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Register a new userHigh Temperature Superconductivity: the explanation
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A. S. Alexandrov
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Soon after the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 the late Sir Nevill Mott answering his own question Is there an explanation? [Nature v 327 (1987) 185] expressed a view that the Bose-Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of real space tightly bound pairs, but with a purely electronic mechanism of pairing rather than with the electron-phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-space pairing) scenario as incompatible with some angle-resolved photoemission spectra (ARPES), with experimentally determined effective masses of carriers and unconventional symmetry of the superconducting order parameter in cuprates. Since then the controversial issue of whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or weak and inessential has been one of the most challenging problems of contemporary condensed matter physics. Here I outline some developments in the bipolaron theory suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron-electron correlations with a significant finite-range (Froehlich) EPI, and that the theory is fully compatible with the key experiments.
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Superconductivity in organic conductors is often tuned by the application of chemical or external pressure. With this type of tuning, orbital overlaps and electronic bandwidths are manipulated, whilst the properties of the molecular building blocks remain virtually unperturbed.Here, we show that the excitation of local molecular vibrations in the charge-transfer salt $kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br$ induces a colossal increase in carrier mobility and the opening of a superconducting-like optical gap. Both features track the density of quasi-particles of the equilibrium metal, and can be achieved up to a characteristic coherence temperature $T^* approxeq 50 K$, far higher than the equilibrium transition temperature $T_C = 12.5 K$. Notably, the large optical gap achieved by photo-excitation is not observed in the equilibrium superconductor, pointing to a light induced state that is different from that obtained by cooling. First-principle calculations and model Hamiltonian dynamics predict a transient state with long-range pairing correlations, providing a possible physical scenario for photo-molecular superconductivity.
The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids (Fig 1a). Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate $t/{hbar}$ and across the charge-transfer energy gap E, generate superexchange spin-spin interactions of energy $Japprox4t^4/E^3$ in an antiferromagnetic correlated-insulator state1. Hole doping the CuO2 plane disrupts this magnetic order while perhaps retaining superexchange interactions, thus motivating a hypothesis of spin-singlet electron-pair formation at energy scale J as the mechanism of high-temperature superconductivity. Although the response of the superconductors electron-pair wavefunction $Psiequiv<c_uparrow c_downarrow>$ to alterations in E should provide a direct test of such hypotheses, measurements have proven impracticable. Focus has turned instead to the distance ${delta}$ between each Cu atom and the O atom at the apex of its CuO5 pyramid. Varying ${delta}$ should alter the Coulomb potential at the planar Cu and O atoms, modifying E and thus J, and thereby controlling ${Psi}$ in a predictable manner. Here we implement atomic-scale imaging of E and ${Psi}$, both as a function of the periodic modulation in ${delta}$ that occurs naturally in $Bi_2Sr_2CaCu_2O_{8+x}$. We demonstrate that the responses of E and ${Psi}$ to varying ${delta}$, and crucially those of ${Psi}$ to the varying E, conform to theoretical predictions. These data provide direct atomic-scale verification that charge-transfer superexchange is key to the electron-pairing mechanism in the hole-doped cuprate superconductor ${Bi_2Sr_2CaCu_2O_{8+x}}$.
In the last two decades there have been tremendous attempts to built an adequate theory of high-temperature superconductivity. Most studies (including our efforts) used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is apriori unknown. Hence one has to start with the generic Hamiltonian including unscreened Coulomb and Froehlich electron-phonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might fail. Using such a generic Hamiltonian I have built the analytical theory of high-temperature superconductivity in doped polar insulators predicting the critical temperature in excess of a hundred Kelvin without any adjustable parameters. The many-particle electron system is described by an analytically solvable polaronic t-Jp Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced antiferromagnetic exchange, Jp >> t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering.
We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds paramagnon spectra are nearly identical apart from an energy scale factor of $sim130%$ that matches the ratio of $T_mathrm{c}$s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer that the strength of magnetic interactions determines how high $T_mathrm{c}$ can reach. Our finding can be viewed as a magnetic analogue of the isotope effect, thus firmly supporting models of magnetically mediated high-temperature superconductivity.
A great variety of novel phenomena occur when two-dimensional materials, such as graphene or transition metal dichalcogenides, are assembled into bilayers with a twist between individual layers. As a new application of this paradigm, we consider structures composed of two monolayer-thin $d$-wave superconductors with a twist angle $theta$ that can be realized by mechanically exfoliating van der Waals-bonded high-$T_c$ copper oxide materials, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$. On the basis of symmetry arguments and detailed microscopic modelling, we predict that for a range of twist angles in the vicinity of $45^{rm o}$, such bilayers form a robust, fully gapped topological phase with spontaneously broken time-reversal symmetry and protected chiral Majorana edge modes. When $thetaapprox 45^{rm o}$, the topological phase sets in at temperatures close to the bulk $T_csimeq 90$ K, thus furnishing a long sought realization of a true high-temperature topological superconductor.
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