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We consider the four-component two-valley Dirac operator on a wedge in$\mathbb{R}^2$ with infinite mass boundary conditions, which enjoy a flip atthe vertex. We show that it has deficiency indices $(1,1)$ and we parametrizeall its self-adjoint extensions, relying on the fact that the underlyingtwo-component Dirac operator is symmetric with deficiency indices $(0,1)$. Therespective defect element is computed explicitly.  We observe that there exists no self-adjoint extension, which can bedecomposed into an orthogonal sum of two two-component operators. In physics,this effect is called mixing the valleys.

Self-adjoint extensions of the two-valley Dirac operator with discontinuous infinite mass boundary conditions