Magnetoresistance and gating effects in ultrathin NbN-$\rm Bi_2Se_3$ bilayers

Ultrathin $\rm Bi_2Se_3$-NbN bilayers comprise a simple proximity system of a topological insulator and an s-wave superconductor for studying gating effects on topological superconductors. Here we report on 3 nm thick NbN layers of weakly connected superconducting islands, overlayed with 10 nm thick $\rm Bi_2Se_3$ film which facilitates enhanced proximity coupling between them. Resistance versus temperature of the most resistive bilayers shows insulating behavior but with signs of superconductivity. We measured the magnetoresistance (MR) of these bilayers versus temperature with and without a magnetic field H normal to the wafer (MR=[R(H)-R(0)]/\{[R(H)+R(0)]/2\}), and under three electric gate-fields of 0 and $\pm2$ MV/cm. The MR results showed a complex set of gate sensitive peaks which extended up to about 30 K. The results are discussed in terms of vortex physics, and the origin of the different MR peaks is identified and attributed to flux-flow MR in the isolated NbN islands and the different proximity regions in the $\rm Bi_2Se_3$ cap-layer. The dominant MR peak was found to be consistent with enhanced proximity induced superconductivity in the topological edge currents regions. The high temperature MR data suggest a possible pseudogap phase or a highly extended fluctuation regime.


INTRODUCTION
Surface edge states of topological superconductors (TOS) are expected to support zero energy modes or Majorana fermions which are robust against disorder and decoherence [1,2]. These zero energy excitations could therefore be useful in potential application in spintronics and quantum computing [3,4]. Bulk TOS such as copper doped Bi 2 Se 3 should have been the simplest materials to study TOS properties, but complications due to their inherent inhomogeneity [5] and the presence of possible superconducting impurity phases such as CuSe 2 [6], make them less attractive for such investigations. An alternative way for realizing TOS is by inducing superconductivity in a topological insulator or in semiconductor-nanowires with strong spin-orbit interaction via the proximity effect (PE) [7][8][9][10]. Unconventional superconductivity in these systems, such as revealed by the presence of zero bias conductance peaks (ZBCP), indicates zero energy bound states that might be due to Majorana zero energy modes, but could also originate in zero energy Andreev bound states. It is hard to distinguish between these two different phenomena, and efforts are ongoing in order to achieve this goal [11,12].
Spatial sharpness of the boundary region between the superconductor and the topological or semi-conducting material is also essential in order to distinguish between the near-zero-energy end states originating in Andreev bound states, and the Majorana zero energy modes in the topological case [13]. Since this boundary is generally created by gating in the experiments, its unavoidable gradual spatial change adds more uncertainty to the interpretation of the observed ZBCPs as due to the Majorana modes [9,10,14]. The role of gating in these nanowire-superconductor experiments was further investigated and a variety of additional phenomena such as ZBCP oscillations versus gate voltage and magnetic field were observed and interpreted in the context of Majorana modes as well as alternatives such as Kondo and disorder effects [15]. Hence, gating is sufficiently important in these studies and we decided to use a arXiv:1506.08584v1 [cond-mat.supr-con] 29 Jun 2015 ~0.35 nm rms roughness  simple proximity system of a bilayer comprising of a topological insulator and a 2D superconductor for studying gating effects on topological superconductors [16]. In continuation to our previous studies of Bi 2 Se 3 − N bN junctions [17,18] we used ultra-thin bilayers of this system, even thinner than used before [16], where the superconducting N bN islands with weak-links in between them are overlayed with a thicker Bi 2 Se 3 layer which enhances the coupling between the N bN islands via the (inverse) proximity effect. Here we report on gating effects on the magnetoresistance (MR) of this hybrid system, which shows a highly gate sensitive, non-monotonous behavior versus temperature.

Preparation and surface morphology of the films and bilayers
The NbN and Bi 2 Se 3 thin films were prepared as described in detail previously [16].  [19]. In addition, Fig. 1 shows a few 1-3 nm deep holes of about 60 nm diameter while the overall rms roughness of this film is ∼0.35 nm.
All the Bi 2 Se 3 − N bN bilayers in the present study were obtained using an "in-situ" process where both the 3 nm thick N bN film and the 10 nm thick Bi 2 Se 3 cap layer were prepared in the same deposition run without breaking the vacuum. This kept the interface between the NbN and Bi 2 Se 3 layers protected against contamination and oxidation which occur if the NbN surface is exposed to air [16,20]. Fig. 2 shows an AFM        It also shows that above 5 K, its MR is zero to within the noise of the measurement. This is different from the bilayer data of  voltage. The resistivity of this film is ∼6 mΩcm or 6kΩ per square, which corresponds to an electron density of about 10 17 cm −3 [21]. Thus the electron doping of this film is quite low, which results from the Se rich target used in its deposition process [16]. The R versus T data of show a linear R versus H behavior at low fields up to about 0.1 T with saturation at higher fields.
The linear MR in Bi 2 Se 3 is generally attributed to weak anti-localization (WAL) [22,23]. If we assume that this is correct, we can use the HLN model [24] to calculate the phase coherence length L φ as a function of temperature from our data. For a field of H = 1 T and L φ in nm, the HLN model yields: where ψ is the digamma function. Since both R(H = 1T ) and R(0) were measured as a function of temperature, Eq. (1) allows us to extract L φ which is thus also a function of temperature. The result is shown in the inset to Fig. 7 for another 10 nm thick Bi 2 Se 3 film on FS. One can see that the resulting L φ is very sensitive to the contact location on the wafer, probably because the coherent WAL scattering process is very sensitive to even slight inhomogeneities in the film. Also, since C2 is closer to the edge of the wafer than C4, edge effects can affect the resulting L φ . Both however, decrease very rapidly versus T at low T and then decay more gradually. Again, this is not a proof that WAL occurs here, but if it does, these are the calculated L φ (T) curves from our measurements.  where under 0 Vg T c is higher by ∼0.3 K than at -100 Vg.
The main panel of Fig. 10 shows that the MR above 12-13 K and up to 90 K is within the noise of the measurements (±0.1 %). This is in contrast to the observation in the bilayer of Fig. 6 where an MR of a few percents is observed even much above T c . If we determine T c in Fig. 10   In addition, the T c = 12 K value coincides with the temperature value of maximum resistance as seen in Fig. 9. Therefore, we conclude that this is the T c of the thicker NbN islands in the bilayer.

