Phenomenological description of the coexistence between charge density waves, discommensurations and superconductivity in 1T-TiSe₂

The underlying mechanisms for charge density wave (CCDW) and superconductivity (SC), as well as their interplay, in 1T-TiSe₂ is still under debate. Recent experiments have suggested that, under electron doping, the commensurate CDW (CCDW) order becomes incommensurate (ICDW) and the SC order persists inside the discommensuration (DC) regions of the CDW. Motivated by the pioneering work of McMillan and others, we developed a phenomenological Ginzburg-Landau (GL) theory that describes the interplay between CCDW, ICDW and SC phases in this system through coupling of the superconducting order parameter to the CDW fluctuations. By numerically solving the saddle point (Euler-Lagrange) equations, we trace the phase diagram of the system, according to which: (i) upon doping, the CDW order transitions to incommensurate beyond a critical threshold, (ii) ICDW and SC order coexist in that regime, (iii) the SC order arises first within the CDW discommensurations, all of which are consistent with existing experimental results on 1T-TiSe₂.