Universal scaling relations in molecular superconductors

Abstract

Scaling relations between the superconducting transition temperature Tc, the superfluid stiffness ρs and the normal state conductivity σ0(Tc) are identified within the class of molecular superconductors. These new scaling properties hold as Tc varies over two orders of magnitude for materials with differing dimensionality and contrasting molecular structure, and are dramatically different from the equivalent scaling properties observed within the family of cuprate superconductors. These scaling relations place strong constraints on theories for molecular superconductivity. PACS numbers: 76.75.+i, 74.25.Nf, 74.25.Fy, 74.70.Kn, 74.20.De Understanding the phenomenon of superconductivity, now observed in quite disparate systems, such as metallic elements, cuprates and molecular metals, involves searching for universal trends across different materials, which might provide pointers towards the underlying mechanisms. One such trend is the linear scaling between the superconducting transition temperature (T c ) and the superfluid stiffness (ρ s = c 2 /λ 2 , where λ is the London penetration depth), first identified by Uemura et al for the underdoped cuprates [1]. Recently, scaling relations between ρ s and the normal state conductivity σ 0 have also been suggested and a linear relation between ρ s and the product σ 0 (T c )T c was demonstrated for cuprates and some elemental superconductors [2]. Here we show that these specific linear scaling relations do not hold for molecular superconductors, but a different form of powerlaw scaling is found to link ρ s , σ 0 (T c ) and T c . These scaling properties hold as T c varies over several orders of magnitude for materials with differing dimensionality and contrasting molecular structure, and the scaling is dramatically different from that of the cuprates. Our findings have considerable implications for the theory of superconductivity in molecular systems.Molecular superconductors are generally regarded as members of the wider group of 'exotic' superconductors that have attracted much research effort in recent years. However, the number of different examples of molecular superconductors is now sufficiently large that systematic studies of their properties may be made independently of the other non-molecular exotic superconductors. A general feature of all these exotic superconductors is the large carrier scattering rate observed in the normal state [3] leading to a picture of them as 'bad metals' [4]. The scattering rate at temperatures near T c may have particular relevance for the superconductivity, since it is expected that similar carrier interaction mechanisms would be dominant in the normal state resistance and in the pairing of carriers that leads to the formation of the superconducting state. It is therefore useful to study the correlation between σ 0 (T c ) and superconducting parameters such as T c and ρ s . Fig. 1(a) shows ρ s /c 2 (= ne 2 /m * ǫ 0 c 2 ) and T c derived from µSR measurements in the vortex state [5,6], plotted against σ 0 (T c ) in the highest c...

Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

“…The earliest pattern was referred to as the Uemura relation [1][2] 𝑇 𝑐 ∝ 𝜌 𝑠 (0) , which works reasonably well for the underdoped materials. Later, a more universal relation, the Homes' law [3][4][5][6] 𝑇 𝑐 ∝ 𝜌 𝑠 (0) 𝜎 𝑑𝑐 ⁄ was found to hold regardless of underdoped, optimally doped, and overdoped materials, where 𝜎 𝑑𝑐 denotes the dc conductivity measured at approximately 𝑇 𝑐 . Theoretically, Homes' law has been well known as a mean-field result of the dirty-limit BCS theory [4,[7][8].…”

Superconducting fluctuations in organic molecular metals enhanced by Mott criticality

“…However, in strongly correlated superconductors (those for which Coulomb interactions influence the electronic state from which superconductivity forms), the structure of the normal state may influence the nature of this transition. Indeed, it was recognised some time ago that the observed transition temperatures for a range of unconventional superconductors is found to coincide with the temperature scale at which thermal fluctuations of the superconducting phase might be expected to destroy the longrange phase coherence [9][10][11]. This motivates a picture of an alternative kind of transition out of the superconducting state, into a state which does not exhibit the signatures of long range phase coherence such as zero resistance, but which does preserve certain features such as a gapped or pseudo-gapped spectrum, a degree of quasiparticle pairing, and remnants of the vortex physics.…”