How Do Quasielectrons and Holes Impact Superconductors and Metals?

[pleasehelpmeno]

Simply what are these particles and how are they relevant to superconductors and normal metals?

 

[citw]

Holes are quasiparticles by definition. A hole is just the absence of an electron. We assign holes all of the characteristics of a real particle (mass, charge, etc.), but a hole is not a real particle, unlike a positron (which has a place in the standard model). Holes have the opposite charge and sign of energy of electrons. In other words, if we apply an electric field, holes will travel in the same direction as the field, while electrons will travel in the opposite direction. The charge of a hole is $q=+\lvert e\lvert$, while, of course, the charge of an electron is $q=-\lvert e\lvert$.

When we imagine electrons in energy bands, we assume they don't travel as they would in free space. That is, we assign an effective mass to the electron, which describes the curvature of the band, i.e. the effective mass of an electron is given by


$$m_e^*=\hbar^2\left(\frac{\partial^2E}{\partial k^2}\right)^{-1}.$$


In this way, we can imagine the energy electron in a solid in the same way as a free electron, with the adjustment of the effective mass:

$$E=\frac{\hbar^2k^2}{2m_e^*}.$$


So "quasielectrons" are electrons with an effective mass, traveling through the solid, as opposed to rest-mass electrons in free space. The same applies to holes. Holes also have effective mass, but unlike electrons, they are not based on real particles, but the absence of real particles. If $E$ is the energy of the electron, $$E_h=-E$$ is the energy of the hole, and its effective mass is given by

$$m_h^*=\hbar^2\left(\frac{\partial^2E_h}{\partial k^2}\right)^{-1}.$$

In addition to all of this, $k$ is not the same as the momentum of a free electron/hole, but rather the crystal momentum. This takes into account to interaction of the crystal, allowing us to consider the electrons/holes as "free", with the information regarding the lattice potential embedded in the crystal momentum. So all in all, we make these adjustments to the bare electron, making it a quasiparticle for our intents and purposes. The same applies with the hole, but again, it's just the absence of an electron.