Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field

Abstract

The proximity induced pair potential in a topological insulator-superconductor hybrid features an interesting superposition of a conventional spin-singlet component from the superconductor and a spin-triplet one induced by the surface state of the topological insulator. This singlet-triplet superposition can be altered by the presence of a magnetic field. We study the interplay between topological order and superconducting correlations performing a symmetry analysis of the induced pair potential, using Green functions techniques to theoretically describe ballistic junctions between superconductors and topological insulators under magnetic fields. We relate a change in the conductance from a gapped profile into one with a zero-energy peak with the transition into a topologically nontrivial regime where the odd-frequency triplet pairing becomes the dominant component in the pair potential. The nontrivial regime, which provides a signature of odd-frequency triplet superconductivity, is reached for an out-of-plane effective magnetization with strength comparable to the chemical potential of the superconductor or for an in-plane one, parallel to the normal-superconductor interface, with strength of the order of the superconducting gap. Strikingly, in the latter case, a misalignment with the interface yields an asymmetry with the energy in the conductance unless the total contribution of the topological surface state is considered.

Theory of the Josephson current on a magnetically doped topological insulator

“…A possible alternative to the FI/SC junction is a superconducting junction on a magnetically doped TI. There are several theoretical works on systems with coexisting magnetization and superconducting pairing in the same spatial region 14,[26][27][28][29] . Chiral Majorana modes are predicted to appear in such systems.…”

Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping

“…where f 0 is the spin-singlet component (↑↓ − ↓↑), f x and f y are the combinations of equal spin triplet components, (↑↑ − ↓↓) and (↑↑ + ↓↓), correspondingly, while f z is the hetero-spin triplet component, (↑↓ + ↓↑) [22]. We can write these pairing wave functions explicitly as [18],…”

“…It was shown by Asano and Tanaka that in a onedimensional nano-wire, proximity coupled to a topological superconductor, the OTE pairing and the Majorana fermion are "two sides of a same coin" [16]. It was also argued that similar assumption is valid for two-dimensional topological surface states of a three-dimensional topological insulator in proximity with an s-wave superconductor [18,19,20,21,22]. We note here that the symmetry of the induced pair potential in S/TI structures in the diffusive case was studied in [29,30].…”

Asymmetric d -wave superconducting topological insulator in proximity with a magnetic order

“…For finite magnetization, the odd-frequently triplet components, which occur in topological insulator with proximity in a singlet pairing symmetry can become dominant, resulting in a noticeable superconductor subgap structure with emerging low-energy peaks (see, for example Ref. [20,21,22]). In Nambu (particle-hole) and spin space, with basis…”

“…However, ' ) ( -based cuprate ' ) (0010 is found to be a candidate for anisotropic spin-singlet -wave superconducting gap [15,16,17,18,19]. Very recently, the coexistence of proximity-induced a conventional superconducting pair potential and a ferromagnetic order at the same time in the surface of 3DTI has been theoretically investigated [20,21,22]. The superconducting topological insulator quasiparticle excitations are found to present a new renormalized effective gap by means of a magnetic order.…”