Spectroscopic evidence of odd frequency superconducting order

Spin filter superconducting S/I/N tunnel junctions (NbN/GdN/TiN) show a robust and pronounced Zero Bias Conductance Peak (ZBCP) at low temperatures, the magnitude of which is several times the normal state conductance of the junction. Such a conductance anomaly is representative of unconventional superconductivity and is interpreted as a direct signature of an odd frequency superconducting order.

drop in resistance is observed below 14 K due to the superconducting transition of the NbN layer.Below 14 K, the observed rise in low bias resistance is due to the opening of the NbN gap and freezing out of sub-gap conductance.This rise of resistance below 14 K is reflective of a decreasing sub-gap resistance R S to normal state resistance R n ratio at low temperatures, and is therefore a signature of good quality junctions 21 .The drop in resistance below 4 K is due to the evolution of a zero bias conductance peak.To confirm the non-superconducting nature of the TiN used in these experiments, the temperature dependence of the resistance of un-patterned films of TiN/GdN grown in the same deposition run as that of the junctions, is shown in the bottom inset to Fig. 1.This shows no detectable superconducting transition above 1.6 K (the temperature limit of the cryostat used for Resistance vs Temperature (RT) measurements).
We observed that a wide range of properties can be obtained in TiN films by altering the nitrogen concentration.In order to obtain non-superconducting TiN, we have tuned the nitrogen concentration (8%) in the sputtering gas mixture.
In Fig. 2, we show the differential conductance curves of a junction with a 3 nm GdN barrier.The curves clearly show the emergence of a strong ZBCP as the junction is cooled to low temperatures.Identical characteristics have been found in all eight junctions on the same chip, and similar characteristics have also been found in all 8 junctions on the same chip of a thinner 2 nm GdN thickness tunnel junction which has spin-polarization  (P)~65% at 4 K.The ZBCP in all junctions is extremely robust, reproducible, and independent of magnetic field history.The behaviour of these S/I/N junctions at temperatures above which the ZBCP disappears (> 3 K), is well understood and has been addressed in detail in a previous publication 17 .
It has been theoretically predicted that for spin active interfaces, in the tunnelling limit, a subgap state appears due to spin-dependent phase-shifts 22 .This interface state is manifested via strong conductance peaks at a voltages eV = ± Δ 0 cos(ϑ/2) where ϑ is the spin-dependent phase shift that is present due to the FI.For ϑ = π the state is pinned to the Fermi level (zero bias).The appearance of this interface state is intimately linked to odd-frequency pairing 13 .
ZBCPs are known to occur in several superconducting systems and for a variety of underlying physical mechanisms 4,[23][24][25] .A ZBCP analogous to our experiment observation is the case of d-wave superconductors 24 , which occurs due to the sign change of the order parameter at regions in the a-b plane.
For s-wave superconductors, analogous phenomenon can be observed for sign change of the spin dependent phase shift due to the FI which translates to a phase shift of π.Such strong phase shifts 26,27 can be obtained when (a) quasiparticles normal to the interface are the major contributors to the transport process, (b) when spin polarization by the barrier is high, (c) when the barrier profile is not sharp.All the above conditions are met by an NbN/GdN/TiN tunnel junction system, especially that of high spin polarization.An order of magnitude difference between Fermi vectors of NbN 28 and TiN 29 results in quasiparticles normal to the interface being the major contributors to the transport.A previous study has shown that NbN/GdN barrier is different from a conventional box type potential barrier, as a Schottky barrier forms at the NbN/GdN interface 20 .The fact that all the conditions for obtaining a large spin-dependent phase-shift at the interface are met, taken in conjunction with the fact that the conductance spectra demonstrate a ZBCP is a clear indication that this phase-shift is likely to have a value very close to π.
Theoretical model.The experimental data in Fig. 2 can be modelled by the theoretical conductance of an S/FI/N structure with a spin-dependent phase-shift close to π, as shown in Fig. 3.The conductance for a ballistic S/FI/N structure has been studied previously 22 , and we have followed their analysis when fitting our experimental data.In the tunneling limit, we neglect the suppression of the superconducting order parameter and use the following expression for the current density across the junction where The following quantities have been defined in Eq. ( 1): D = D ↑ + D ↓ , J N is the current density when the superconductor is in its normal state (J N ∝ D), D σ and R σ are the probability coefficients for transmission and reflection of spin σ carriers, respectively, β = (k B T) −1 , V is the applied voltage, T is the temperature, E is the quasiparticle energy, ∆ is the superconducting gap, ϑ is the spin-dependent phase-shift due to the magnetic barrier, and acos( / ) for , acosh( / ) for (2)   For the theoretically simulated conductance plots, we have differentiated Eq. ( 1) with respect to voltage and normalized the conductance against the normal-state conductance obtained at large voltages eV ≫ ∆ .To model inelastic scattering, we have incorporated a Dynes parameter via the relation E → E + iΓ where Γ provides the quasiparticles with a finite lifetime.The model also accounts for the large difference in tunnelling probability for majority and minority carriers, as expected for a strongly polarized FI.The temperature-evolution of the conductance spectra matches only qualitatively: the ZBCP vanishes experimentally more rapidly with temperature than in the theory, the reason for this is unclear.However, it must be noted that the temperature dependence of ZBCP is consistent with previous experimental observations of qualitatively similar origins of ZBCP.STM measurements of LDOS in Nb/Ho systems (due to odd frequency triplet superconductivity) observed the ZBCP disappearing at 660 mk 7 -far below the superconducting transition of Nb used in the experiment (T c,Nb ~6.6 K, please refer to supplementary information section of ref. 7), while ZBCPs in YBCO (originating due to sign change of order parameter in d-wave superconductors) were only observed until 40 K and 60 K (T c,YBCO ~90 K) in refs 24 and 30 respectively.We therefore assume that the temperature dependence arises due to aspects of theory which have not been fully understood.

