error: sigma is zero since no k points contribute to the calculations of MR

[Simba2805]

Dear WT users and developers,

I am using the latest version of WannierTools (2.6.1). I am able to produce the sigma files but in the rho files I am getting the following error: error: sigma is zero since no k points contribute to the calculations of MR

Could anyone please tell me the source of this error and how to resolve this?

Thanks

[AKB-OU]

Dear Simba2805

Hi.

I think the error comes from condition judgment if (abs(det3(rho))>eps6) written around lines 657 and 738 in sigma_OHE.f90. (eps6 = 1e-6)

I do not know the details of your system, but I guess there are very small values in your conductivity components.

Best, AKB

[Simba2805]

Dear AKB,

Thank you for your kind response. My system (2D slab) does not contain the z-components (xz, zx, yz, zy, and zz are zero). Only xx, yy, and xy components are non-zero. The reason could be its 2D nature. sigma_xx, xy and yy components are of the order of 10^(19).

Is this the reason that I am getting this error (zero values of z-components)?

If this is the reason can't I use 2x2 matrices of sigma instead of 3x3 sigma tensors? { {sigma_xx,sigma_xy} , {sigma_yx,sigma_yy} }

Regards

[AKB-OU]

Dear Shubham,

OK, you are calculating a 2D system. I am not a specialist, but I think zz = 0, which is unique in 2D materials, is critical for the above error. The determinant of a conductivity tensor is det(sigma) = -xz yy zx + xy yz zx + xz yx zy - xx yz zy - xy yx zz + xx yy zz. In your case, this is equal to zero because all terms contain zeros. So the condition "abs(det3(rho))>eps6" fails.

In 3D system, on the other hand, the diagonal components xx, yy, and zz are always finite. So normally det(sigma) takes non-zero value (even in the absence of magnetic fields).

I guess WT originally does not assume MR calculation of 2D system.

But I do not think that the obtained sigma_xx and sigma_xy are meaningless. In-plane transport properties that you want will be obtained by inversion of { {sigma_xx,sigma_xy} , {sigma_yx,sigma_yy} } using a handmade script.

Best, AKB

[quanshengwu]

WT only selects k points 50meV around the Fermi surface. If the Fermi level is not well set, then there will be no k points contributing to the magnetoresistance. You can post the band structure and wt.in here.