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A Weyl point is a crossing of two bands. A two-band crossing can be described using the general Hamiltonian: $$\hat{H}(\mathbf{k})=d_0(\mathbf{k})+d_1(\mathbf{k})\sigma_1+d_2(\mathbf{k})\sigma_2+d_3(\mathbf{k})\sigma_3$$ where $\sigma_i$ are the Pauli matrices. The eigenvalues are given by $E_{\pm}=d_0\pm\sqrt{d_1^2+d_2^2+d_3^2}$, so that a band crossing ...

7

Here are a few thoughts: Weyl semimetal Weyl point. A Weyl point is a point at which 2 bands cross. This places severe constraints on which type of material can host Weyl points, because in materials with both time-reversal and inversion symmetries, bands are already doubly-degenerate (spin up and down have the same energy at every $\mathbf{k}$-point), so ...

5

A Weyl point does indeed have linear dispersion. The effective mass tensor you are using $\frac{1}{m^*_{ij}}\propto\frac{\partial^2\varepsilon(k)}{\partial k_i \partial k_j}$ is not really well-defined here. After all, we only define the effective mass that way to match the common non-relativistic equation $\varepsilon = \frac{\hbar^2 k^2}{2m^*}$. A Weyl ...

3

You left off a key phrase from the paper. Noncentrosymmetric systems with time reversal symmetry don't have nonreciprocal linear response. Linear response on its own doesn't have this property. For example Electric Polarizability is the linear response of the dipole to a change in the electric field and this in general is nonzero for noncentrosymmetric and ...

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