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At present, topological insulators are the most efficient thermoelectric materials at room temperature. However, at non-zero temperatures, it seems to arise a conflict between having time-reversal symmetry, which implies minimal entropy, and the Seebeck coefficient, which is the entropy carried by each electric charge unit. This has obliged us to analyze the mathematical and physical background taking into account relativistic phonons besides the electrons within quantum field theory. In this search, we found an approximate expression for the intrinsic topological field b in terms of the Chern number, the Fermi velocity $v_F$ and the electron effective mass $m$, which allows to connect the topologically non-trivial insulator with the trivial one, being consistent with their topological properties and physical robustness. Thanks to this, we demonstrate that for three-dimensional topological insulators in thin-film conditions, among others, phonons have chirality coupling in a novel way to electron dynamics which preserves time-reversal symmetry. This explains the compatibility of the thermoelectricity within topological insulators and shows explicitly how it adapts to the family of topological insulators Bi$_2$Se$_3$.
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Topological edge states are predicted to be responsible for the high efficient thermoelectric response of topological insulators, currently the best thermoelectric materials. However, to explain their figure of merit the coexistence of topological electrons, entropy and phonons can not be considered independently. In a background that puts together electrodynamics and topology, through an expression for the topological intrinsic field, we treat relativistic phonons within the topological surface showing their ability to modulate the Berry curvature of the bands and then playing a fundamental role in the thermoelectric effect. Finally, we show how the topological insulators under such relativistic thermal excitations keep time reversal symmetry allowing the observation of high figures of merit at high temperatures. The emergence of this new intrinsic topological field and other constraints are suitable to have experimental consequences opening new possibilities of improving the efficiency of this topological effect for their based technology.
We discuss the phase dependent nonlocal thermoelectric effect in a topological Josephson junction in contact with a normal-metal probe. We show that, due to the helical nature of topological edge states, nonlocal thermoelectricity is generated by a purely Andreev interferometric mechanism. This response can be tuned by imposing a Josephson phase difference, through the application of a dissipationless current between the two superconductors, even without the need of applying an external magnetic field. We discuss in detail the origin of this effect and we provide also a realistic estimation of the nonlocal Seebeck coefficient that results of the order of few $mu V/K$.
We introduce the concept of Berrys phase in Josephson junctions and consider how this geometric phase arises due to applied oscillating electric fields. The electromagnetic field excites topological quasi-particles from the junction vacuum which affect Cooper-pair tunneling across the Josephson junction barrier. A finite Berrys phase can be detected by its renormalization of the electric field amplitude absorbed by the junction. This has implications for the designing of accurate Josephson junction microwave detectors.
Topological Insulators are the best thermoelectric materials involving a sophisticated physics beyond their solid state and electronic structure. We show that exists a topological contribution to the thermoelectric effect that arise between topological and thermal quantum field theories applied at very low energies. This formalism provides us with a quantized topological mass proportional to the temperature T, being both quantities directly related with an electric potential V and getting a Seebeck coefficient where we identify an anomalous contribution that we associate to the creation of real electron-hole Schwingers pairs close to the topological bands. Finally, we find a general expression, considering the electronic contribution, for the dimensionless figure of merit of these topological materials, getting a value of 2.73 that is applicable to the Bi$_2$Te$_3$, for which it was reported a value of 2.4, using only the most basic topological numbers (0 or 1).
Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the observed QAHE appears only at ultralow temperatures. Therefore, intrinsic magnetic topological insulators are highly desired for increasing the QAHE working temperature and for investigating topological quantum phenomena further. The realization and characterization of such systems are essential for both fundamental physics and potential technical revolutions. This review summarizes recent research progress in intrinsic magnetic topological insulators, focusing mainly on the antiferromagnetic topological insulator MnBi2Te4 and its family of materials.
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