Conductance oscillations and zero-bias anomaly in a single superconducting junction to a three-dimensional $Bi_2Te_3$ topological insulator

TL;DR

This study explores Andreev transport and conductance oscillations in a superconductor-topological insulator junction, revealing proximity-induced superconductivity effects in the topological surface state.

Contribution

It provides experimental evidence of conductance oscillations and zero-bias anomalies linked to proximity-induced superconductivity in a Bi2Te3 topological insulator.

Findings

Conductance oscillations are nearly periodic and occur in transparent junctions.

Zero-bias conductance anomalies are observed alongside oscillations.

Effects disappear above the superconducting transition or in resistive junctions.

Abstract

We experimentally investigate Andreev transport through a single junction between an s-wave indium superconductor and a thick film of a three-dimensional $Bi_2Te_3$ topological insulator. We study $Bi_2Te_3$ samples with different bulk and surface characteristics, where the presence of a topological surface state is confirmed by direct ARPES measurements. All the junctions demonstrate Andreev transport within the superconducting gap. For junctions with transparent $In-Bi_2Te_3$ interfaces we find a number of nearly periodic conductance oscillations, which are accompanied by zero-bias conductance anomaly. Both effects disappear above the superconducting transition or for resistive junctions. We propose a consistent interpretation of both effects as originating from proximity-induced superconducting correlations within the $Bi_2Te_3$ topological surface state.

Full text

I Introduction

Recent interest to Andreev reflection is mostly connected with new materials, which can be characterized by Dirac spectrum. They are graphene geim , three- hasan and two-dimensional konig ; kvon topological insulators, topological Dirac semimetals semid ; semid1 . Classical Andreev reflection andreev allows low-energy electron transport from normal metal to superconductor by creating a Cooper pair, so a hole is reflected back to the normal side of the junction tinkham . The Andreev process is more complicated for relativistic materials. For example, the scattering potential BTK at the normal-superconductor (NS) interface do not suppress the current yung due to the Klein paradox klein ; klein1 . Also, the interband reflection is possible, where a reflected hole appears in the valence band, which is known as specular Andreev reflection been1 ; been2 . This process has been recently reported for graphene efetov and for two-dimensional semimetals nbgasb .

Proximity-induced superconductivity is regarded to be responsible for conductance oscillations in transport along the topological surface state. Bogoliubov quasiparticles are predicted adroguer to experience Fabry-Perot-type transmission resonances for energies above the superconducting gap within the region of induced superconductivity for a long $L>>\xi$ single NS junction, $\xi$ is a coherence length. On the other hand, subgap conductance oscillations were demonstrated finck for a short $L<<\xi$ three-dimensional $Bi_{2}Se_{3}$ topological insulator sandwiched between superconducting and normal leads. These effects are the representations of Tomasch tomasch1 ; tomasch2 and MacMillan-Rowell mcmillan1 ; mcmillan2 geometrical resonances, which originates in classical tomasch1 ; mcmillan1 ; mcmillan2 ; tomasch_exp1 ; tomasch_exp2 NS junctions due to the space restriction in the S or N regions, respectively.

Three-dimensional topological insulators like $Bi_{2}Te_{3}$ are usually characterized hasan ; volkov by both topological surface and trivial bulk transport contributions. Following Ref. adroguer , it seems to be reasonable to search for resonances also in charge transport through wide $L>>\xi$ superconducting junctions to these materials, which could also help to distinguish between two transport channels.

Here, we experimentally investigate Andreev transport through a single junction between an s-wave indium superconductor and a thick film of a three-dimensional $Bi_{2}Te_{3}$ topological insulator. We study $Bi_{2}Te_{3}$ samples with different bulk and surface characteristics, where the presence of a topological surface state is confirmed by direct ARPES measurements. All the junctions demonstrate Andreev transport within the superconducting gap. For junctions with transparent $In-Bi_{2}Te_{3}$ interfaces we find a number of nearly periodic conductance oscillations, which are accompanied by zero-bias conductance anomaly. Both effects disappear above the superconducting transition or for resistive junctions. We propose a consistent interpretation of both effects as originating from proximity-induced superconducting correlations within the $Bi_{2}Te_{3}$ topological surface state.

