Josephson supercurrent through the topological surface states of strained bulk HgTe

Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (30,000 cm^2/Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K with critical supercurrents of several microamperes. Moreover, we observe a magnetic field induced Fraunhofer pattern of the critical supercurrent, indicating a dominant 2\pi-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.

and obstructs an unambiguous investigation of induced superconductivity in the topological surface states. Contrary to the Bi-based topological insulators, the bulk of strained HgTe is effectively insulating [4], enabling the exploration of the Josephson effect in its topological surface states [7]. For this reason, we have fabricated lateral HgTe-based Josephson junctions (with closely spaced superconducting Nb electrodes on the top surface [22]) to study the occurrence of Andreev bound states at the surface, and to investigate superconducting transport through these unconventional states (Fig. 1a).
First we identify the origin of electronic transport in the 70 nm thick strained HgTe layer that we used as weak link. For this purpose, we have fabricated from the same wafer as the superconducting devices described below, a six-terminal Hall bar device with a channel length of 600 μm and width of 200 μm (same geometry as the device in Ref. 4), and measured the magnetic field dependence of its Hall resistance at cryogenic temperatures (Fig. 1b). From the low-field data, the mobility and charge density of the conduction electrons are extracted: μ ≈ 26,000 cm 2 /Vs and n ≈ 5.5⋅10 11 cm -2 . Interestingly, figure 1b shows a series of quantization plateaus of the Hall resistance when the magnetic field is increased above B ≈ 2 T. This observation provides evidence that transport is effectively through two-dimensional states. The magnetic field dependence of the Hall conductivity (inset of Fig. 1b)  Hall plateaus corresponding to even as well as odd filling factors, with the odd ones as most robust at low magnetic fields, is characteristic of a single family of Dirac states at top as well as bottom surface with slightly different densities. This implies that the bulk is effectively free of mobile carriers, and electronic transport is predominantly through the two-dimensional surface states of strained HgTe [4][5][6][7].
Having identified that electronic transport occurs effectively through Dirac surface states, we can now investigate transport through a lateral Josephson junction, and study the nature of induced superconductivity in the topological surface states ( Fig. 2a; this junction has been fabricated from the same HgTe layer by using two Nb contacts at the top surface as superconducting electrodes [22]). We measured the differential resistance dV/dI of the junction as function of current bias, temperature and magnetic field in a measurement setup equipped with appropriate low-pass filters for supercurrent measurements [23]. In order to have the Nb electrodes in the superconducting state, the measurements were all done at temperatures well below the critical temperature of Nb (T c ≈ 9 K). Our measurements at the base temperature (T = 25 mK) of the dilution refrigerator clearly show two transport regimes (Fig. 2b): a dissipationless supercurrent appears in the junction when the bias is lower than a critical value I c (i.e., R = 0 if I < I c ), while a dissipating current occurs at higher current bias (with R n ≈ 50 Ω).
Let us inspect the resistive regime in more detail. When dV/dI is plotted versus the measured voltage across the junction (Fig. 2c), we observe that the differential resistance slightly decreases when the voltage is below  [11].
