# What is zero and infinite effective mass?

• I
• anahita
In summary, effective mass is a concept that describes the mass of a particle within a solid material, taking into account its interactions with other particles. The effective mass can be modified and can even be negative or infinite depending on the shape of the dispersion of the particle's energy versus momentum. A parabolic curve represents a standard case with small curvature corresponding to low mass and a flat curve corresponding to large mass. Negative effective mass is caused by interactions, and a linear dispersion corresponds to zero effective mass.
anahita
What is effective mass?
What is zero and infinite effective mass?

Last edited:
anahita said:
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?

phinds said:
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
Cthugha said:
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.

## What is zero effective mass?

Zero effective mass refers to the property of a particle having no resistance to acceleration. This means that the particle has no inertia and can move at any speed without experiencing any force.

## What is infinite effective mass?

Infinite effective mass refers to the property of a particle having an infinitely large resistance to acceleration. This means that the particle has an infinite amount of inertia and cannot be accelerated by any force.

## How is effective mass different from rest mass?

Effective mass is a concept used in solid state physics to describe the behavior of particles in a crystal lattice. It is different from rest mass, which is the mass of a particle at rest in the absence of any external forces.

## What is the significance of zero and infinite effective mass?

Zero and infinite effective mass have significant implications in the behavior of particles in a crystal lattice. Zero effective mass allows for particles to move freely without any resistance, while infinite effective mass causes particles to be immobile.

## Can particles have effective mass values other than zero and infinite?

Yes, particles can have effective mass values that are neither zero nor infinite. This value can vary depending on the properties of the crystal lattice and the type of particle. For example, electrons in a semiconductor have an effective mass that is different from their rest mass.

• Atomic and Condensed Matter
Replies
2
Views
2K
• Atomic and Condensed Matter
Replies
1
Views
1K
• Atomic and Condensed Matter
Replies
5
Views
2K
• Atomic and Condensed Matter
Replies
6
Views
2K
• Atomic and Condensed Matter
Replies
3
Views
3K
• Atomic and Condensed Matter
Replies
1
Views
2K
• Atomic and Condensed Matter
Replies
10
Views
909
• High Energy, Nuclear, Particle Physics
Replies
1
Views
281
• Atomic and Condensed Matter
Replies
2
Views
3K
• Special and General Relativity
Replies
12
Views
422