Narrow Results

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons, P_e, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynamic (QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows: P_e is related to the magnetic field B, matter density ρ, and electron fraction Y_e; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star (NS) due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star.

This work investigates a d-p Hubbard model by the n-pole approximation in the hole-doped regime. In particular, the spectral function A(ω, k) is analyzed varying the filling, the local Coulomb interaction and the d-p hybridization. It should be remarked that the original n-pole approximation (Phys. Rev.184, 451 1969) has been improved in order to include adequately the k-dependence of the important correlation function 〈S_j·S_i〉 present in the poles of the Green's functions. It has been verified that the topology of the Fermi surface (defined by A(ω = 0, k)) is deeply affected by the doping, the strength of the Coulomb interaction and also by the hybridization. Particularly, in the underdoped regime, the spectral function A(ω = 0, k) presents very low intensity close to the antinodal points (0, ±π) and (±π, 0). Such a behavior produces an anomalous Fermi surface (pockets) with pseudogaps in the region of the antinodal points. On the other hand, if the d-p hybridization is enhanced sufficiently, such pseudogaps vanish. It is precisely the correlation function 〈S_j·S_i〉, present in the poles of the Green's functions, plays an important role in the underdoped situation. In fact, antiferromagnetic correlations coming from 〈S_j·S_i〉 strongly modify the quasiparticle band structure. This is the ultimate source of anomalies in the Fermi surface in the present approach.

We consider many-fermion systems with singular Fermi surfaces, which contain Van Hove points where the gradient of the band function k ↦ e(k) vanishes. In a previous paper, we have treated the case of spatial dimension d ≥ 3. In this paper, we focus on the more singular case d = 2 and establish properties of the fermionic self-energy to all orders in perturbation theory. We show that there is an asymmetry between the spatial and frequency derivatives of the self-energy. The derivative with respect to the Matsubara frequency diverges at the Van Hove points, but, surprisingly, the self-energy is C¹ in the spatial momentum to all orders in perturbation theory, provided the Fermi surface is curved away from the Van Hove points. In a prototypical example, the second spatial derivative behaves similarly to the first frequency derivative. We discuss the physical significance of these findings.

Electrons, when scattered by static random disorder, form standing waves that can be imaged using scanning tunneling microscopy. Such interference patterns, observable by the recently developed technique of Fourier transform scanning tunneling spectroscopy (FT-STS), are shown to carry unique fingerprints characteristic of the electronic order present in a material. We exploit this feature of the FT-STS technique to propose a test for the nature of the enigmatic pseudogap phase in the high-T_c cuprate superconductors. Through their sensitivity to the quasiparticle spectra and coherence factors, the FT-STS patterns, in principle, carry enough information to unambiguously determine the nature of the condensate responsible for the pseudogap phenomenon. In practice, the absence of a detailed understanding of the scattering mechanism, together with the experimental uncertainties, prevent such an unambiguous determination. We argue, however, that the next generation of FT-STS experiments, currently underway, should be able to distinguish between the pseudogap dominated by the remnants of superconducting order from the pseudogap dominated by some competing order in the particle-hole channel. Using general arguments and detailed numerical calculations, we point to certain fundamental differences between the two scenarios and discuss the prospects for future experiments.