LOCALITY OF THE DENSITY MATRIX IN METALS, SEMICONDUCTORS, AND INSULATORS
LOCALITY OF THE DENSITY MATRIX IN METALS, SEMICONDUCTORS, AND INSULATORS
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金属、半导体和绝缘体中密度矩阵的位置
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
T. Arias
中科院分区：
文献类型：
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作者：
S. Ismail‐Beigi;T. Arias
我们给出了单粒子密度矩阵$\rho（\vec r，\vec r '）\sim\exp（-\gamma）的空间衰减率$\gamma$的解析研究|\vec r-\vec r'|）$的系统描述的单粒子轨道在任意尺寸的周期势。这种衰变反映了凝聚态系统中的电子局域性，也是O（N）密度泛函方法的关键。我们发现$\gamma$的行为与传统的观点相反，传统的观点是绝缘体中的$\gamma\propto\sqrt{\Delta}$和金属中的$\gamma\propto\sqrt{T}$，其中$\Delta$是直接带隙，$T$是温度。相反，在半导体$\gamma\propto\Delta$，并在金属在低温$\gamma\propto T$。
We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that $\gamma$ behaves contrary to the conventional wisdom that generically $\gamma\propto\sqrt{\Delta}$ in insulators and $\gamma\propto\sqrt{T}$ in metals, where $\Delta$ is the direct band gap and $T$ the temperature. Rather, in semiconductors $\gamma\propto\Delta$, and in metals at low temperature $\gamma\propto T$.