Abstract
Symmetry relations are manifestations of fundamental principles and constitute cornerstones of modern physics. An example are the Onsager relations between coefficients connecting thermodynamic fluxes and forces, central to transport theory and experiments. Initially formulated for classical systems, these reciprocity relations are also fulfilled in quantum conductors. Surprisingly, novel relations have been predicted specifically for thermoelectric transport. However, whereas these thermoelectric reciprocity relations have to date not been verified, they have been predicted to be sensitive to inelastic scattering, always present at finite temperature. The question whether the relations exist in practice is important for thermoelectricity: whereas their existence may simplify the theory of complex thermoelectric materials, their absence has been shown to enable, in principle, higher thermoelectric energy conversion efficiency for a given material quality. Here we experimentally verify the thermoelectric reciprocity relations in a four-terminal mesoscopic device where each terminal can be electrically and thermally biased, individually. The linear response thermoelectric coefficients are found to be symmetric under simultaneous reversal of magnetic field and exchange of injection and emission contacts. Intriguingly, we also observe the breakdown of the reciprocity relations as a function of increasing thermal bias. Our measurements thus clearly establish the existence of the thermoelectric reciprocity relations, as well as the possibility to control their breakdown with the potential to enhance thermoelectric performance
Highlights
Symmetry relations are manifestations of fundamental principles and constitute cornerstones of modern physics
We find evidence for a breakdown of the relations when we increase the thermal bias, indicating that the symmetries can be experimentally controlled, either by inelastic scattering or by non-linear thermal transport, analogous to the symmetry-breakdown in purely electronic transport at finite voltages in mesoscopic systems[19,20,21,22,23,24,25,26]
We have verified that the TE reciprocity relations predicted more than 20 years ago[5] manifest themselves in a mesoscopic device in the linear transport regime
Summary
We first spell out the properties of the four terminal device. It was defined by patterning the two-dimensional electron gas (2DEG) formed in an InP/Ga0.23In0.77As heterostructure by using electron-beam lithography and shallow wet etching (for details, see Ref.[7]). We checked carefully that the electric bias measurements were in the linear response regime (see Appendix A for details on device properties). Β=α where Vα and θα are the voltage and temperature, respectively, at terminal α, and Gαβ and Lαβ are the electrical conductance and thermoelectric coefficients, respectively, between terminals α and β. Since the thermoelectric coefficients depend directly on the transmission function, Lαβ should obey the same symmetry properties as Gαβ. This gives, writing out the diagonal and off-diagonal relations separately, Lαα(B) = Lαα(−B), Lαβ(B) = Lβα(−B) . Thereafter, the thermoelectric coefficients are investigated by thermally biasing the system under zero-electric-current conditions (with floating terminals), measuring the resulting potentials in all reservoirs, and using Eq (1) as explained in the following. We assume that ∆θγ(2) is independent of B, so that all of the B-field dependence in Lαγ∆θγ(2) comes from Lαγ
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