Superfluid density in the underdoped YBa₂Cu₃O_(7-x): Evidence for d-density wave order of pseudogap

The investigation of the penetration depth \lambda_{ab}(T,p) in YBa_2Cu_3O_{7-x} crystals allowed to observe the following features of the superfluid density n_s(T,p)\propto \lambda_{ab}^{-2}(T,p) as a function of temperature T<Tc/2 and carrier concentration 0.078\le p\le 0.16 in CuO_2 planes: (i) n_s(0,p) depends linearly on p, (ii) the derivative |dn_s(T,p)/dT|_{T\to 0} depends on p slightly in the optimally and moderately doped regions (0.10<p\le 0.16); however, it rapidly increases with p further lowering and (iii) the latter finding is accompanied by the linear low-temperature dependence [-\Delta n_s(T)]\propto T changing to [-\Delta n_s(T)]\propto \sqrt{T}. All these peculiarities can be treated in the framework of d-density wave scenario of electronic processes in underdoped high-Tc materials.