Theory of tunnelling into and from cuprates

A single-particle spectral density is proposed for cuprates taking into account the bipolaron formation, realistic band structure, thermal fluctuations and disorder. Tunnelling and photoemission (PES) spectra are described, including the temperature independent gap observed both in the superconducting and normal states, the emission/injection asymmetry, the finite zero-bias conductance, the spectral shape in the gap region and its temperature and doping dependence, dip-hump incoherent asymmetric features at high voltage (tunnelling) and large binding energy (PES). PACS numbers:74.20.-z,74.65.+n,74.60.Mj Typeset using REVTEX 1 The strong-coupling extension of the BCS theory based on the 1/λ multi-polaron perturbation technique firmly predicts the transition to a charged Bose liquid in the crossover region of intermediate values of the BCS coupling constant λ [1]. There is a fundamental difference between the bipolaron theory of high-Tc cuprates [2] and other theories involving real-space pairs (bosons) tightly bound by a field of a pure electronic origin. As emphasised by Emery et al [3] such ‘electronic’ theories are a priori implausible due to the strong short-range Coulomb repulsion between two carriers. The direct (density-density) repulsion is usually much stronger than any exchange interaction. On the other hand, the Frohlich electron-phonon interaction can provide mobile intersite bipolarons in the CuO2 plane condensing at high Tc [4]. The (bi)polaronic nature of carriers in cuprates explains a very small coherence volume in the superconducting state, the mid-infrared conductivity [5], the isotope effect on the carrier mass [6]. Although the charged Bose liquid of bipolarons describes anomalous thermodynamics and kinetics of cuprates [7], finite frequency/momentum response functions of bipolaronic superconductors remain to be established. In this letter we derive a single-particle spectral function of strongly coupled carriers in a random potential which provides a quantitative description of recent tunnelling spectra [8,9] and explains some photoemission features (see [10] and references in [8–10]). In the framework of our theory the ground state of cuprates is a charged Bose-liquid of intersite bipolarons with single polarons existing only as excitations with the energy ∆/2 or larger. Different from the BCS description the pair binding energy ∆ is temperature independent. Hence, there is no other phase transition except a superfluid one at T = Tc. The characteristic temperature T ∗ of the normal phase is a crossover temperature of the order of ∆/2 where the population of the upper polaronic band becomes comparable with the bipolaron density. Along this line the theory of tunnelling in the bipolaronic superconductors was developed both for two-particle [11] and singleparticle [12] transitions through a dielectric contact. It allowed us to understand the temperature independent gap and the asymmetry of the current-voltage characteristics, observed already in the earlier 2 tunnelling experiments [13]. However, an attempt to fit the conductance structure led us to a very narrow (bi)polaronic band with a bandwidth of the order or even less than Tc [11,12]. Such a bandwidth is not compatible with the experimental estimate of the effective carrier mass, m ≃ 2−10me (depending on doping) from the London penetration depth [7]). It is also incompatible with the theoretical estimate [4] of the (bi)polaron bandwidth (c.a. 100meV or larger) based on the well-established value of the Frohlich interaction. Moreover, any description based on the Bloch representation is hardly justifiable for cuprates with the mean free path often comparable with the lattice constant. One has to consider a random potential and thermal fluctuations along with a strong pairing potential and band-structure effects. We apply a single-particle tunnelling Hamiltonian describing the injection of an electron into a single hole polaronic state P with the matrix element Pk,ν and into a paired hole (bipolaronic) state B with the matrix element Bk,ν,μ (Fig.1), Htun = ∑