Bi2Se3 − N bN bilayers
We now present the main part of this study, namely, the properties of a highly resistive 10 nm  Vg is somewhere in between these two at 3.5 K, but then becomes closer to the -100 Vg data at 6-7 K. At higher temperatures the MR data becomes even more complex, but clearly it goes down at 25-30 K, where it tends to follow the reference Bi 2 Se 3 film. It should be stressed here that the MR behavior of Fig. 12 for the C4 contact, was observed also for the other contacts on this wafer (C6 and C8), while C7 had an additional strong oscillatory behavior above 10 K as shown in Fig. 13 for 0 Vg. This oscillatory behavior was washed out under ±100 Vg. The inset to Fig. 13 is a zoom-in on weaker oscillations or plateaus in the MR of C7 in the range of 3-8 K. Such plateaus and knees, although weaker, appear also in the other contacts. As far as we know, there is no theory that predicts oscillations of MR versus temperature in a 2D topological superconductor.
To find out whether these oscillations and plateaus originate in magnetic field effects, we measured R versus H for all the contacts on the wafer of Fig. 11 Fig. 11. The oscillations were smeared out under ±100 Vg. The inset is a zoom in on the data at low temperatures. Only this C7 contact showed the pronounced oscillations versus temperature, although plateaus and less pronounced knees were observed also in the other contacts as seen in the inset and marked by the arrows. In the context of vortex physics, the MR peaks seen in Fig. 12  We shall now analyze the MR results of Fig. 12 under different gate voltages and try to explain the two prominent peaks at 3.5 and 6 K under -100 Vg and +100 Vg, respectively. We note that transport, and therefore also the MR data, is strongly dependent on the conductance of regions II and IV, since they comprise the weak-links for current flow in the bilayer.
As a result, they will be more sensitive to gating than region I. Under -100 Vg, the depletion layer in Fig. 4 in between the NbN islands (region II), is positively charged or simply electron depleted. This makes region II, (as well as the adjacent region IV just above it), less conducting (or more insulating), thus lowering its T c onset to about 4 K compared to its value without gating (onset at ∼6.5 K). The MR peak at 3.5 K under -100 Vg is consistent with this scenario, and therefore seems to originate in region II. The large MR peak at 1.9 K seems to be unaffected by either of the present gate voltages of ±100 Vg, and this again might originate in topological effects in region IV. Under +100 Vg, the depletion layer is electron rich (more conducting), thus its proximity induced T c in region II is higher than the 4 K obtain before under -100 Vg. The MR peak at 6 K under +100 Vg can thus originate also in region II. Fig.   12 shows extra MR features under gating besides the two prominent peaks at 3.5 and 6 K. These include the broad hump under +100 Vg between 10 and 25 K, and the broad peak between 15 and 30 K under -100 Vg. As discussed before, superconductivity dies off at about 15 K, and any proximity induced T c will obviously be lower.
Therefore, if one wishes to invoke vortex motion as the origin of these extra MR features, one has to assume the existence of a pseudogap phase for the present bilayers.
Signature of such a phase was found in point contact conductance spectra measurements of copper doped where the pseudogap phase is well established, such vortices were detected in thermoelectric measurements under a magnetic field (the Nernst effect) [30].
Finally, we focus on the intensity or magnitude of the MR peaks in Fig. 12, and on what might contribute extra strength to the dominant peak at 1.9 K. We note that the volume fraction of the superconducting NbN islands with the highest T c values is apparently very small, as can be inferred from the very small resistive transition at 2.5 K in Fig. 11. Previously, in the vortex pinning context, we attributed the MR double peak under 0 Vg at 7-15 K to regions I and III, the knee between 2.5 and 6.5 K to region II, and the large MR peak below 2.5 K to region IV. It was hard to reconcile how region IV, with its presumably weakest superconductivity, leads to such a large MR peak. Thus, if the enhanced MR peak at 1.9 K is still due to pinning effects, we are led to the conclusion that region IV must have enhanced superconductivity just as well. Such en-hancement might originate in a longer normal coherence length ξ N in the Bi 2 Se 3 at low temperatures, which is possibly enhanced further by hybridization of the helical surface currents of regions IV and VI. We know of no theory that predicts such effects, and therefore this interpretation is only a hypothesis at the present time. An alternative scenario for the interpretation of our results is that the MR knee between 2.5 and 6.5 K is due to pinning effects in both region II and region IV. This would leave the dominant MR peak at 1.9 K unaccounted for, and other effects as for its origin should be explored.