It was Yoichiro Nambu who introduced the concept of SSB in elementary particle physics, for which he has been chosen for this year’s Nobel award. In 1956, John Bardeen, Leon Cooper and Robert Schrieffer (BCS) found the long-sought theory to understand the puzzle of superconductivity (Nobel Prize, 1972), a mechanism by which electricity suddenly begins to conduct with zero resistance in certain materials under certain conditions. They showed that in the quantum domain lattice vibrations caused electrons to overcome the electrostatic repulsion between them and combine to form bound states, called Cooper pairs. Nambu tried to understand the BCS theory in terms of the breaking of the gauge symmetry of electromagnetism. It took two years for him to solve this problem. Through this formulation, he discovered SSB in the language of quantum field theory used in particle physics.
Nambu realised the crucial fact that for SSB to occur the properties of the “vacuum”, or the ground state of the theory, were important. He observed that in SSB, while the fundamental equations respected a symmetry, the ground state need not. In superconductivity, he showed that the vacuum was a charged state, with a charge of -2, formed by the “condensation” of Cooper pairs and was not an empty state with zero charge. This broke the gauge symmetry of electromagnetism. The really bold assumption that Nambu made in 1960 was to extend the idea that SSB could also exist in theories of elementary particles. (“The term spontaneous symmetry breaking,” says Nambu, “is not a succinct one. But it has stuck for lack of a better one.”) It is the mathematical tools that he developed in this context that have found applications in the Standard Model and in the Higgs mechanism.
So if anyone ever argues with you that the study of condensed matter isn't "fundamental", you point to him/her this very fact.