Electrical and thermal transport in a twisted heterostructure of transition metal dichalcogenide and CrI3 connected to a superconductor

The broad tunability of the proximity exchange effect between\ntransition-metal dichalcogenides (TMDCs) and chromium iodide (CrI$_3$)\nheterostructures offers intriguing possibilities for the use of TMDCs in\ntwo-dimensional magnetoelectrics. In this work, the influence of the twist\nangle and the gate electric field on the electric and thermal transport in a\nTMDC/CrI$_3$ junction is investigated using the Dirac -Bogoliubov-de Gennes\nequation. We show that significant amounts can be controlled by spin-splitting\nof band structures due to spin-orbit interaction, and that the\nexchange-splitting of bands arises from the proximity effect. The property of\nthe Andreev reflection (AR) process is highly dependent on the spin valley\npolarized states due to spin-orbit coupling. Remarkably, perfect spin valley\npolarized AR is possible over a wide bias range by using a gate voltage to tune\nthe local Fermi energy and varying the type of charge doping. The proposed\nstructure with $p$-type doping is found to have larger spin valley polarized\nAndreev conductance and high thermal conductance. We further show that,\ndepending on the TMDC material and chemical potential of the TMDC/CrI$_3$\nlayer, twisting can lead to suppression or a significant increase in Andreev\nconductance as well as enhancement of thermal conductance for chemical\npotentials smaller than that of the superconducting regime.\n