Superfluid density in the underdoped YBa₂Cu₃O₇₋ₓ: Evidence for d-density wave order of pseudogap

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The investigation of the penetration depth λab(T,p) in YBa₂Cu₃O₇₋ₓ crystals allowed to observe the following features of the superfluid density nₛ(T,p)∝ λab⁻²(T,p) as a function of temperature T<Tc/2 and carrier concentration 0.078≤ p≤ 0.16 in CuO₂ planes: (i) nₛ(0,p) depends linearly on p, (ii) the derivative |dnₛ(T,p)/dT|ₜ→ ₀ depends on p slightly in the optimally and moderately doped regions (0.10<p≤ 0.16); however, it rapidly increases with p further lowering and (iii) the latter finding is accompanied by the linear low-temperature dependence [-Δnₛ(T)]∝ T changing to [-Δnₛ(T)]∝ √T. All these peculiarities can be treated in the framework of d-density wave scenario of electronic processes in underdoped high-Tc materials.