Nonlinear response of the static and dynamic phases of the vortex matter

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In the mixed state of type II superconductors, the external magnetic field penetrates the superconducting material in the form of normal cored regions, each carrying a quantum of flux (Φ0 = 2.07×10-7 G-cm2). These normal cores have radii equal to the coherence length (ξ). Surrounding each normal core is a vortex of supercurrent that decays over a characteristic length scale known as the penetration depth (λ). These elastic string-like normal entities (or vortices) mutually repel each other leading to the formation of triangular vortex lattices in ideal superconductors (Blatter et al., 1994; Natterman & Scheidl, 2000). However, real samples always have defects (point defects, dislocations) and inhomogeneities. The superconducting order parameter is preferentially suppressed at these random defect locations, thereby energetically favoring pinning of vortices at these locations. But, pinning also leads to loss of long range order in the vortex lattice. The vortex matter can be considered as a typical prototype for soft materials, where pinning forces and thermal fluctuations are comparable to the elastic energy scale of the vortex lattice. The perennial competition between elastic interactions in the vortex lattice, which establishes order in the vortex state and effects of pinning and thermal fluctuations which try to destabilize the vortex lattice, leads to a variety of pinning regimes, viz., the weak collective pinning regime and the strong pinning regime (Blatter et al., 2004). The competition in different portions of the field-temperature (H,T) phase space leads to the emergence of a variety of vortex phases, like, the Bragg glass, vortex glass, vortex liquid (for review see, Blatter et al., 1994; Natterman & Scheidl, 2000) and transformation amongst them, along with the appearance of significant thermomagnetic history dependent response. The competing effects ever present in the vortex lattice also lead to a quintessential phenomenon called the peak effect (PE), which we shall discuss in the next section.