Quantum critical fluctuations

In the following section, two mainstream theoretical concepts will be briefly described, namely the resonating valence bond (RVB) theory of Anderson, and Varma s pairing model of quantum critical fluctuation (QCF), as the origin of high-Tc superconductivity. 

Fig. 5. The low temperature crossover diagram of a one-dimensional CDW. t and K are proportional to the temperature and the strength of quantum fluctuations, respectively. The amount of disorder corresponds to a reduced temperature tu 0.1. In the classical and quantum disordered region, respectively, essentially the t = 0 behavior is seen. The straight dashed line separating them corresponds to At 1, i.e., K 1, where At is the de Broglie wave length. In the quantum critical region, the correlation length is given by At- Pinning (localization) occurs only for t = 0, K

We like to mention that at a quantum critical point where antiferromagnetic order is on the verge to disappear, the value of a is expected to be 3/2, whereas a value of 5/3 hints to the presence of ferromagnetic fluctuations. The actual experimental value for a for x> 0.006 is equal to 1.6, i.e. in between the two above given values. Specific-heat... 

Here r measures the (almost T-independent) distance from the quantum critical point, F denotes the characteristic energy scale of the fluctuations and c, are constants. The frequency magnetic coq vanishes at the ordering vector Q of the magnetic stmcture. In the dirty limit the variation with temperature of the resistivity is given by... 

Coexistence of FM order and superconductivity under pressure The experimental phase diagram of FM collapse under pressure and simultaneous appearance of superconductivity is shown in fig. 43. The critical pressure for disappearance of FM order is pc2 = 16-17 kbar. The SC phase appears between pc = 10 kbar and pc2 = 16 kbar which is also the critical pressure for the FM-PM transition. The critical temperature Tx p) of the jc-phase hits the maximum of Tdp) at the optimum pressure pm = 12.5 kbar. As mentioned before the nature of the order parameter in the jc-phase remains elusive. The coincidence of maximum Tc with vanishing jc-phase order parameter suggests that the collective bosonic excitations of the X-phase which supposedly become soft at pm mediate superconductivity and not quantum critical FM spin fluctuations which are absent due to the persisting large FM... 

From the previous discussion of experimental evidence the superconducting mechanism via ferromagnetic fluctuations can be ruled out since the ferromagetic polarization at pm where Tc is largest is still 65% of the maximum value at ambient pressure (Pfleiderer and Huxley, 2002). Therefore models based on the FM quantum critical point scenario that follow the original work of Fay and Appel (1980) are not relevant for UGe2. On the other hand the phe-... 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

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