# Definition Time-Reversal Invariant Momenta are points at the [[Brillouin Zone|Brillouin zone]] center and corners that obey: $ -\pmb{k} = \pmb{k} \mod \pmb{G} $ where $G$ is a reciprocal lattice vector. There's $2^d$ of them in $d$-dimensions. In 3D they can be written as $ \Lambda_{n_1 n_2 n_3} = \frac{n_1}{2} \pmb{b}_1 + \frac{n_2}{2} \pmb{b}_2 + \frac{n_3}{2} \pmb{b}_3, \quad n_{1,2,3} = 0, 1 $ where $\pmb{b}_i$ are the primitive reciprocal lattice vectors. Below are 2 figures showing these points in 2 and 3 dimensions for a square lattice. These lattices can be smoothly deformed into any other shape so the definition of the TRIM does not change. ![[Pasted image 20210617162026.png]] ![[Pasted image 20210617162842.png]]