Quantum materials: Where many paths meet

In Nature, there exist materials with exotic properties that cannot be understood in the framework of classical theories. Such properties, however, are beautifully described by more sophisticated theoretical tools involving quantum mechanics.  Such materials are now known as the “quantum materials”. The range of exotic properties exhibited by the quantum materials is extremely broad and includes superconductivity, superfluidity, ferromagnetism, quantum hall effect, spin-liquidity, topological insulation, to name a few.

Superconductors, discovered by Kammerlingh Onnes, 1911, were first to emerge as quantum materials. In normal metals, the resistance arises due to inelastic scattering between the charge carriers (electrons) and defects in the periodic crystal lattice. The defects or scattering centres can be any distortion to the periodicity of the lattice like those due to presence of impurity or the thermal vibration of the lattice points. In superconductors, surprisingly, the resistance becomes zero despite the presence of a large number of impurities and at high temperatures where the lattice points can undergo vigorous thermal vibration. The question that how the charge carriers remained insensitive to such strong scattering centres could not be answered within any classical picture. A microscopic understanding of superconductivity was first provided by Bardeen, Cooper and Schrieffer (BCS) in 1951, only after substantial development of quantum mechanics and quantum field theories – the theories where quantum mechanics is combined with Einstein’s theory of relativity. In 1986 after the discovery of the high Tc superconductors, it was clear that BCS theory, though extremely successful for describing superconductivity in a large number of elemental metals and their alloys, had its limitations. Though several theoretical models have been proposed for the high temperature superconductors over past several decades, there is still no fully satisfactory consensus view of how high-temperature superconductors work. Hence, these quantum materials continue to be favorites of experimentalists and theorists alike.

Almost simultaneously with the emergence of the high Tc superconducting materials, another class of quantum materials emerged where surprising quantization of the Hall resistance of certain clean two-dimensional systems was observed. The phenomenon is known as quantum Hall effect. The connections between high-temperature superconductors, the QHE, and 2D electron gases are, in retrospect, clear enough: in particular, the reduced dimensionality, interaction of electronic and magnetic or electron-spin properties, and the importance of electron correlations and quasiparticle descriptions. These aspects all come together in the much-vaunted “wonder material” graphene, exhibiting the exotic physics. Pauli has a great contribution to devise the theoretical model, called Dirac theory, to understand the quantum phenomena where the quasiparticle are Dirac fermions. 

Like Dirac semimetal, in Graphene at fermi level conduction and valence bands touch at a single point (called Dirac point), Graphene is also named as a 2D Dirac semimetal. While the Dirac cones in 2D graphene are symmetry-protected, there’s an extra degree of such protection in 3D Dirac semimetals such which comes from the topology of the electron states—more akin to the prohibition of transforming a left-handed glove into a right-handed one. Because of this, 3D Dirac semimetals are said to be “topological semimetals”, existing other exotic particles Weyl fermions, Majorana fermions have tremendous application in Quantum computing.

Recently the topic related to Quantum spin liquid is growing attention. However, they are hard to study experimentally. “The problem with realizing spin liquids experimentally is that they are balanced on a knife edge,” Blundell explains. “When they are cooled down, they should show no order even down to absolute zero, but as you cool them down, all sorts of minor effects that you can ignore at high temperature start to come into play.”

Surprising, what we see in nature, all are quantum where material properties derive more spectacularly from seemingly unusual quantum states. Quantum Materials, takes a wider view, seeing the field as “a very broad set of topics having largely to do with the electronic properties of novel solids and solid-state devices in which the quantum character of the electrons is important.