Resistivity tensor and Magnetoresistance

[Jan Hidding]

Hey everyone,

I'm currently trying to understand the resistivity and conductivity tensor of a 2D sample. If a current carrying metal bar is placed inside a magnetic field the Hall Effect comes into play. I tried to search for explanations on how to obtain the resistivity tensor of the metal bar in this configuration but I can seem to understand how it is obtained.

Secondly, I have read that there should be a classical $$ B^2 $$ dependence of the resistance of the sample but I also do not understand what is the origin.

Thanks in advance!

 

[eljose79]

Hi there,

Understanding the resistivity and conductivity tensor of a 2D sample can be a complex topic, but I'll try to break it down for you. The resistivity tensor is a mathematical representation of how a material responds to an electric field in different directions. It is a 3x3 matrix that relates the electric field and current density vectors. Similarly, the conductivity tensor is the inverse of the resistivity tensor and represents how a material conducts electricity in different directions.

In the case of a current carrying metal bar placed in a magnetic field, the Hall Effect comes into play. This effect occurs when a magnetic field is applied perpendicular to the direction of current flow in a conductor. The resulting electric field, known as the Hall field, causes a voltage perpendicular to both the current and magnetic field. This voltage is known as the Hall voltage and is directly proportional to the strength of the magnetic field and the current density.

To obtain the resistivity tensor in this configuration, you would need to measure the Hall voltage for different values of the magnetic field and current density. This data can then be used to calculate the components of the resistivity tensor. Similarly, the conductivity tensor can be obtained by measuring the current density for different values of the electric field.

As for the classical $$ B^2 $$ dependence of the resistance, this is due to the Lorentz force experienced by the moving charges in the metal bar. As the magnetic field increases, the Lorentz force also increases, leading to a higher resistance. This effect is known as magnetoresistance and is commonly observed in materials with a high carrier mobility, such as metals.

I hope this helps to clarify things for you. Let me know if you have any further questions. Good luck with your research!