# Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

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## Abstract

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## 1. Introduction

## 2. Thermoelectric Relations

## 3. Thermoelectric Coefficient in the Conformal Invariant Point in Dirac Semimetals

## 4. The Hall Conductivity

## 5. The Mott Relation

## 6. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Landau level structure of a single chirality in a Dirac semi-metal. The green straight line represents the chiral zeroth LL. The inset shows the thermoelectric coefficient ${\chi}^{xy}={\alpha}^{xy}/T$ computed in ref. [31].

**Figure 2.**The Hall conductivity ${\sigma}^{xy}$ computed in this work as a function of the chemical potential in the range $-\hslash {\omega}_{c}\le \mu \le \hslash {\omega}_{c}$ for various values of the temperature. At $T=0$, the conductivity is linear in $\mu $.

**Figure 3.**Behaviour of ${\chi}^{ij}/{\partial}_{\mu}{\sigma}^{ij}$ as a function of the temperature. The Mott relation is not satisfied for $T=0$, where the ratio presents a finite value.

**Figure 4.**Temperature dependence of the Mott ratio between the thermoelectric response function ${\chi}^{xy}$ and the derivative of the electric conductivity ${\partial}_{\mu}{\sigma}^{xy}$ at $\mu =0$. Red dots are the numerical calculation and the blue line is the fit to the function $f\left(\tilde{T}\right)=1+9.27{\tilde{T}}^{2}$. The deviation is smaller than the size of the points.

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**MDPI and ACS Style**

Arjona, V.; Borge, J.; Vozmediano, M.A.H. Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals. *Symmetry* **2020**, *12*, 814.
https://doi.org/10.3390/sym12050814

**AMA Style**

Arjona V, Borge J, Vozmediano MAH. Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals. *Symmetry*. 2020; 12(5):814.
https://doi.org/10.3390/sym12050814

**Chicago/Turabian Style**

Arjona, Vicente, Juan Borge, and María A. H. Vozmediano. 2020. "Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals" *Symmetry* 12, no. 5: 814.
https://doi.org/10.3390/sym12050814