Vortex states and quantum magnetic oscillations in conventional type-II superconductors

Theory of quantum oscillations in the vortex-liquid state of high-Tc superconductors

“…This is a state with a non-zero local d-wave pairing amplitude in which mobile vortices lead to phase fluctuations that make superconducting correlations short ranged in both space and time. Our analysis generalizes earlier studies of the mixed state of s-wave superconductors [19][20][21] in two ways-d-wave pairing and dynamical phase fluctuations-both of which are very important for quantum oscillations in cuprates.…”

“…The separable form (equation (1)) simplifies the algebra, but a more elaborate non-separable correlator with G ¼ Dq 2 , where D is the vortex diffusion coefficient, is not expected to change our conclusions qualitatively 30,31 . We will also find it useful to compare our results for dynamic phase fluctuations (Ga0) with the static case D mn ðr; tÞ ¼ s mn D 2 expð À r 2 =2' 2 Þ with time-independent phase fluctuations [19][20][21] .…”

“…(1) is on the magnetic length scale ' ¼ ffiffiffiffiffiffiffiffiffiffiffiffi ffi " hc=eH p ; set by the average inter-vortex separation in the extreme type-II limit. Such a form for the spatial part is natural for a vortex state and can be motivated by considering a disordered vortex assembly or by using GinzburgLandau theory, as discussed in Maki 19 , Stephen 20 and Maniv 21 for the s-wave case. We work in a regime where the cyclotron radius R c ) ' ) x 0 \k À 1 F ; where x 0 is the vortex core radius and k À 1 F is the interparticle spacing.…”

Quantum oscillations in the high- T c cuprates

“…The appearance of Fermi-Dirac statistics (figure 4) suggests that the low-energy state of the vortex liquid being accessed in the regime where quantum oscillations are measured in underdoped YBa 2 Cu 3 O 6+x can be described as a Fermi liquid [35,36]. While additional damping is expected to reduce the quantum oscillation amplitude within the mixed state, any further effect of the superconducting pair potential on the average density of states is not apparent within experimental resolution [37,38]. Quantum oscillations have also previously been reported in conventional type II superconductors in a similar limit as the current measurements on the underdoped cuprates (hu c D, where D is the superconducting pairing potential) with the same frequencies and effective masses as the normal state [39,40].…”

Quantum oscillations probe the normal electronic states of novel superconductors

“…When R S = 0, the spin-up and spin-down Fermi surfaces beat out of phase to produce a spin-zero minimum in the dHvA amplitude. In an SC state, the dHvA amplitude of oscillations suffers further exponential damping in a magnetic field, R SC , which can be understood on the basis of the model of the quasi-particle scattering by the random vortex lattice with large SC (vortex) fluctuation around the mean field H c2 (Maniv et al 2001). Both the effect of the impurity scattering and the thermal smearing broaden the Landau levels (figure 2a), imposing stringent conditions for the observation of quantum oscillations only at low temperatures, in very pure samples and at high magnetic fields (which are often large enough to allow access to the normal state of superconductors).…”