Ask for Help: Is there this creation operators?

[PRB147]

Ask for Help: Is this operator reasonable in physics?

Is this kind of the operator is reasonable in physical sense?
$$\sum\limits_{\bf k_x,k_y} \alpha k_x c^\dag_{k_x,k_y}c_{k_x,k_y}$$

where $$\alpha$$ is contant, $$k_x , k_y$$ is wavevector
along the x and y direction.

 

[nrqed]

Is this kind of the operator is reasonable in physical sense?
$$\sum\limits_{\bf k_x,k_y} \alpha k_x c^\dag_{k_x,k_y}c_{k_x,k_y}$$

where $$\alpha$$ is contant, $$k_x , k_y$$ is wavevector
along the x and y direction.

It looks to me as if it's simply counting the total x component of the momentum in a two-dimensional system. The c^\dagger c is just the number operator.

Patrick