Superlight small bipolarons: a route to room temperature superconductivity'
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Introduction
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The discovery of high-temperature superconductivity in cuprates [@bed] has widened significantly our horizons of the theoretical understanding of the physical phenomenon. A great number of observations point to the possibility that the cuprate superconductors may not be conventional Bardeen-Cooper-Schrieffer (BCS) superconductors [@bcs], but rather derive from the Bose-Einstein condensation (BEC) of real-space small bipolarons [@alemot; @alebook; @edwards]. Importantly a first proposal for high temperature superconductivity by Ogg Jr in 1946 [@ogg], already involved real-space pairing of individual electrons into bosonic molecules with zero total spin. This idea was further developed as a natural explanation of conventional superconductivity by Schafroth [@sha] and Butler and Blatt [@blatt]. Unfortunately the Ogg-Schafroth picture was practically forgotten because it neither accounted quantitatively for the critical behavior of conventional superconductors, nor did it explain the microscopic nature of attractive forces which could overcome the Coulomb repulsion between two electrons constituting a pair. On the contrary highly successful for low-$T_c$ metals and alloys the BCS theory, where two electrons were indeed correlated, but at a very large distance of about $10^{3}$ times of the average inter-electron spacing, led many researchers to believe that any superconductor 