When we inspect the supercurrent regime of the junction, we clearly observe hysteresis in the measured I-V characteristics (Fig. 3a). The critical current corresponding to the transition from supercurrent to resistive regime is larger than the critical current corresponding to the transition from resistive to supercurrent regime -i.e., at T = 25 mK, the switching and retrapping current are I s ≈ 3.8 μA and I r ≈ 2.5 μA, respectively. The temperature dependence of the I-V characteristics shows that hysteresis is only present in the temperature range up to 1 K, whereas I s and I r exhibit approximately equal values at higher temperatures (Fig. 3b). Switching and retrapping current decrease with increasing temperature, until the supercurrent regime disappears at T > 4 K. Hysteresis usually occurs in underdamped Josephson junctions, i.e., in junctions that are effectively shunted by a large resistance and capacitance [10,11]. However, the capacitance of our lateral junction is very small is the thickness of the superconducting electrodes and  [11]. Since β c << 1, the junction is overdamped and no hysteresis is expected in the I-V characteristics [11]. Alternatively, self-heating effects are known to lead to hysteresis in Josephson junctions with large critical currents [10,30]. In our junction, the power density at the retrapping point is The I c R n product -i.e., the critical current multiplied by the normal state resistance-is a characteristic junction parameter that provides useful information about superconducting transport through the Josephson junction. The I c R n product is usually ~e / Δ for short junctions (i.e., junctions with a Thouless energy E Th larger than the , where D is the diffusion constant and L is the junction length), while it is much smaller for long junctions (i.e., junctions with Δ < Th E ) [31]. For our junction, we obtain I c R n ≈ 0.2 mV at the lowest temperature, which is about five times smaller than mV 1 / ≈ Δ e . Possibly, this indicates that the junction is in the long junction limit, where the superconducting coherence length ξ is smaller than the spacing d between both Nb electrodes (i.e., ξ < d ≈ 200 nm). Alternatively, the suppressed I c R n product may be an indication of insufficient interface transparency [32].
The measurements discussed so far do not identify a contribution from zeroenergy Majorana bound states to the supercurrent. Contrary to Andreev bound states in conventional materials, which give rise to a 2π-periodic Josephson effect ( the presence of zero-energy Majorana states in topological insulators yields a 4π periodic ) [8,9]. It is therefore beneficial to study the currentphase relation to identify a contribution from Majorana states to the supercurrent. The critical supercurrent is maximum at zero field, and decreases with increasing magnetic field in an oscillatory way, yielding a Fraunhofer diffraction pattern if the supercurrent flows uniformly through the junction [11]. The periodicity is is the flux quantum, and A is the junction area).
However, it is predicted that the periodicity is twice as large for a 4π-periodic supercurrent [9], i.e.
. Thus, exploring the magnetic field dependence of the critical current of our junction is expected to be an effective method to identify the nature of the supercurrent carrying states.
When we measure I-V characteristics as a function of an applied perpendicular magnetic field, we clearly observe a Fraunhofer-like diffraction pattern of the critical current, with a periodicity of mT 1.1 ≈ ΔB (figure 4a). The pattern deviates from a perfect Fraunhofer pattern, and indicates that the supercurrent is not fully uniform (note that measurements on different junctions have shown that this deviation is indeed samplespecific) [11]. To determine the magnetic flux through the junction, we need to consider the effective junction area, which is larger than the area between the electrodes, because the penetration length of the niobium films in a perpendicular magnetic field is approximately nm 350 ≈ λ [7]. Thus, the periodicity of the Fraunhofer pattern corresponds very well to , implying a dominating 2π-periodic supercurrent through the topological surface states [33]. Note that we do not expect Josephson screening currents to affect our measurements, because the junction is in the narrow junction regime (i.e., the junction width is smaller than the Josephson penetration depth: In contrast to some recent claims in the literature [19], this should not come as a surprise. Actually, theory expects that quasiparticle scattering in the junction removes unprotected, zero-energy modes, leaving an energy gap in the Andreev bound states -similar to conventional junctions [12,35]. Effectively, the 4π-periodicity of the unprotected Andreev bound states turns into a 2π-periodicity when the spectrum is gapped. Only the zero-energy Andreev bound states with the momentum perpendicular to the interface are topologically protected and remain ungapped, but since this number of modes is predicted to be orders of magnitude smaller than the number of unprotected modes  . The presence of zero-energy modes is predicted to give rise to a 4π-periodic supercurrent through the topological surface states [8]. However, normal scattering in the weak link can remove unprotected zero modes, leading to a 2π-periodic Josephson effect [9,17,35]. (b) Differential resistance versus current bias at T = 25 mK (ascending bias sweep). In the high-current regime, the differential resistance converges to the value of the normal resistance R n ≈ 50 Ω. When the current is decreased below a critical value, the differential resistance drops to zero, corresponding to a supercurrent regime.