# Metal–Insulator Transition in Three-Dimensional Semiconductors

## Abstract

**:**

## 1. Introduction

## 2. Model and Symmetries

## 3. Self-Consistent Approximation

## 4. Scaling Relation of the Average Two-Particle Green’s Function

## 5. Discussion and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Phase diagram of the metal–insulator transition of the three-dimensional random gap model from Equation (11), where disorder is the parameter $\gamma $ and the average gap is $\Delta $.

**Figure 2.**Average density of states of the three-dimensional random gap model for fixed $\eta =0.04$ and average gap $\Delta =0.4$ (full curve) and $\Delta =0.8$ (dashed curve).

**Figure 3.**Conductivity as a function of disorder for an average gap $\Delta =0.004$ (red curve), $\Delta =0.04$ (green curve) and $\Delta =0.4$ (blue curve). There is a metal–insulator transition at $\gamma \approx 1$, at $\gamma \approx 1.03$ and at $\gamma \approx 1.37$, respectively.

**Figure 4.**This plot demonstrates the crossover in the critical regime of the conductivity (green curve) through the fitting (red) curve $0.47{(\gamma -{\gamma}_{c})}^{0.6}$. The latter fits the conductivity very well away from the critical point ${\gamma}_{c}$ for $\Delta =0.01$.

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Ziegler, K.
Metal–Insulator Transition in Three-Dimensional Semiconductors. *Symmetry* **2019**, *11*, 1345.
https://doi.org/10.3390/sym11111345

**AMA Style**

Ziegler K.
Metal–Insulator Transition in Three-Dimensional Semiconductors. *Symmetry*. 2019; 11(11):1345.
https://doi.org/10.3390/sym11111345

**Chicago/Turabian Style**

Ziegler, Klaus.
2019. "Metal–Insulator Transition in Three-Dimensional Semiconductors" *Symmetry* 11, no. 11: 1345.
https://doi.org/10.3390/sym11111345