X-ray spectrum of a pinned charge density wave

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We calculate the X-ray diffraction spectrum produced by a pinned charge density wave (CDW). The signature of the presence of a CDW consists of two satellite peaks, asymmetric as a consequence of disorder. The shape and the intensity of these peaks are determined in the case of a collective weak pinning using the variational method. We predict divergent asymmetric peaks, revealing the presence of a Bragg glass phase. We deal also with the long range Coulomb interactions, concluding that both peak divergence and anisotropy are enhanced. Finally we discuss how to detect experimentally the Bragg glass phase in the view of the role played by the finite resolution of measurements.