Odd-frequency triplet superconductivity at the helical edge of a topological insulator

Abstract

Non-local pairing processes at the edge of a two-dimensional topological insulator in proximity to an s-wave superconductor are usually suppressed by helicity. However, additional proximity of a ferromagnetic insulator can substantially influence the helical constraint and therefore open a new conduction channel by allowing for crossed Andreev reflection (CAR) processes. We show a oneto-one correspondence between CAR and the emergence of odd-frequency triplet superconductivity. Hence, non-local transport experiments that identify CAR in helical liquids yield smoking-gun evidence for unconventional superconductivity. Interestingly, we identify a setup -composed of a superconductor flanked by two ferromagnetic insulators -that allows us to favor CAR over electron cotunneling which is known to be a difficult but essential task to be able to measure CAR. PACS numbers: 74.45.+c, 74.78.Na, 71.10.Pm, 74.20.Rp Introduction.-The influence of strong spin-orbit coupling and the constraint of time reversal symmetry are responsible for the appearance of helical electronic channels at the edge of two-dimensional (2D) topological insulators [1][2][3]. Ample evidence for the experimental detection of these edge states has been seen in transport [4][5][6] and scanning SQUID experiments [7]. Proximity of an ordinary s-wave superconductor can induce pairing at the helical edge [8,9]. Interestingly, the interplay of helicity and superconducting order gives rise to unconventional proximity-induced superconductivity (SC) in these systems. However, it is fair to say that it is very difficult to unambiguously probe the emergence of unconventional SC because -often times -conventional and unconventional signatures of SC look alike. Several recent experiments have demonstrated (as a first step towards the detection of unconventional SC) that helical liquids as boundary states of quantum spin Hall systems can indeed be brought in proximity to s-wave superconductors [10] and serve, for instance, as conducting channels of a Josephson junction [11,12]. Importantly, helicity guarantees perfect local Andreev reflection [13] -the conversion of an electron into a hole with opposite spin -at the interface between the normal and the proximity-induced superconducting region called NS junction. Evidently, perfect local Andreev reflection can give rise to sub-gap Andreev states, for instance, in Josephson junction setups. Among these sub-gap states, the one with zero excitation energy is its own chargeconjugate state. It has been coined Majorana (bound) state and has attracted a lot of attention because of potential applications of this anyonic state for topological quantum computing [14]. If a ferromagnet (FM) is placed in vicinity to the NS interface the Majorana (bound) state can be localized in the region between the FM and the SC [9]. This localization allows us to make a formal connection to the physics of a finite-size 1D p-wave topological superconductor [15], and its potential realizations in spin-orbit nanowires [16,17]. In this Letter, ...

Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI

“…[23] to obtain differential conductance spectra of the S/N/FI/N' junction. Here, we would like to present the way of constructing the retarded Green's function which has recently been applied to relativistic system like Graphene [54,55], and 1D helical states on TI [56]. In our system, the translational invariance along the y-axis is preserved, thus the retarded Green's function with respect to Eq.1 has the formǦ(x, x ′ , y, y…”

Majorana STM as a perfect detector of odd-frequency superconductivity

“…Then, pairing mechanisms that are odd in frequency, triplet in spin space, and even in spatial parity (OTE) [10] are allowed by symmetry. Exciting new physics is attributed to OTE pairing, e.g., related to a long-range proximity effect in hybrid Josephson junctions based on ferromagnetism and superconductivity [22][23][24][25], cross correlations between the end states in a topological wire [26], the interplay of superconductivity and magnetism in double quantum dots [27], or its connection to crossed Andreev reflection at the helical edge of a 2D topological insulator [28].…”

Pair symmetry conversion in driven multiband superconductors

“…While some research has been dedicated to the thermodynamic stability of intrinsically odd-ω phases [3][4][5][6] , a great deal of previous research has been devoted to the identification of heterostructures in which odd-ω pairing could be induced including: ferromagnetic -superconductor heterostructures [7][8][9][10][11][12][13] , topological insulator -superconductor systems [14][15][16][17] , normal metal -superconductor junctions due to broken translation symmetry [18][19][20][21][22] , two-dimensional bilayers coupled to conventional s-wave superconductors 23 , and in generic two-dimensional electron gases coupled to superconductor thin films 24 . In addition to theoretical studies, there are experimental indications of the realization of odd-ω pairing at the interface of Nb thin films and epitaxial Ho 25 .…”