Theory of spin-selective Andreev reflection in the vortex core of a topological superconductor

Abstract

Majorana zero modes (MZMs) have been predicted to exist in the topological insulator (TI)/superconductor (SC) heterostructure. Recent spin polarized scanning tunneling microscope (STM) experiment 1 has observed spin-polarization dependence of the zero bias differential tunneling conductance at the center of vortex core, which may be attributed to the spin selective Andreev reflection, a novel property of the MZMs theoretically predicted in 1-dimensional nanowire.2 Here we consider a helical electron system described by a Rashba spin orbit coupling Hamiltonian on a spherical surface with a s-wave superconducting pairing due to proximity effect. We examine in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wavefunction of the MZM at the center of the vortex core, r = 0, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in 1-dimensional nanowire 2 . The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

“…Our results agree well with Ref. [20], which shows that the helical edge states exist even in the presence of B y . In addition, the spin Hall conductance is shown in Fig.…”

“…For a QSH insulator in the presence of an out-of-plane magnetic field, the spin Chern number is shown to remain unchanged up to the magnetic field when the Landau levels cross [15,17,21]. While for an inverted InAs/GaSb quantum well in the presence of an in-plane magnetic field, the edge states and the quantized conductance are shown to be robust till a strong magnetic field of 20 T [20]. In a recent experiment, it was shown that the helical edge conduction survives up to an in-plane magnetic field of 12 T [22].…”

“…However, as pointed out in several theoretical works [12][13][14][15][16][17][18][19][20], the QSH effect is not destroyed immediately by the application of TR symmetry breaking terms. A few theoretical studies have been devoted to understanding the robustness of the QSH effect under broken TR symmetry.…”

“…There is a freedom to choose the vector potential, and here we use the Landau gauge A = (−B z y + B y z, 0, 0). To model the spatial separation of the electron and hole for the bilayer system, we set the electron layer on y = z o /2 plane, while the hole layer on the y = −z o /2 plane, where z o is the thickness of the quantum well and taken to be one lattice constant [20]. Thus, the vector potential for the electron(hole) layer is A = (−B z y + (−)B y zo 2 , 0, 0).…”

Detection of Majorana zero mode in the vortex

“…[42][43][44] Via an spin-polarized STM, 45,46 we can inject spin-polarized tunneling current in STS measurements and observe the zero bias conductance change caused by the SSAR from the MZM when flipping the spin of the tunneling electrons. 47,48 It is worth noting that only a small magnetic field is sufficient to excite vortices on the TI surface and hence the spin-polarized MZM in the vortex core. On the other hand, the spin polarization of other surface states and finite energy quasiparticle states is still negligibly small.…”