Abstract:
We show that the single-particle polaron Green's function describes SIS tunnelling in cuprates, including the absence of Ohm's law at high voltages, the dip/hump features in the first derivative of the current, a substantial incoherent spectral weight beyond quasiparticle peaks and unusual shape of the peaks. The theory allows us to determine the characteristic phonon frequencies, normal and superconducting gaps, impurity scattering rate, and the electron-phonon coupling from the tunnelling data.

Abstract:
We describe strongly attractive carriers in cuprates in the framework of a simple quasi-one dimensional Hamiltonian with a local attraction. In contrast with the conventional BCS theory there are two energy scales, a temperature independent incoherent gap $\Delta_p$ and a temperature dependent coherent gap $\Delta_c (T)$ combining into one temperature dependent global gap $\Delta=(\Delta_p^2 +\Delta_c^2)^{1/2}$. The temperature dependence of the gap and single particle (Giaver) tunnelling spectra in cuprates are quantitatively described. A framework for understanding of two distinct energy scales observed in Giaver tunnelling and electron-hole reflection experiments is provided.

Abstract:
A theory capable of explaining intrinsic and extrinsic tunnelling conductance in underdoped cuprates has been devised that accounts for the existence of two energy scales, their temperature and doping dependencies. The asymmetry and inhomogeneity seen in extrinsic (normal metal - superconductor (NS)) tunnelling and the normal-state gapped intrinsic (SS) conductance is explained, as well as the superconducting gap and normal state pseudogap and the temperature dependence of the full gap.

Abstract:
Control of dopants in silicon remains the most important approach to tailoring the properties of electronic materials for integrated circuits, with Group V impurities the most important n-type dopants. At the same time, silicon is finding new applications in coherent quantum devices, thanks to the magnetically quiet environment it provides for the impurity orbitals. The ionization energies and the shape of the dopant orbitals depend on the surfaces and interfaces with which they interact. The location of the dopant and local environment effects will therefore determine the functionality of both future quantum information processors and next-generation semiconductor devices. Here we match observed dopant wavefunctions from low-temperature scanning tunnelling microscopy (STM) to images simulated from first-principles density functional theory (DFT) calculations. By this combination of experiment and theory we precisely determine the substitutional sites of neutral As dopants between 5 and 15A below the Si(001):H surface. In the process we gain a full understanding of the interaction of the donor-electron state with the surface, and hence of the transition between the bulk dopant (with its delocalised hydrogenic orbital) and the previously studied dopants in the surface layer.

Abstract:
There is strong experimental evidence for pairing of polaronic carriers in the normal state, two distinct energy scales, d-wave superconducting order parameter,and charge segregation in the form of stripes in several cuprates.All these remarkable phenomena might be unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Extending the BCS theory towards an intermediate and strong-coupling regime we show that there are two energy scales in this regime, a temperature independent incoherent gap and a temperature dependent coherent gap combining into one temperature dependent global gap. The temperature dependence of the gap and single particle (Giaver) tunnelling spectra in cuprates are quantitatively described. A framework for understanding of two distinct energy scales observed in Giaver tunnelling and Andreev reflection experiments is provided. We suggest that both d-wave superconducting order parameter and striped charge distribution result from the bipolaron (center-of-mass) energy band dispersion rather than from any particular interaction.

Abstract:
We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.

Abstract:
Hawking radiation is nowadays being understood as tunnelling through black hole horizons. Here, the extension of the Hamilton-Jacobi approach to tunnelling for non-rotating and rotating black holes in different non-singular coordinate systems not only confirms this quantum emission from black holes but also reveals the new phenomenon of absorption into white holes by quantum mechanical tunnelling. The role of a boundary condition of total absorption or emission is also clarified.

Abstract:
In this letter, Parikh-Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is extended, and the emission rate of a charged particle tunnelling from the Kerr-Newman black hole is calculated. The emission spectrum takes the same functional form as that of uncharged particles and consists with an underlying unitary theory but deviates from the pure thermal spectrum. Moreover, our calculation indicates that the emission process is treated as a reversible process in the Parikh-Wilczek tunnelling framework, and the information conservation is a natural result of the first law of black hole thermodynamics.

Abstract:
High-$T_c$ cuprates differ from conventional superconductors in three crucial aspects: the superconducting state descends from a strongly correlated Mott-Hubbard insulator, the order parameter exhibits d-wave symmetry and superconducting fluctuations play an all important role. We formulate a theory of the pseudogap state in the cuprates by taking the advantage of these unusual features. The effective low energy theory within the pseudogap phase is shown to be equivalent to the (anisotropic) quantum electrodynamics in (2+1) space-time dimensions (QED$_3$). The role of Dirac fermions is played by the nodal BdG quasiparticles while the massless gauge field arises through unbinding of quantum vortex-antivortex degrees of freedom. A detailed derivation of this QED$_3$ theory is given and some of its main physical consequences are inferred for the pseudogap state. We focus on the properties of symmetric QED$_3$ and propose that inside the pairing protectorate it assumes the role reminiscent of that played by the Fermi liquid theory in conventional metals.

Abstract:
I discuss the problem of phase separation in cuprates from the point of view of the Landau theory of Fermi liquids. I calculate the rate of growth of unstable regions for the hydrodymanics and collisionless limit and, in presence of long range Coulomb interactions, the size of these regions. These are analytic results valid for any strength of the Landau parameters.