Nanoscale Proximity Effect in the High Temperature Superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+}$$_{δ}$ Colin V. Parker, 1 Aakash Pushp, 1, ∗ Abhay N. Pasupathy, 1 Kenjiro K. Gomes, 1, † Jinsheng Wen, 2 Zhijun Xu, 2 Shimpei Ono, 3 Genda Gu, 2 and Ali Yazdani 1 $^{1}$Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA $^{2}$Condensed Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, NY 11973, USA $^{3}$Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan (Dated: November 1, 2018) High temperature cuprate superconductors exhibit extremely local nanoscale phenomena and strong sen- sitivity to doping. While other experiments have looked at nanoscale interfaces between layers of different dopings, we focus on the interplay between naturally inhomogeneous nanoscale regions. Using scanning tunneling microscopy to carefully track the same region of the sample as a function of temperature, we show that regions with weak superconductivity can persist to elevated temperatures if bordered by regions of strong superconductivity. This suggests that it may be possible to increase the maximum possible transi- tion temperature by controlling the distribution of dopants. PACS numbers: 74.72.Gh, 74.55.+v, 74.62.En Keywords: Many properties of high temperature cuprate superconductors, such as the transition temper- ature T$_{c}$ , and the presence of pseudogap, have a strong doping dependence. What happens when two regions with different doping are put into contact? Since pairing in cuprate superconduc- tors has a very local character[1–4], one ex- pects the coherence length to be short, and any proximity effects to occur only on microscopic length scales. Nonetheless, some experiments have demonstrated that high- T$_{c}$ Josephson junc- tions can be made with thicknesses many times the coherence length[5]. Other experiments on bilayers have shown transition temperatures higher than that of either layer in isolation[6– 8]. Microscopic theories to explain these phe- nomena include Josephson coupling between superconducting islands[9], and enhancement 1 arXiv:1002.0884v2 [cond-mat.supr-con] 7 Feb 2010 Abstract