Quantum phase transition inside the superconducting dome of Ba(Fe_1−xCo_x)₂As₂ from diamond-based optical magnetometry

Abstract

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature Tc acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe1−xCox)2As2. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe2(As1−xPx)2 compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic-magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

Cluster structure of superconducting phase and the nature of peaks in the doping dependences of the London penetration depth in iron pnictides

“…In the intermediate interval 0.056 < x < 0.062 the London penetration depth will have a maximum. The indicated position of the maximum is in good agreement with the experimental result [8].…”

“…With the decay of large domains into small ones, the rigidity of the superconducting medium will decrease and λ, accordingly, will increase. This is what we believe is observed in [8,21,22].…”

“…Thus, based on the proposed model, one should expect that in Ba (Fe 1− x Co x ) 2 As 2 the concentration range corresponding to the existence of CT clusters is 0.03 < x < 0.11, which is in good agreement with the region of the superconducting dome on phase diagram of this compound (Fig. 1 f) [8].…”

“…Additional support of the validity of the proposed model can be obtained from an analysis of the results of measurements of the dependence of the London penetration depth λ on the doping level in Ba (Fe 1− x Co x ) 2 As 2 and BaFe 2 (As 1− x P x ) 2 [8,21,22]. As can be seen from (Fig.…”

Quasiclassical Theory of C4-Symmetric Magnetic Order in Disordered Multiband Metals

“…Most recently, several non-trivial phenomena have been observed in a family of iron-based superconductors and their alloys [6]. One example of such phenomena is an observation of the peak in the penetration depth in BaFe 2 (As 1−x P x ) 2 as a function of phosphorus concentration [7][8][9][10], in Ba 1−x K x Fe 2 As 2 as a function of potassium concentration [11] and, most recently in Ba(Fe 1−x Co x ) 2 As 2 as a function of cobalt concentration [12]. Another example is the experimental observation of the spin-density-wave order which is characterized by two magnetic ordering vectors, Q 1 and Q 2 , in various iron-based superconducting alloys [13][14][15][16][17][18][19][20].…”