Thermoelectric properties of topological chains coupled to a quantum dot

Topological one-dimensional superconductors can sustain in their extremities zero energy modes that are protected by different kinds of symmetries. The observation of these excitations in the form of Majorana fermions is one of the most intensive quests in condensed matter physics. Their study is not only interesting in itself, but also because they have promising applications in the area of quantum computation. In this work we are interested in another class of one dimensional topological systems, namely topological insulators. These also present symmetry protected end modes with robust properties and do not require the low temperatures necessary for topological superconductivity. We consider the simplest kind of topological insulators, namely chains of atoms with hybridized $sp$ orbitals. We study the transport properties of these chains in the trivial, non-trivial topological phases and at the quantum topological transition. We use a simple device consisting of two semi-infinite hybridized $sp$-chains connected to a quantum dot and obtain the thermoelectric properties of this system as a function of temperature and distance to the topological transition. We show that the electrical conductance and the Wiedemann-Franz ratio of the device at the topological transition have universal values at very low temperatures. The thermopower gives direct evidence of fractional charges in these systems.