Enhancement ofT_cin the superconductor–insulator phase transition on scale-free networks

Abstract

A road map to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors is to study a Random Tranverse Ising Model on complex networks with a scale-free degree distribution regularized by and exponential cutoff p(k) ∝ k −γ exp [−k/ξ]. In this paper we characterize in detail the phase diagram of this model and its critical indices both on annealed and quenched networks. To uncover the phase diagram of the model we use the tools of heterogeneous mean-field calculations for the annealed networks and the most advanced techniques of quantum cavity methods for the quenched networks. The phase diagram of the dynamical process depends on the temperature T , the coupling constant J and on the value of the branching ratiowhere k is the degree of the nodes in the network. For fixed value of the coupling the critical temperature increases linearly withwhich diverges with the increasing cutoff value ξ for value of the γ exponent γ ≤ 3. This result suggests that the fractal disorder of the superconducting material can be responsible for an enhancement of the superconducting critical temperature. At low temperature and low couplings T ≪ 1 and J ≪ 1, instead, we observe a different behavior for annealed and quenched networks. In the annealed networks there is no phase transition at zero temperature while on quenched network we observe a Griffith phase dominated by extremely rare events and a phase transition at zero temperature. The Griffiths critical region, nevertheless, is decreasing in size with increasing value of the cutoff ξ of the degree distribution for values of the γ exponents γ ≤ 3. The interplay between disorder and superconductivity has attracted the interest of physics in the last decades. Disorder is expected to compete with superconductivity by enhancing the electrical resistivity of a system. In this situation by increasing the random disorder, the system undergoes a superconductor-insulator phase transition [1]. The theoretical explanation of the interplay between disorder and superconductivity is still a problem of intense debate for granular superconductors. results is guaranteed to be valid in quenched networks we have to approach the problem by the recently introduced quantum cavity method and by the mapping of this solution to the random polymer problem. We find that the phase diagram on annealed networks is significantly different from the phase diagram of the quenched networks as long as the second moment of the degree distribution remains finite. In particular we found a phase transition at zero temperature not predicted by the mean-field approach and a replica symmetry broken phase a low temperatures. Instead, as the second moment of the degree distribution diverges k(k − 1) → ∞ the mean-field predictions approach the quenched solution. Therefore we identify the second moment of the degree distribution as a key quantity characterizing the disorder of the topology of the network. As the second moment of the degr...

Optimum inhomogeneity of local lattice distortions in La 2 CuO 4+ y

“…This result points again toward the importance of connectivity and an optimum inhomogeneity for high critical temperature (12,26). It is also in qualitative agreement with the theoretical prediction of the increase of T c in a granular superconductor on an annealed complex network with a finite cutoff (55,56). In fact, for a power-law distribution of links in a granular superconductor with an exponent α ¼ 2.6 the critical temperature is predicted to increase as a function of the cutoff with an exponent 3 − α, as observed experimentally.…”

“…Our quantitative results should be tested against theories of composite, granular superconductors proposed for cuprates (10,14,15,25,(30)(31)(32)(55)(56)(57)(58)(59)(60)(61)(62). The X-ray data indicate that these theories must take into account not only the usual superconducting proximity effects, but also the effects of the strains the two components exert on each other.…”

Scanning micro-x-ray diffraction unveils the distribution of oxygen chain nanoscale puddles in YBa2Cu3O6.33

“…[43][44][45][46] The formation of nanoscale ordered grains in YBa 2 Cu 3 O 6+y with Ortho-II lattice in the basal plane is highly relevant for the electronic structure of the system and for models of superconductor-to-insulator transition. 19,20 The oxygen chain puddles had the Ortho-II lattice superstructure, like the YBa 2 Cu 3 O 6.5 , which showed band folding and Fermi surface reconstruction measured by photoemission and quantum oscillations experiments. 48,49 The granular structure of Ortho-II puddles favored the 7 K superconductivity; in fact, in the rapidly quenched sample from T > 450 K, where the Ortho-II puddles were not formed, the critical temperature drops to zero.…”

“…[12][13][14][15] Recently, several theories have been proposed based on the presence in HTS of networks of nanoscale superconducting grains. [16][17][18][19][20][21] The nanoscale phase separation related to the selforganization of defects is not a unique feature of cuprates like superoxygenated La 2 CuO 4+y , 22 La 2−x Sr x CuO 4 , 6,23,24 and Bi 2 Sr 2 CaCu 2 O 8+y , 25 but it has been found also in Al 1−x Mg x B 2 , 26 doped iron-chalcogenides, [27][28][29] and other functional materials like manganites. 30 Thermal treatments control defect organization 31-34 on photo-induced effects, 35 muon-spin resonance (μSR) 36 showed that lattice complexity controls T c in YBa 2 Cu 3 O 6+y .…”

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

“…Very recently, Griffiths phases have been reported in a study of the random transverse Ising model on complex networks with a scale-free degree distribution regularized by and exponential cutoff p(k) ∝ k −γ exp[−k/ξ ] [42]. This model was devised to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors.…”