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In the field of valleytronics, they refer to valley coherence as: "the phase relationship between a particle in a superposition of two different valleys" [S. Vitale et al., Small 1801483 (2018)]. The first time they claimed valley coherence was in this paper: https://www.nature.com/articles/nnano.2013.151

Other papers have then measured valley coherence, e.g., through four-wave mixing: https://www.nature.com/articles/nphys3674#Sec2

According to all works that I've seen, valley coherence refers to the fact that if one excites the 2D crystal with linearly polarized light, the relative phase of the electrons in the states K and K' remains unchanged during the excitation process.

However, the crystal is initially in a mixed state. The coherence - as defined by the reduced density matrix - is zero between K and K', i.e., there is initially no fixed phase relation between the K and K' states*, which are thus not in a quantum superposition.

If there is no K-K' coherence before the excitation, how can there be a coherence after? How can one talk about a valley coherence in an initially mixed state?

*I note that K and K' are not coherent in a single-active electron picture, but they are coupled if one includes mean-field or higher-order correlation effects. Yet, none of these works mention that valley coherence comes exclusively from correlations. In fact, usually the opposite is emphasized: electron-electron interactions lead to intervalley scattering, which destroys the fixed phase relation between K and K' and thus the valley coherence.

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