of the phase stiffness in underdoped regions by proximity to overdoped regions[7, 10, 11]. Such scenarios are inherently interesting due to the possibility that interface superconductiv- ity can occur at temperatures above the maxi- mum possible in bulk samples. To date no ex- periments have been performed to investigate proximity effects locally at microscopic length scales. Here we report a proximity effect in the cuprate superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+}$$_{δ}$ us- ing scanning tunneling microscopy (STM) and the intrinsic nanoscale spatial variation of the sample. We show that indeed patches of the sample with weaker superconductivity can be enhanced if surrounded by patches with stronger superconductivity, demonstrating that the col- lapse of superconductivity is caused by more than local thermal pair breaking. Our experiments were performed in a com- pact variable temperature scanning tunneling microscope (STM), with the unique ability to acquire spectroscopy on nearly identical grids of points over a wide range of temperatures. This allows us to perform spatial correlations using data from multiple temperatures. The pairing gap is measured from the local differential con- ductance ( dI/dV ), which is proportional to the local density of states. Figure 1 shows a rep- resentative dI/dV spectrum for the high tem- perature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+}$$_{δ}$(Bi- 2212). At 30 K there is a visible gap in the spectrum, by 70 K it has diminished consider- ably, and by 78 K it is gone completely. The gap has been previously described by a d -wave extension to the BCS theory with the addition of a lifetime broadening term[12, 20]. For high temperature cuprate superconduc- tors, the superconducting gap varies from small- est to largest by a factor of two on nanome- ter scales[1–4]. By identifying the same atoms in the topography at multiple temperatures we are able to measure dI/dV spectra for the same point at different temperatures. Recently, we have used this technique to visualize the de- velopment of superconductivity on the atomic scale in Bi-2212. We have found that the tem- 2 FIG. 1: Representative dI/dV spectrum at the same point at different temperatures. The setpoint was at -200 mV. The evolution of the spectrum shows a gap that closes near 74 K ( T$_{c}$ is 65 K). The inset shows the gap as extracted from the peak location as a func- tion of temperature. 30K 40K 50K 60K 62K 64K 66K 70K 74K 78K 80K 82K 86K Bias (mV) Differential C o nductance (pS) −100 −50 0 50 100 0 50 100 150 200 ��������� � ���� � �� � � � � �� ��