskii (ES) 两人的“变程跃迁导电”（variable-range-hopping conduction）理论预测的函数形式完全相同。ES理论处理的是掺杂半导体中的局域态导电行为，这些局域态都是点缺陷（施主或受主）。但在颗粒膜中，金属颗粒常为数纳米大小，包含数千至上万个原子，有明确的费米能级，它的物理性质与点缺陷局域态迥异。

    胡梓俊、林志忠和沈平认为ES理论不能套用到颗粒膜导电问题，并提出一个基于“几何逾渗条件”的“紧邻临界路径模型”（immediate-neighbor critical-path method），直接就能推导出上述的温度变化行为。这个理论概念与ES的想法完全不同，而且跟组成颗粒膜的纳米尺度金属材料完全无关，因此可以用于解释文献中的众多实验结果，并且对样品参数值无严苛限制。这项工作将为颗粒膜的实验与理论研究带来新启示、开展新方向。

An alternative vista on the granular hopping conduction problem

Composites comprising conducting particles dispersed in insulating matrix are very common in our everyday world. It is therefore somewhat surprising that there can be a puzzle in the underlying reason for the universally-observed temperature dependence of such composites’ conductivity  , where T is temperature, and  T_o is a sample-dependent constant. For the past forty years, this so-called granular hopping conduction problem has attracted numerous attempts for its solution, but none was very successful.  One very popular theory is that by Efros and Shklovskii (ES for short), which was originally formulated for point defects and atomic impurities in semiconductors. When applied to granular conduction, the requirement that there must be one-step electronic transport between distant conducting particles has led to theoretical complexities that should be reserved as the last resort when all other possibilities for a physical explanation are exhausted.

In the present article, the authors present a simple and direct explanation for this universal temperature variation of granular hopping conduction, involving only electronic tunneling between immediate neighbor pairs. The theory does not impose any restriction on the type of conducting and insulating materials involved in the system, nor any local correlations between the separation between the conducting particles and their size. Hence the theory is broadly applicable to all types of such composites. The explanation invokes the critical path approach originally formulated by Ambegoakar, Halperin, and Langer to derive the famous Mott’s hopping conduction law, but in the context of immediate-neighbor hopping.

The present work presents an alternative perspective on the granular hopping conduction problem that both illuminates the underlying physics as well as opens up new directions for the study of metal-insulator composites. 

 颗粒膜电阻对温度的变化行为。蓝圆点是理论计算结果，黑方框是银—二氧化锡薄膜实验值，红圆点是数值模拟结果。三者高度吻合（取自本篇论文图2）。 

全文下载：
Tsz Chun Wu, Juhn-Jong Lin, and Ping Sheng, A critical path approach for elucidating the temperature dependence of granular hopping conduction, Front. Phys. 13(5), 137205 (2018)
 

颗粒膜相关科普文章：

林志忠. 十年一瞬间——巨霍尔效应的故事. 物理 41(10), 689 (2012)