Possibly the most famous fact about electrons is their negative charge. This is the smallest integer charge possible and for all electrons the thing that defines their interactions both with other particles, electromagnetic fields and each other. Occasionally superconductors can get around the repulsion by having electrons that form pairs and bonds at low temperatures but there is another idea about making electrons go near each other.
By using the repulsion from surrounding electrons it was proposed that electrons could be forced to act attractive to one another and to an outside observer appear as if there was a force acting attractively between them. This idea was called excitonic attraction, not to be confused with excitons (although related there is a large difference), and no evidence of it has been found in the fifty years since it was proposed. There has, however, recently been a published paper which begins to make steps in the right direction. It proved that two electrons could be made to attract one another provided there was an external electronic system helping them along. This is not quite the perfect internal attraction the theory supposes but it is a welcome breakthrough in decades worth of unfruitful research..