Haldane Model: Does edge current exist for a filled band?

[Teek]

Hi all,

I'm currently trying to investigate the edge current on a finite strip of Zigzag Haldane model (spinless, pi/2 phase) and I measure the current (in my code) by taking the expectation value of my current operator which is a function of wavevector k, for each eigenvector of the wavevector-dependent Hamiltonian H(k). The current operator is the net directional hopping matrix when considering only a line across the sample.

When I set the fermi level at the point of the top of the edge mode band, I get zero net current, for a quantum hall system, should this not be a non-zero current? I am confused

Thanks.

 

[nonequilibrium]

Hello. Can you write down this current operator you speak of?

What exactly do you mean by 'the point of the top of the edge mode band'?

I suppose in general I am confused about a few things: since you talk about k it seems you are doing periodic boundary conditions, but since you mention edge mode band it sounds like you are doing open boundary conditions?
Also, do we expect a current if there is no applied electric field?
Both of these questions might have to do with me not knowing what the current operator is you are using?