2.4.4 Transport Coefficients without a Magnetic Field

If the magnetic field is zero, the transport coefficients are multiples of basic driving forces. Equivalently, the transport coefficients are symmetric tensors. Three of them can be identified.

2.4.4.1 Heat Conductivity

The isothermal heat conductivity of electrons (holes) $\kappa_n$ ($\kappa_p$) describes the electron (hole) heat current density $\mathbf{Q_n}$ ( $\mathbf{Q_p}$) driven by a temperature gradient $\nabla T$ under zero current conditions:

$$\kappa_{n,p} = - \frac{\mathbf{Q_{n,p}} \cdot \nabla T}{\vert\nabla T\vert^2} \quad \mathbf{J_{n,p}}=0$$ (2.7)

2.4.4.2 Electric Conductivity

The isothermal electric conductivity of the electrons (holes) $\sigma_n$ ($\sigma_p$) describes the electron (hole) current $\mathbf{J_n}$ ( $\mathbf{J_p}$) driven by a gradient of the quasi Fermi level; the inverse of $\sigma_n$ ($\sigma_p$) is defined as

$$\sigma_{n,p}^{-1} = - \frac{\mathbf{J_{n,p}} \cdot \nabla \phi_{n,p}} {\vert\mathbf{J_{n,p}}\vert^2} \quad \nabla T = 0$$ (2.8)

2.4.4.3 Thermoelectric Power

The absolute thermoelectric power $P_n$ ($P_p$) characterizes the gradient of the quasi Fermi potential $\nabla\phi_n$ ( $\nabla\phi_p$) induced by a temperature gradient under zero current conditions:

$$P_{n,p} = - \frac{\nabla\phi_{n,p}\cdot\nabla T}{\vert\nabla T\vert^2} \quad \mathbf{J_{n,p}}=0$$ (2.9)