= Dirac point
{c}
A Dirac point is a momentum-space point where two <energy bands> touch and their leading splitting is linear in displacement from that point. A local two-band <Hamiltonian> often takes the form $H=E_D I+\hbar v_xq_x\sigma_x+\hbar v_yq_y\sigma_y$, where $\mathbf q$ is measured from the touching point and the <Pauli matrices> act on a two-component internal basis.
Its <energy eigenvalues> are $E_D\pm\hbar\sqrt{v_x^2q_x^2+v_y^2q_y^2}$, producing a <Dirac cone>. The two components can label sublattices rather than real <spin>. Adding a symmetry-allowed term $m\sigma_z$ opens a gap $2|m|$, illustrating why the symmetries protecting the touching matter. Distinct <Dirac valleys in graphene> are regions around different Dirac points.
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