Fig. 2: Amplitude and phase modes in the CDW state of CuTe.

a 3D plot of a large scale STM topography at 78.3 K and sample bias voltage 700 mV. The stripy structure represents the alternation of the α (purple) and β (blue) domains. b Line profile extracted perpendicular to the stripe domains in a, whose details are shown in c. The CDW maxima of the α structure oscillate in a oscillatory wave and periodically change into the β structure whenever the neighboring (second) maxima become comparable in their height. Thus, the amplitude oscillations of the α and β CDW can be extracted by the envelope of the first and the second CDW maxima of a CDW unitcell as shown in b and c with red and blue lines, respectively. d α and β CDW amplitude oscillations are plotted together with the lateral phase shifts of each CDW, which are extracted as shown in Fig. 3. The entanglement of the amplitude and phase oscillations follows well the prediction of a soliton lattice model (or the phase-amplitude lock-in transition) except for the existence of two amplitude modes.