Conclusions
We have not seen oscillatory behaviour in the intensity of ZBCPs with the application of magnetic field, thus ruling out the possibility of attributing the observed ZBCP to possible Majorana bound states 4 .ZBCPs occurring due to Kondo effects, on application of an external magnetic field, should separate out to a double peak structures 31 .The strong intensity of the ZBCP (3.5 times the normal state conductance) rules out other possibilities like de Gennes-Saint-James resonances 23 or a pin hole mediated junction which in accordance to the BTK theory 32 should give rise to a maximum ZBCP intensity of twice the normal state conductance.ZBCPs could also occur due to the TiN layer turning superconducting thus facilitating a critical current.However, the monotonic field-suppression and the observation of the ZBCP at high magnetic fields clearly indicate that Josephson effects do not cause the ZBCPs.Moreover, the top inset to Fig. 1 -shows that the ZBCPs start to evolve at 2.8 K, 3.8 K and 3.6 K for 3 nm, 2 nm and 1 nm barrier thicknesses respectively.Since the TiN layer for all these films were grown without breaking the vacuum and with the same plasma, this non-monotonic behaviour cannot be related to any possible superconductivity in TiN.However, such temperature dependence again points to an incomplete understanding of theoretical origins for ZBCPs for unconventional superconducting orders.For a more detailed analysis -which rules out superconductivity in TiN layer -please refer to the supplementary information section.Hence, none of the above possibilities are suitable in explaining the observed ZBCPs in our experiment.
The ZBCPs in NbN/GdN/TiN tunnel junctions therefore clearly establish an unconventional non-BCS type DOS indicating odd frequency superconductivity evolving at NbN/GdN interfaces.The current discovery of odd frequency pairing is not only relevant in understanding superconductivity beyond the conventional scope of BCS theory; but also firmly establishes FIs as important material systems for developing active devices for superconducting spintronics 33 .

Methods
The trilayered films of NbN/GdN/TiN are grown without breaking the vacuum in an ultra high vacuum chamber, by means of reactive dc magnetron sputtering in an atmosphere of Argon and Nitrogen.TiN is here grown as a (non-superconducting) metallic layer.Mesa type tunnel junctions were fabricated from sputtered tri-layered films by means of a fabrication procedure described elsewhere 21 .The only difference was that instead of plasma etching, TiN had to be Ar ion milled controllably.Measurements were performed using a 3He dip probe in a closed cycle liquid helium cooled variable temperature insert capable of cooling down to 0.3 K. Spin polarization was calculated from resistance vs temperature measurements using a procedure described in a previous publication 16 .

Figure 1 .
Figure 1.Temperature dependence of junction resistance.A 3 nm GdN junction measured at low bias.Top inset shows the Resistance vs Temperature (RT) dependence below superconducting transition of the NbN layer for junctions of 3 thicknesses -1, 2, 3 nms.Bottom inset shows the RT dependence of a bilayer film of GdN and TiN to demonstrate the absence of superconducting transition in TiN films used in this work.

Figure 2 .
Figure 2. Evolution of Zero Bias Conductance Peak (ZBCP) with temperature.Differential conductance (dI/dV) measurements normalised to the normal state conductance of an 100 nm NbN/3 nm GdN/30 nm TiN tunnel junction showing evolution of a ZBCP with decreasing temperature.Inset to the figure shows the temperature dependence of the intensity of the ZBCP.

Figure 3 .
Figure 3. Theoretical dI/dV curves for an S/FI/N junction as a function of applied voltage eV.Following the framework of ref. 22, we have used transmission probabilities D ↑ = 0.20 and D ↓ = 0.015 for each spin species, a spin-mixing angle of 0.98π , and set the Dynes parameter to 0.05Δ 0 .Inset: the formation of a zero-energy bound state at the interface due to spin-active Andreev reflection (AR) by the gap Δ 0 (indicated by red circles) where an additional phase-shift close to π is picked up by the quasiparticles.