We investigate the spatial and doping evolutions of the superconducting properties of tri-layer cuprate Bi2Sr2Ca2Cu3O10+δ by using scanning tunneling microscopy and spectroscopy. Both the superconducting coherence peak and gap size exhibit periodic variations with the structural supermodulation, but the effect is much more pronounced in the underdoped regime than at optimal doping. Moreover, a new type of tunneling spectrum characterized by two superconducting gaps emerges with increasing doping, and the two-gap features also correlate with the supermodulation. We propose that the interaction between the inequivalent outer and inner CuO2 planes is responsible for these novel features that are unique to tri-layer cuprates.

One of the central issues concerning the mechanism of high temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity.Here we use scanning tunneling microscopy to investigate the evolution of charge order from the optimally doped to strongly overdoped Bi2Sr2CuO6+δ cuprates. We find that with increasing hole concentration, the long-range checkerboard order gradually evolves into short-range glassy patterns consisting of diluted charge puddles. Each charge puddle has a unidirectional nematic internal structure, and exhibits clear pair density modulations as revealed by the spatial variations of superconducting coherence peak and gap depth. Both the charge puddles and the nematicity vanish completely in the strongly overdoped non-superconducting regime, when another type of short-range order with √2 × √2 periodicity emerges. These results shed important new lights on the intricate interplay between the intertwined orders and the superconducting phase of cuprates.

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We use scanning tunneling microscopy to investigate Bi2Sr2Ca2Cu3O10+δ trilayer cuprates from the optimally doped to overdoped regime. We find that the two distinct superconducting gaps from the inner and outer CuO2 planes both decrease rapidly with doping, in sharp contrast to the nearly constant TC. Spectroscopic imaging reveals the absence of quasiparticle interference in the antinodal region of overdoped samples, showing an opposite trend to that in single-and double-layer compounds. We propose that the existence of two types of inequivalent CuO2 planes and the intricate interaction between them are responsible for these highly anomalous observations in trilayer cuprates.