De Haas-van Alphen effect in a 2d lattice

[cavalier3024]

when calculating the frequencies of 1\H's oscillation using De Haas-van Alphen, we need to find the extremal cross-section of the fermi surface perpendicular to the magnetic field direction.
in 3d i can understand this. but when talking about a 2d lattice where the magnetic field is perpendicular to the lattice plane, what do i take as the extremal fermi surface cross section?

and another question, back to 3D - if i have several bands, each of them have different fermi surface, right? so i need to take the extremal cross section at each of them?

 

[BigJDubs]

In the case of a two-dimensional lattice, the extremal cross-section of the Fermi surface is the intersection of the Fermi surface with the plane perpendicular to the magnetic field. This intersection is often called the Fermi line. In the case of multiple bands in a three-dimensional lattice, each band will have its own Fermi surface and thus each will need its own extremal cross-section for calculating the frequencies of 1\H's oscillation using De Haas-van Alphen.

 

[charng]

I can explain the De Haas-van Alphen effect in a 2D lattice and address the questions raised. The De Haas-van Alphen effect is a quantum phenomenon where the oscillation frequency of a material's magnetic susceptibility changes as a function of the applied magnetic field. This effect is observed in materials with a Fermi surface, which is a surface in momentum space that separates the filled and empty states of a material's electronic structure.

In a 2D lattice, the Fermi surface is a 2D surface in momentum space, rather than a 3D surface as in a 3D lattice. Therefore, when calculating the frequencies of 1\H's oscillation using De Haas-van Alphen, we need to find the extremal cross-section of the Fermi surface perpendicular to the magnetic field direction. This means that we need to find the points on the Fermi surface that are closest to the magnetic field direction and use those points to calculate the oscillation frequency.

In terms of the extremal cross-section in a 2D lattice, it will depend on the specific geometry and symmetry of the lattice. In general, the extremal cross-section will be the points on the Fermi surface that are closest to the magnetic field direction. This can be determined by analyzing the electronic structure and symmetry of the lattice.

Moving on to the question about multiple bands in a 3D lattice, it is correct that each band will have its own Fermi surface. Therefore, to calculate the frequencies of oscillation for each band, we would need to determine the extremal cross-section for each band separately. This can be a complex task, as the multiple bands can have different shapes and orientations in momentum space.

In summary, the De Haas-van Alphen effect in a 2D lattice can be understood by finding the extremal cross-section of the Fermi surface perpendicular to the magnetic field direction. In a 3D lattice with multiple bands, the extremal cross-section needs to be determined for each band separately. This highlights the importance of understanding the electronic structure and symmetry of the lattice when studying the De Haas-van Alphen effect.