Switching of magnetic domains reveals spatially inhomogeneous superconductivity

Abstract

The interplay of magnetic and charge fluctuations can lead to quantum phases with exceptional electronic properties. A case in point is magnetically-driven superconductivity 1,2 , where magnetic correlations fundamentally affect the underlying symmetry and generate new physical properties. The superconducting wave-function in most known magnetic superconductors does not break translational symmetry. However, it has been predicted that modulated triplet p-wave superconductivity occurs in singlet d -wave superconductors with spin-density wave (SDW) order 3,4 . Here we report evidence for the presence of a spatially inhomogeneous p-wave Cooper pair-density wave (PDW) in CeCoIn 5 . We show that the SDW domains can be switched completely by a tiny change of the magnetic field direction, which is naturally explained by the presence of triplet superconductivity. Further, the Q-phase emerges in a common magnetosuperconducting quantum critical point. The Q-phase of CeCoIn 5 thus represents an example where spatially modulated superconductivity is associated with SDW order.Superconductivity emerges in solids when electrons form Cooper pairs at low temperatures and condense in a macroscopically coherent quantum state, leading to zero-resistance and diamagnetism. For most phonon-mediated superconductors, the symmetry of the superconducting gap function is an isotropic singlet s-wave that does not break the symmetries of the underlying lattice. Unconventional superconductors 5,6 adopt more complex wave-functions: singlet d -wave in cuprates, extended s-wave for the pnictides and p-wave in ruthenates 7 . Although co-existing wave-functions are theoretically possible, most superconductors are adequately described by just a single wave-function. Here we provide evidence that p-wave superconductivity emerges in a d -wave superconductor and couples to a SDWforming a unique quantum phase with a spatially inhomogeneous superconducting Cooper pair-density wave.The stoichiometric heavy-fermion superconductor CeCoIn 5 serves as a model material for studies of d x 2 −y 2 -wave superconductivity 8,9 . It shares many properties with the cuprate superconductors, such as the zero-field superconducting wave-function 10-12 symmetry, a quasi-two-dimensional Fermi surface 13 and a spin resonance in the superconducting state 14 . Superconductivity emerges below T c (0) = 2.3 K and is Pauli-limited. The superconducting phase transition becomes first-order 15 close to H c2 (0), where SDW order has been observed that only exists in the Q-phase situated inside the superconducting phase [16][17][18] . The SDW propagation is pinned along the d x 2 −y 2 -line nodes, where low-energetic quasiparticles allow for electron nesting 17 (see Fig. 1a). In some microscopic theories addressing the nature of the Q-phase, the formation of a spatially modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state plays a central role 19 . Other theoretical approaches emphasize SDW nesting 20,21 . Phenomenologically it has been shown 3,16 that SDW order in a d -wave super...

Unconventional superconductivity

“…Subsequent NMR results (B.-L. Young et al [237]; Koutroulakis et al [238]) revealed evidence for a local moment in this region of the phase diagram, rather than the long wavelength spin density modulation expected for the FFLO phase. Using sensitive high field neutron diffraction on a 155 mg single crystal of CeCoIn5, Gerber et al [239] concluded that modulated triplet p-wave superconductivity occurs in the Q-phase due to the interaction of the host's d-wave superconductivity with the spindensity-wave (SDW) order discovered by NMR.…”

Spin susceptibility of Andreev bound states

“…This last goal is particularly relevant for several materials. In heavy-fermion superconductor CeCoIn 5 , can an FFLO phase be the origin of coexistence [11][12][13] of antiferromagnetism (AFM) and superconductivity? On the other hand, is recently observed 14 enhancement of relaxation rate T −1 1 in organic superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2 , indeed explained by Andreev bound states at FFLO domain walls?…”

Possible Field–Temperature Phase Diagrams of Two-Band Superconductors with Paramagnetic Pair-Breaking

“…(28) and then, with Eq. (29), we find Calculation of Ω (4) In this case, after performing the ξ n (p) integral, the expression of…”

“…(3). Next, the details of the derivation of the GL quadratic term Ω (2) and the quartic one Ω (4) are explained. The treatment to derive Ω (2) and Ω (4) given below closely follows that in the previous work [10].…”

“…In the quasi-two-dimensional (2D) heavyfermion superconductors CeCoIn 5 [1] and NpPd 2 Al 5 [2], the SC transition at high fields and hence at low temperatures has been shown to be nearly discontinuous, and, on the basis of this and the temperature dependence of the resulting H c2 (T ) curve, an extremely strong PPB effect in these materials has been clarified. Furthermore, the strange high-field phase [3,4] found in CeCoIn 5 in a field parallel to the SC layers has been interpreted, by an approach based on a single-band electronic model, as a vortex lattice corresponding to the appearance of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [5,6] with a PPB-induced spatial modulation parallel to the magnetic field [7,8]. The appearance of the PPB-induced spatial modulation parallel to the field rather than the corresponding perpendicular modulation [9] is a rare event [10] in the weak-coupling BCS model and has been interpreted [11] as a reflection of the fact that this material at ambient pressure is close to an antiferromagnetic quantum critical point.…”