Probing the helical edge states of a topological insulator by Cooper-pair injection

Adroguer, Pierre; Grenier, Charles; Carpentier, David; Cayssol, Jérôme; Degiovanni, Pascal; Orignac, Edmond

doi:10.1103/physrevb.82.081303

Cited by 68 publications

(100 citation statements)

References 37 publications

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“…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.…”

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confidence: 99%

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

2015

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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, ...

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confidence: 99%

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

2015

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“…The only possible scattering channels are the electron transmission and reflection as a hole (Andreev reflection). When the excitation energy lies within the superconducting gap electron transmission must be zero and perfect Andreev reflection was predicted for both geometries, provided that the width of the ribbon is large enough to separate the counter propagating edge channels [27,28]. From matching the wave functions at the interface at x = 0 …”

Section: Transport Within the Btk Formalismmentioning

confidence: 99%

“…4a. If the system is large enough, the counter-propagating edge states with opposite spin do not hybridize and can be treated independently, while perfect Andreev reflection occurs at the NSC interface [27,28]. When a bias V is applied across the NSC junction we calculate the excess current I ex as well as the dI/dV characteristics within the BTK formalism [21,26] at finite temperature k B T = 0.1∆.…”

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confidence: 99%

Superconducting quantum spin Hall systems with giant orbitalgfactors

2015

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Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. We examine hybrid QSHS/superconductor structures in an external magnetic field and predict a gapless superconducting state with protected edge modes. It originates entirely from the orbital magnetic-field effect caused by the locking of the electron spin to the momentum of the superconducting condensate flow. We show that such spin-momentum locking can generate a giant orbital g-factor of order of several hundreds, allowing one to achieve significant spin polarization in the QSHS in the fields well below the critical field of the superconducting material. We propose a three-terminal setup in which the spin-polarized edge superconductivity can be probed by Andreev reflection, leading to unusual transport characteristics: a non-monotonic excess current and a zerobias conductance splitting in the absence of the Zeeman interaction.PACS numbers: 72.25. Dc, 73.23.Ad, 74.45.+c Introduction. Spin-Hall effects are one of the most active fields in modern solid state physics [1][2][3][4][5][6][7][8]. In particular, the quantum spin-Hall effect [5, 6, 9, 10] allows one to generate and convert charge and spin currents in protected edge channels [11]. Combining quantum spin-Hall systems (QSHSs) with superconductors (SCs) leads to a broader spectrum of interesting observable phenomena [12][13][14]. These include quantum interference effects reported in [13,14], indicating superconducting transport through the edge states in the QSH regime. Understanding edge superconductivity in QSHS/SC hybrids is also instrumental to the proposals to realize Majorana zero modes in topological insulators (see, e.g., [15] and reviews [16,17]).In this paper we predict a unique magnetic-field response of QSHS/SC hybrids which is characterized by very large effective g-factors reaching the order of several hundreds. It originates from the locking of the electron spin to the momentum of the superconducting condensate flow generated by an external magnetic field. We show that this orbital effect has the form similar to the Zeeman spin splitting in thin superconducting films [18], but involves an effective g-factor determined by the parameters of the QSHS/SC structure, viz.: the edge-state velocity, v, the thickness of the SC material, d SC , and the London penetration depth, λ L :

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“…Since there is perfect Andreev reflection at a QSH insulator/superconductor junction, this contribution should be 4e 2 /h (2e 2 /h per edge) 26 . In the metallic regime, the large number of channels makes this edge conductance negligible with respect to the bulk conductance.…”

Section: Experimental Realizationmentioning

confidence: 99%

“…Combining these unique topological phases with conventional superconductivity raises fundamental questions about topological superconductors 17,18 , and may lead to the discovery of novel exotic modes such as Majorana fermions [19][20][21][22][23][24] with potential applications for spintronics and quantum computing 25 . Previously most studies have focused on proximity induced superconductivity within 1D edge states 20,26 or 2D surface states 19,[21][22][23] . In doped TIs (resp.…”

Section: Introductionmentioning

confidence: 99%