II Samples and technique

Single crystals of $Bi_{2}Te_{3}$ were grown using the modified Bridgman method, see Ref. teresch for details. It was shown bathon , that solidification of 61 or 62 mol.% Te melts provides transition from regions of p- to n- type bulk carriers along the growth direction, which is caused by Te segregation. Apart from the narrow compensated region, both p- and n-parts of the crystal show high low-temperature (4 K) carrier mobility $\approx 10^{4}$cm2/Vs for carrier concentration $\approx 10^{19}$cm*-3*.

Different samples are exfoliated from p- or n-type parts of a single $Bi_{2}Te_{3}$ crystal, see in Fig. 1 (a). Exfoliation produces thick (below 1 $\mu$m) $Bi_{2}Te_{3}$ films with freshly cleaved (0001) surface. Superconducting contacts are made by thermal evaporation of 100 nm indium through the shadow mask on this surface, see the sample sketch in Fig. 1 (b).

The evaporated In film is checked to undergo superconducting transition at $T_{c}=3.4~{}K$, in good accordance with the known literature data kittel . At lower temperatures, every $Bi_{2}Te_{3}-In$ contact represents single NS junction of macroscopic, $\approx 1$ mm, lithographic dimensions, which exceeds well the indium correlation length indium $L>>\xi_{In}\approx 300$ nm. The latter requirement is obligatory within the framework of Ref. adroguer , so we use thick $Bi_{2}Te_{3}$ films of macroscopic dimensions, instead of the commonly used micrometer-size thin flakes finck .

We study charge transport across one particular NS junction in a three-point technique, as depicted in Fig. 1 (b): one superconducting In contact is grounded; two others are used to feed a current $I$ through the junction and to measure the potential $V$. In general, $V$ reflects the in-series connected resistances of the grounded $Bi_{2}Te_{3}-In$ junction and some part of $Bi_{2}Te_{3}$ crystal between the ground and potential contacts, see Fig. 1 (b). If the former term is dominant, the obtained $I-V$ curve should be independent of the particular choice of current/voltage probes, which is the experimental test on relative bulk influence.

We sweep the dc current from -50 $\mu$A to +50 $\mu$A. To obtain $dV/dI(V)$ characteristics, the dc current is modulated by a low (0.1 $\mu$A) ac (110 Hz) component. We measure both the dc ($V$) and ac ($\sim dV/dI$) components of the $Bi_{2}Te_{3}$ surface potential by using a dc voltmeter and a lock-in amplifier, respectively. The lock-in signal is independent of the modulation frequency up to 1 kHz, which is defined by applied ac filters. To investigate Andreev transport, the measurements are performed below $T_{c}$.

One can expect a complicated transport behavior for the $Bi_{2}Te_{3}-In$ NS junction, since topological surface state is present at the $Bi_{2}Te_{3}$ surface. Fig. 1 (c) shows typical ARPES data obtained at T=300 K on the vacuum cleaved (0001) surface of p-type $Bi_{2}Te_{3}$ crystals along the $\Gamma$K direction at a photon energy of $h\nu$= 23 eV. The topological surface state and the topmost bulk valence band can be seen in Fig. 1 (c).

III Experimental results

Fig. 2 presents typical examples of $dV/dI(V)$ characteristics. They demonstrate behavior, which is qualitatively consistent with standard Andreev one for single SN junction tinkham . At high temperature $T=4.2$ K, $dV/dI$ differential resistance is nearly linear, see Fig. 2 (a). At low $T=1.6$ K, there is a wide drop in $dV/dI$ within $eV\approx\pm 0.5$ mV bias region, see Fig. 2 (a) and (b), which corresponds well to the indium superconducting gap kittel $\Delta_{In}=0.5$ mV. According to standard BTK theory BTK , the drop in $dV/dI$ within the superconducting gap is a fingerprint of Andreev reflection at the transparent NS interface tinkham .

In general, $dV/dI(V)$ curves could contain some admixture of bulk $Bi_{2}Te_{3}$ resistance, as it can be seen from Fig. 1 (b). However, at given concentrations and mobilities, a characteristic bulk resistance value is much below 1 Ohm. This estimation is experimentally verified by changing the current/voltage probes in Fig. 2 (b). Thus, the $dV/dI(V)$ curves in Fig. 2 reflect only the $In-Bi_{2}Te_{3}$ junction transport characteristics.

