In this talk, we will discuss different Josephson junctions based on semimetals, metals and topological insulators proximitized with s-wave superconductors. We show that thermal response can be more sensitive to Majorana bound states than an electrical response [1,2,3]. Moreover, due to the 4π periodicity of topological Josephson junctions, the thermal engines built on them are more efficient as the ones on the classical Josephson junctions [4]. Furthermore, we predict that the 2D Luttinger materials describing hole state with j=3/2 proximitized by s-wave superconductor are able to host Majorana bound states even in the absence of BIA and Rashba spin-orbit couplings [5]. This originates from the hybridization of the light and heavy hole bands of the j=3/2 states in combination with the superconducting pairing. We dub this effect as an intrinsic emergence of Majorana bound states [5]. We predict that Majorana bound states should be seen in many classes of materials like p-doped GaAs, bulk HgTe, as well as many half-Heusler compounds [5].
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