Phase-sensitive determination of nodal d-wave order parameter in single-band and multiband superconductors
Physical Review B American Physical Society (APS) 101:21 (2020) 214505
Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity.
Proceedings of the National Academy of Sciences of the United States of America 117:26 (2020) 14805-14811
Abstract:
The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.Imaging the energy gap modulations of the cuprate pair-density-wave state.
Nature 580:7801 (2020) 65-70
Abstract:
The defining characteristic1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling5, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8) (where a0 is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+δ.The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond
Annual Review of Condensed Matter Physics Annual Reviews 11:1 (2020) 231-270
Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging.
Proceedings of the National Academy of Sciences of the United States of America 117:10 (2020) 5222-5227