Quasiparticle spectrum

A around its minimum the low-lying quasiparticle spectrum takes the form... 

Consider again non-relativistic fermions. Their BCS spectrum (for homogeneous systems) is isotropic when the polarizing field drives apart the Fermi surfaces of spin-up and down fermions the phase space overlap is lost, the pair correlations are suppressed, and eventually disappear at the Chandrasekhar-Clogston limit. The LOFF phase allows for a finite center-of-mass momentum of Cooper pairs Q and the quasiparticle spectrum is of the form... 

An immediate consequence of symmetry is the nature of the quasiparticle spectrum. The density of states p(co) can be calculated from the knowledge of the quasi-particle energies. For singlet states Ek,+ = Ek, with... 

A corollary of the above results is that one should expect isotope effects in the quasiparticle spectrum measured in the pseudogap state, since once localized, the hot quasiparticles can become strongly coupled to the lattice. (When not localized, the coupling of the hot quasiparticles to phonons is markedly reduced by vertex corrections associated with their magnetic coupling.) Any coupling of cold quasiparticles to the lattice would be very much smaller. These conclusions appear consistent with the ARPES results reported by Lanzara at this workshop, ft leads me to predict that no isotope effect will be found for hot quasiparticles in overdoped materials. 

Fig. 7. Left panel Cooper pairs (—k, k) and electron-hole (Peierls) pairs (—k, —k + Q) for the n.n. tight binding Fermi surface (thick line) with perfect nesting vector Q. Saddle points (S) of 6(k) at (0, .7t) and ( 7T, 0) lead to DOS peak at the Fermi energy. Therefore unconventional pair states can only have nodes away from S, i.e., at the Dirac points D ( j, j) where the quasiparticle spectrum takes the form of eq. (54). This is the case for a

Giant diamagnetism The susceptibility has been analysed in detail (Nersesyan and Vachnadze, 1989 Nersesyan et al, 1991). Strong anomalies in the diamagnetic susceptibility for both d-CDW and -SDW are predicted at low fields. This is due to the peculiar conical or relativistic quasiparticle spectrum around the nodal Dirac points (D) in fig. 7. For T the spectrum can be linearized and consists of two bands... 

The low temperature dependence of the specific heat is apparently described by a power law behaviour Q T" with n between 2 and 3 (Hilscher and Michor, 1999). Thermal conductivity Kxx (Boaknin et al., 2001) clearly exhibits T-linear behaviour for T < Tc suggesting the presence of nodal lines or second order node points as introduced below which would be compatible with n = 2 for the specific heat. Furthermore the investigation of field (and field-angle) dependence of Cs (T, H) and Kij T, H) (/, j =x,y,z) is a powerful method to obtain information on the quasiparticle spectrum and hence on the anisotropy properties of the gap function (sect. 2). In a conventional superconductor with isotropic gap the quasiparticles at low temperature are confined to the vortex core where they form closely spaced bound states with an energy difference much smaller than kT. Therefore, they can be taken as a... 

It is instructive to start with the excitation spectrum in the case of the ordinary 2SC phase when dfi = 0. With the conventional choice of the gap pointing in the anti-blue direction in color space, the blue quarks are not affected by the pairing dynamics, and the other four quasi-particle excitations are linear superpositions of ur>g and dr(J quarks and holes. The quasi-particle is nearly identical with a quark at large momenta and with a hole at small momenta. We represent the quasi-particle in the form of Q(quark, hole), then the four quasiparticles can be represented explicitly as Q(ur,dg), Q(ug, dr), Q(dr,ug) and Q(dg,ur). When S/i = 0, the four quasi-particles are degenerate, and have a common gap A. 

The absorption spectrum is proportional to the imaginary part of the macroscopic dielectric function. Adopting the same level of approximation that we have introduced to obtain GW quasiparticle energies, i.e. neglecting the vertex correction by putting T = 55, we get the so called random phase approximation (RPA) for the dielectric matrix. Within this approximation, neglecting local field effects, the response to a longitudinal field, for q 0, is ... 

J.V. Ortiz, Partial third order quasiparticle theory Comparisons for closed-shell ionization energies and an application to the borazine photoelectron spectrum. J. Chem. Phys. 104, 7599-7605 (1996)... 

The physics of free carriers is dominated by the Fermi surface. Looking at the linearized spectrum of Fig. 2, one realizes that electron-hole or electron-electron excitations involving quasiparticles (electrons or holes) on each side of the Fermi surface are gapless. This greatly influences the response functions to external fields. Let an external field Fa(q) couple to the operator Oa(q), where... 

In the papers by Van Kranendonk (7), (8) only the bound states of two different quasiparticles were considered under the condition that the motion of one of them can be ignored in a first approximation (the Van Kranendonk model, see Subsection 6.2.3). This made the Van Kranendonk model inapplicable for analysis of the biphonon spectrum in the frequency region of overtones, as well... 

Of course, it is an approximation to regard quasiparticles as particles, and this approximation can be expected to break down in several ways. First, core holes always have a finite lifetime, i.e. they are broadened, and disperse on a short timescale. The effects of core-hole broadening will be discussed in chapters 8 and 11. Secondly, the very concept of a core hole may become inapplicable, i.e. it may prove impossible to identify a single structure in the spectrum as the result of exciting a quasiparticle. This form of breakdown is discussed in chapter 7. Experience shows that well-characterised holes tend to be the deepest ones, which are fully screened, while vacancies in the subvalence shells cannot always be described in this way. Thus, the concept of core holes is most useful in X-ray spectroscopy, but can sometimes break down quite severely at lower excitation energies. 

In case (a) of the figure, we show a typical photoelectron spectrum containing just one line, which corresponds to the excitation of one electron and results in just one ionic state. In case (c), the typical X-ray spectrum is dominated by one line, which represents the quasiparticle, with a few... 

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