Quantum materials for thermoelectricity
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Introduction The use of quantum size effects in semiconductor nanostructures strongly stimulated research on thermoelectricity over the past decade,1–3 especially stimulated by the prediction of a significant boost in the thermoelectric (TE) figure of merit ZT = (S2 σ T)/(κph + κel )(S is the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity with contributions from electrons and phonons, κel and κph, and T absolute temperature) due to the transition from bulk to nanostructured materials by Hicks and Dresselhaus.4,5 Quantum size effects lead to a modification of the energy levels of the charge carriers and enhance their kinetic energy. Additionally, classical size effects result in an enhanced surface scattering of electrons and phonons.
Topological insulators Recently, research interest has shifted from quantum size effects in conventional/classical semiconductors to new types of quantum materials (e.g., topological insulators [TIs], Weyl and Dirac semimetals) characterized by their nontrivial electronic topological order. Topological order is a classification of matter by the internal structure of its quantum ground state. The class of TI materials hereby represents the most relevant quantum materials for thermoelectricity. Conventional semiconductors are characterized by a bulk band structure that is
constituted by a valence band and a conduction band with parabolic bands and an energy bandgap Egap < 3 eV. TE materials for near-room-temperature applications have this type of band structure, typically with Egap around 0.1 eV to 0.25 eV for high performance in the low- to mid-temperature regime. TIs also exhibit this conventional bulk band structure of a semiconductor, but feature additional topological surface states with a linear dispersion relation. As in graphene, this results in relativistic carrier transport with extremely high carrier mobility, µ, and a small effective carrier mass, meff, which, in the ideal case, equals zero. Hence, in a primitive picture, TIs are characterized by graphene-like states on the surface of a conventional semiconductor. TIs therefore provide two different transport channels, one of graphene-like surfaces and the other of the (conventional) semiconducting bulk inner part. Ordinary crystals are three-dimensional (3D) objects. If the crystal exhibits topological surface states completely surrounding the outer surface in all facet directions, this is called a 3D TI, also classified as a strong TI. If only certain or highsymmetry facets exhibit TI properties, the material is called a weak TI or topological crystalline insulator (TCI). Topological surface states are protected from backscattering between equal and opposite momentum by time-reversal symmetry.6 Therefore, the TI properties are robust, and they
Johannes Gooth, Max Planck Institute for Chemical Physics of Solids, Germany; Harvard University, USA; [email protected] Gabi Schierning, Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden), Germany; g.schierning@i
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