Tailoring Quantum Matter in the Second Quantum Revolution

Matter comes to us inmany different forms,whose deep theoretical under standing and high experimental control is leading science into the so-called second quantum revolution, where condensed matter physics is gaining the centre of the stage. In this dizzying process, schools keep building up physics knowledge in chronological order, often starting late enough that modern physics is barely touched at all, resulting into a huge knowledge gap endangering the formation of even a basic culture.While numerous efforts are being conducted to introduce in high schools simple concepts of quantum mechanics, the urgent question arises about how students’ minds can be prepared to face an imminent future, that requires a basic understanding of the essential ideas underlying the physics of many interacting quantum particles, and of how this quantum matter can be tailored. In this contribution, we propose a conceptual framework to develop understanding on the occurrence of quantum matter ordering, trace the minimal needed toolbox, and discuss one specific example, i.e. the energy bands and transport properties of electrons in crystals.