Andreev Reflection In Multi-Weyl Semimetal/Superconductor Heterostructures

In 1929,Weyl found that the Dirac equation can be decoupled into two Weyl equations when the mass term vanishes.Weyl equations define two types of fermions with opposite chirality.In recent years,with the study of topological materials and graphene,people have found a class of special metals known as Weyl semi-metal whose low-energy excitations can be described by the Weyl equations.Materials hosting Weyl fermions are called Weyl semimetals,where the crossing points of the conduction and valence bands are known as the“Weyl nodes”.These Weyl nodes occur in pairs with the linear dispersion and are protected due to either time-reversal or inversion symmetry breaking.Although the bulk energy band is gapless,it still has topological non-trivial behaviors,such as discontinuous Fermi arc and negative magnetoresistance.Since the emergence of Weyl semi-metal,the study of Weyl semi-metal and the Weyl semi-metal/superconductor heterostructures has become a hot spot,Scientists predict that the pairing properties of Weyl fermions will break the BCS theory and create more novel quantum phenomena.An effective method to detect them is by Andreev reflection spectrum.Recently,a new kind of Weyl semimetal with topological winding number greater than1 and weyl points having nonlinear dispersion in two transverse direction has been discovered.Such materials are termed as multi-Weyl semimetals since their nonlinear dispersion occurs due to merger of two or more Weyl nodes with same chirality.Such a merger is found to be topologically protected by point group symmetries.Because of the anisotropic dispersion in transverse direction,the change of density of states and special topological characteristics,Multi-Weyl semimetal exhibit unique optical and transport properties.The focus of this paper is to explore the Andreev reflection of the multi-Weyl semimetal/superconductor heterojunction.When the topological winding number J is1,we find that only Andreev reflection occurs when the incident angle is zero,and the sum of Andreev reflection coefficient A₁ and normal reflection coefficient A₂ is 1 when the E<?,which means the electron-hole conversion at the interface happens with unity probability.When the topological winding number J is 2 or 3,the Andrev reflection coefficient A₁ and normal reflection coefficient A₂ are not zero at zero incident angle,which indicates that both Andreev reflection and normal reflection exist at the interface of multi-Weyl semimetal/Superconductor heterojunctions.Recent progress show that the conic spectrum can be tilted or overtitled to transfrom the Weyl semimetal into the type-? one.Previous studies have found that double Andreev reflection when the superconductor is put in the Weyl semimetal band tilting direction.The directions of the double ARs are symmetric about the normal due to the Fermi surface near the Weyl nodes,but with different AR amplitudes depending on the direction and energy of the incident electron.Only one Andreev reflection occurs when the incident angle is zero,AR coefficients A₁ and A₂ exchange at the chemical potential?.But importantly,the sum of AR coefficients A₁ and A₂ only depends on the gap and energy E,with nothing to do with other parameters.In this paper we numericaly calculate the conductance of the Type-? Weyl semimetal/superconducting heterojunction.We find that at large bias E??,all curves converge to unity.This is expected since at large excitation energies the influence of superconductivity is negligible.For ?/??1 normal reflection is surppressed,leading to perfect Andreev reflection with G=2G₀.In the process of changing the parameter v₁ and v₂,the curve characteristics of conductance change greatly in the case of v₁>v₂ and v₁<v₂.This is due to the change of energy band tilt when v₁>v₂ and v₁<v₂,which leads to the change of transport properties.