Surprisingly, we observe pronounced nearly periodic $dV/dI$ oscillations for biases above the superconducting gap $|eV|>\Delta_{In}$, see Fig. 2 (a) and (b). The oscillations are symmetric in respect to the bias sign and are seen in a wide bias range.

The $dV/dI(V)$ curves also demonstrate the zero-bias transport anomaly, which appears as a $dV/dI$ peak or dip, see Fig. 2 (a) and (b). We wish to mention here, that both the oscillations and the zero-bias anomaly appear together for our samples: they can not be seen for resistive NS junctions, see the inset to Fig. 2 (b) or at high temperature $T>T_{c}$, so they require consistent explanation.

The positions of the oscillations are depicted in Fig. 3 (a). Experimental points cover wide bias range for biases much above $\Delta_{In}$. The data demonstrate clear linear dependencies, so the oscillations are periodic in respect to the bias. As it can be seen from Fig. 3 (a), the period $\Delta V$ is not universal, it is different for different samples. On the other hand, for a particular sample $\Delta V$ is well reproduced in different cooling cycles.

Fig. 3 (b) demonstrates temperature dependence of $dV/dI(V)$ characteristics. The wide $|eV|<\pm$0.5 mV drop in $dV/dI$ disappears exactly above the indium $T_{c}=3.4$ K, as it is expected for Andreev reflection tinkham . The amplitude of the oscillations is suppressed by temperature together with the superconducting gap. On the other hand, $dV/dI$ change is small near $T_{c}^{In}$ in Fig. 3 (b). Thus, despite we observe the transport oscillations for $|eV|>\Delta_{In}$, they are also induced by superconductivity in the $Bi_{2}Te_{3}-In$ junction. The zero-bias $dV/dI$ peak disappears earlier, between 2.7 K and 3.0 K.

IV Discussion

The oscillating behavior requires scattering events at two different interfaces. For example, multiple Andreev reflections tinkham ; MAR are observed in the SNS structures with two superconducting leads. Periodic resonances in a single NS junction appear if there is a space restriction in the superconducting (Tomasch effect tomasch1 ; tomasch2 ) or normal (MacMillan-Rowell one mcmillan1 ; mcmillan2 ) side of the junction. In the former case tomasch1 ; tomasch2 , resonances result from Bogoliubov quasiparticle interferences between an incident electron-like quasiparticle and its hole-like counterpart. The nearly periodic resonances appear for energies above the superconducting gap with $\approx\pi\hbar v_{F}/2L$ period, where $v_{F}$ is the Fermi velocity in the S and $L$ its thickness. In the latter case mcmillan1 ; mcmillan2 , the Andreev-reflected particle experience normal scattering back to the NS interface. Because of the particle type change in Andreev reflection, two reflections are required at the NS interface for the interference to occur in the N, see Fig. 4. Thus, the resonances appears with $\pi\hbar v_{F}/4L$ period, if superconducting correlations survive over $L$.

Tomasch oscillations within the indium film can not be responsible for our experimental results: monotonous $dVdI(V)$ curves are obtained for resistive NS junctions, see an example in the inset to Fig. 2 (b). Because of the same indium film thickness and quality, the resonances are not connected with the space restriction in the S side of the $Bi_{2}Te_{3}-In$ junction.

On the other hand, there are no oscillations above $T_{c}$ in Fig.3 (b), so the oscillations should be connected with induced superconductivity within $Bi_{2}Te_{3}$ films.

(i) A variant of Ref. adroguer for oscillations within the region of proximity-induced superconductivity within the topological surface state is qualitatively appropriate. The Fermi velocity can be directly obtained for the topological surface state from the ARPES data in Fig. 1 (c) as $v_{F}\approx 4.8\times 10^{7}$ cm/s. If we take the minimal value of experimental period in Fig. 3 (a) $\Delta V=0.23$ mV, the maximum $2L$ value can be estimated as $2L\sim\pi\hbar v_{F}/e\Delta V\approx 4\mu$m. The discrepancy with the lithographic value (1 mm) requires strongly inhomogeneous transport, which goes through some region of width $L$ in wide $Bi_{2}Te_{3}-In$ contact area. This is supported by $dV/dI$ values in Fig. 2: every $dV/dI(V)$ curve is still a wide $dV/dI$ drop within the indium superconducting gap, even in the inset to Fig. 2, which implies highly transparent NS interfaces in standard BTK model BTK . In this case, the resistance of 1 mm size junction should be well below 1 Ohm, which obviously contradicts to that we have in Fig. 2.

