# What is zero and infinite effective mass?

• I
• anahita

#### anahita

What is effective mass?
What is zero and infinite effective mass?

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What is the effective mass of zero and infinite?
That does not seem to be a meaningful question. What is it that you are trying to find out?

That does not seem to be a meaningful question. What is it that you are trying to find out?
I was reading about concept of effective mass on Wikipedia and came across the line that effective mass of a particle can be negative , zero and even infinite. How is this possible?

I'm not aware that mass can be infinite and I believe negative mass is speculative. Photons have zero mass.

Well, consider what mass is. If you take some free particle and plot energy versus momentum, you will get a parabolic curve as E=p^2/2m.
The curvature of the parabola tells you something about the mass. large curvature corresponds to low mass, while a rather flat curve corresponds to large mass.

Now, if you consider quasiparticles such as an electron inside the crystal, you will find that its energy will not only depend on its momentum, but also on the interactions with all the other particles in the solid. In many cases, the plot of energy versus momentum will still describe a parabola, but the curvature will not be given by the mass of the electron alone, but also by the interactions with other particles. As the curve is still parabolic, it is a very good approximation to describe this electron as an effective free particle with a modified mass due to the interactions. This is the effective mass. Occasionally, the effect of interactions may be more important than the effect of the bare mass alone. For example this is the case for holes in a semiconductor. Their dispersion looks like an inverted parabola, where the energy is reduced with increasing momentum. This can be described by a negative effective mass and if a force is acting on them, they will indeed show a motion against the direction of the force. However, this is a consequence of the interactions rather than the bare mass of the particle.

Accordingly, the shape of the dispersion determines the effective mass. A parabola is the standard case and a large curvature corresponds to small effective mass and a small curvature to large mass. A parabola facing downwards corresponds to negative mass. A dispersion, which is a flat line and has a constant energy for all values of momentum corresponds to infinite effective mass. Finally, a linear dispersion, such as the one seen for photons, corresponds to zero effective mass.

• DeathbyGreen
Well, consider what mass is. If you take some free particle and plot energy versus momentum, you will get a parabolic curve as E=p^2/2m.
The curvature of the parabola tells you something about the mass. large curvature corresponds to low mass, while a rather flat curve corresponds to large mass.

Now, if you consider quasiparticles such as an electron inside the crystal, you will find that its energy will not only depend on its momentum, but also on the interactions with all the other particles in the solid. In many cases, the plot of energy versus momentum will still describe a parabola, but the curvature will not be given by the mass of the electron alone, but also by the interactions with other particles. As the curve is still parabolic, it is a very good approximation to describe this electron as an effective free particle with a modified mass due to the interactions. This is the effective mass. Occasionally, the effect of interactions may be more important than the effect of the bare mass alone. For example this is the case for holes in a semiconductor. Their dispersion looks like an inverted parabola, where the energy is reduced with increasing momentum. This can be described by a negative effective mass and if a force is acting on them, they will indeed show a motion against the direction of the force. However, this is a consequence of the interactions rather than the bare mass of the particle.

Accordingly, the shape of the dispersion determines the effective mass. A parabola is the standard case and a large curvature corresponds to small effective mass and a small curvature to large mass. A parabola facing downwards corresponds to negative mass. A dispersion, which is a flat line and has a constant energy for all values of momentum corresponds to infinite effective mass. Finally, a linear dispersion, such as the one seen for photons, corresponds to zero effective mass.