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As part of my computational project in topological insulators, I wish to calculate the Z2 invariant in my tight binding model of Kane-Mele Graphene. I have so far produced band structure and surface states consistent with literature, and have been looking at the theory of the Z2 invariant, and in my attempt at writing code to produce the result in a QSH insulator, I cannot seem to get it to work. I simply produce a matrix for time reversal, which is [[0, 1],[-1,0]] tensor identity, and calculate the sewing matrix elements defined in Fu and Kane's paper (2006). However when finding the Pfaffian of the Matrix and dividing by the square route of the determinant for each Time-reversal Invariant momenta in Graphene's 2D BZ, their combined product does not give me a correct answer nor even a quantised one. There isn't really anyone with much knowledge at my institution, so I do not know where to go for advise on this. Is there an effect computational method of calculating the Z2 invariant from the Kane-Mele model in tight binding form?

I really appreciate the help.

Thanks.

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# Calculating the Z2 Invariant in Kane-Mele Model

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