(ii) Another possibility is the MacMillan-Rowell oscillations for bulk carriers in $Bi_{2}Te_{3}$ films, which appears due to the finite film thicknesses. In this case, a bulk particle is scattered between the NS interface and the opposite surface of the film as schematically depicted in Fig. 4. The $4L$ distance can be estimated as $\approx 4\mu$m for the minimal $\Delta V=0.23$ mV, while it is approximately twice smaller ($1.6\mu$m) for the maximal $\Delta V=0.59$ mV. The obtained $L$ values for different samples are in good correspondence with the estimations made in exfoliation process. Also, they are much below the mean free path, which can be estimated as ($l_{e}\approx 60\mu$m for given concentrations and mobility teresch ; bathon .

As a result, interpretation of periodic $dV/dI$ oscillations for finite biases may support topological effects, but does not obligatory require them. The situation is different for the zero-bias anomaly in transparent NS junctions.

The zero-bias anomaly is known for Andreev transport in different regimes. It was previously connected with disorder effects diar or with more exotic scenarios like Majorana fermions Heiblum ; Mourik ; Deng and Andreev surface states ass . It also appears for ballistic transport $l_{e}>>L$, if there is some restricted area within N region heslinga ; klapwijk17 ; akhmerov17 . In our samples, the topological surface state is present at the $Bi_{2}Te_{3}$ surface, see Fig. 1 (c), being separated from the bulk by depletion region. The depletion is usually formed zav1 ; zav2 ; hofman near the surface due to carriers’ localization by adsorbates, heterointerface formation depletion , and defects, it can vary for different junctions. Thus, it is natural to connect the zero-bias anomaly with the superconductivity, induced in the topological surface state on the $Bi_{2}Te_{3}$ surface. Moreover, it explains why the oscillations and the zero-bias anomaly appear together in our samples, as it can be seen in Fig. 2.

As for numerical estimations, the gap $\Delta_{ind}$ induced within the surface state can be obtained from the width of the low-bias structure heslinga ; klapwijk17 as $0.1$ meV in Fig. 2 (a) and as $0.17$ meV in Fig. 2 (b). It should be defined by Thouless energy $\Delta_{ind}\sim E_{Th}$ (see Appendix to Ref. akhmerov17 for recent comprehensive discussion), which is defined as $E_{Th}\sim\hbar v_{F}/L$ in the regime of ballistic transport golubov15 . Obviously, it gives $L$ values of the same order that we have from the oscillation periods in Fig.3 (a). Which is more important, the width of the zero-bias anomaly scales for different junctions exactly as the period of the oscillations (0.17/0.1=0.39/0.23 in Fig. 2 (a) and (b)), which strongly supports our interpretation of the zero-bias anomaly. Also, as expected for $E_{Th}$, it is constant in Fig. 3 (b), until $k_{B}T$ exceeds $\Delta_{ind}$.

V Conclusion

As a conclusion, we experimentally investigate Andreev transport through a single junction between an s-wave indium superconductor and a thick film of a three-dimensional $Bi_{2}Te_{3}$ topological insulator. We study $Bi_{2}Te_{3}$ samples with different bulk and surface characteristics, where the presence of a topological surface state is confirmed by direct ARPES measurements. All the junctions demonstrate Andreev transport within the superconducting gap. For junctions with transparent $In-Bi_{2}Te_{3}$ interfaces we find a number of nearly periodic conductance oscillations, which are accompanied by zero-bias conductance anomaly. Both effects disappear above the superconducting transition or for resistive junctions. We propose a consistent interpretation of both effects as originating from proximity-induced superconducting correlations within the $Bi_{2}Te_{3}$ topological surface state.

Acknowledgements.

We wish to thank Ya. Fominov, D.E. Feldman, V.T. Dolgopolov, and T.M. Klapwijk for fruitful discussions. We gratefully acknowledge financial support by the RFBR (project No. 16-02-00405), RAS, and Saint Petersburg State University (Grant Number 15.61.202.2015). O.E.T. acknowledge financial support by the Russian Science Foundation (project n. 17-12-01047), in part of crystal growth, structural characterization, and ARPES measurements (Fig.1 (c)).