The pseudogap phase in (TaSe$_4$)$_2$I

We have developed the mean-field theory of coexisting charge-density wave (CDW) and unconventional charge-density wave (UCDW). The double phase transition manifests itself in the thermodynamic quantities and in the magnetic response, such as spin susceptibility and nuclear spin-lattice relaxation rate. Our theory qualitatively applies to the quasi-one dimensional CDW material (TaSe$_4$)$_2$I. This material exhibits peculiar properties: above the CDW transition temperature $T_c$, thermal fluctuations were found to die out rapidly, but robust pseudogap behavior is still detected. Namely, the experimental findings include: (i) sharp increase of the static spin susceptibility above $T_c$, (ii) smooth increase of the spin-lattice relaxation rate above $T_c$, (iii) as opposed to conventional CDW, no sharp feature in the spin-lattice relaxation rate below $T_c$. We have found that our coexisting CDW+UCDW model qualitatively describes these observed properties of (TaSe$_4$)$_2$I. Direct calculations for the magnetic response are shown to evidence the agreement. We also argue, that the fluctuations around $T_c$ are suppressed due to the presence of the ``hidden'' UCDW phase, which partially gaps the Fermi surface, and causes non-Fermi-liquid (pseudogap) behavior.