Superconductor-Insulator Transitions in Two Dimensions

Abstract

The current status of the experimental study of the superconductor-to-insulator transition is reviewed for systems which are two-dimensional and nominally homogeneous. Interest in this problem has been heightened by the prospect that the transition may be representative of a new class of quantum phase transitions at zero temperature. An ubiquitous feature of the experiments is that films, depending on their properties, or the value of an applied magnetic field, exhibit either insulating or superconducting behavior in the limit of zero temperature. In particular, there appears to exist a limiting behavior which is associated with a finite zero-temperature resistance. In the case of the zero-field transition the value of the limiting resistance may be universal and very close to h/4e2, the quantum resistance for pairs. The experimental results on both the zero- and finite-field transitions will be reviewed and their implications for a particular theoretical picture, the dirty boson model, will be discussed. It has been argued that this model is relevant to the superconductor-insulator transitions.

Quantum critical behaviour in a high-Tc superconductor

“…3 we display the frequency dependence of jjj in a log-log plot, and the phase in a linear plot. Although the temperature dependence 'leaks out' to surprisingly high frequency in the latter, the data are remarkably consistent with equation (2) for q between k B T and 7,500 cm 21 . The observed power law of the conductivity, jjj ¼ C=q 0:65 corresponds to g ¼ 1.35, and the value of the phase, arctan(j 2 /j 1 ) ¼ 608^28, implies that g ¼ 1.33^0.04.…”

“…As can be seen in Fig. 1, 1/t(q) has a negative curvature in the entire infrared region for all temperatures, and it saturates at around 5,000 cm 21 . Although this departure from linearity may seem to be a minor detail, we will see that it is a direct consequence of the quantum critical scaling of the optical conductivity.…”

“…et al, manuscript in preparation). In order to facilitate comparison with earlier publications [8][9][10] we also present 1/ t(q) for a number of temperatures, adopting q p =2pc ¼ 19; 364 cm 21 for the plasma frequency (where c is the velocity of light). The scattering rate 1/t(q) increases approximately linearly as a function of frequency, and when the temperature T is increased, the 1/t(q) curves are shifted vertically proportional to T. The notion that 1=tðq; TÞ , q þ T in the copper oxides forms one of the centre pieces of the marginal Fermi liquid model 1,11 , and it has been shown to be approximately correct in a large number of experimental papers [8][9][10] .…”

Dynamics and Transport Near Quantum-Critical Points

“…This result is remarkably close to the value, 4e 2 /h (argued [75,76] to be related to self-duality), and to the results of many experiments [66]. Indeed, it was conjectured in Ref [63] that 2πΣ(0) = 1 exactly for N = 2 in d = 2.…”

“…. , − ℓ ≤ m ≤ ℓ (66) and have eigenenergy Jgℓ(ℓ + 1)/2. Compare this single site spectrum with that of a pair of Heisenberg-Dirac spin S quantum spins with an antiferromagnetic exchange K; for a suitably chosen K we get the same sequence of levels and energies but with a maximum allowed value of ℓ = 2S.…”