Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe

The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.

Figure 1

(a) Schematic of the experiment: An $s$-wave superconductor ${\mathrm{S}}_{\mathrm{m}}$ (orange) is inducing superconducting pairing in an underlying topological insulator ${\mathrm{S}}_{\mathrm{p}}$. This state is probed via a point contact. An electron impinging from the 3DTI reservoir N can either be Andreev reflected, normal reflected, or transmitted with probability amplitudes A, B, and C respectively. The current is carried away to the right of $Z_{\mathrm{p}}$ as a supercurrent. (b) Schematic of the device and measurement setup. A niobium strip is covering a HgTe bar which is coupled to an equilibrium reservoir via a small orifice marked with the letter a. The dashed lines mark the contours of the gate. (c) False-color SEM picture of a device without a gate electrode. (d) $dI/dV$ measurements of four devices. The devices differ by the “connectivity” of the HgTe bar, covered by niobium, as indicated in the inset.

Figure 2

(a) Conductance of device 1 normalized to the resistance $R_N$ at $T=9\mathrm{K}$ (purple). At $4.2\mathrm{K}$ an energy gap has clearly opened up due to the niobium being superconducting. Upon lowering the temperature a peak emerges around $V_{\mathrm{SN}}=0$, which splits below $500\mathrm{mK}$. (b) Conductance measured at $30\mathrm{mK}$ for increasing (small) magnetic field values. This response is independent of the direction of the applied magnetic field. For clarity a small vertical shift has been removed in the presentation of the data to highlight that the high-voltage part of the conductance is immune to these magnetic field strengths.

Figure 3

Semiconductor representation of the NcS system for different bias regimes. The normal part is the topological insulator, the constriction is, initially, characterized by a barrier $Z_{\mathrm{p}}$, and the superconductor is characterized by a pair potential ${\mathrm{\Delta }}_{\mathrm{p}}$. In (a) the system is at zero bias and zero temperature. The voltage difference will emerge at the narrow point contact, and Andreev reflections (normal reflections) are occurring there with probability A (B). The TI-Cooper pairs are phase-coherently coupled to the Nb condensate ${\mathrm{\Delta }}_{\mathrm{Nb}}$. They form one superconducting condensate. In (b) at finite temperature and bias, electrons from higher energies are allowed to enter the proximity-induced superconductor. These “hot” electrons are trapped in the proximitized area because Andreev reflection does not carry entropy. The only relaxation mechanism is by electron-phonon relaxation or by contact with a thermal equilibrium reservoir. So the proximity-induced superconducting state ${\mathrm{S}}_{\mathrm{p}}$ is quenched (${\mathrm{\Delta }}_{\mathrm{p}}\to 0$), and the situation as depicted in (c) occurs. Then, at higher voltages transport is measured between a normal reservoir, being the 3DTI HgTe, and the superconductor niobium with an interface resistance characterized by $Z_{\mathrm{m}}$.

Figure 4

In (a) the central split peak [gray zone in (b)] is compared to an analysis using Eq. (1) (cyan) with a fixed value of $Z_{\mathrm{p}}=0.4$ and a broadening parameter $\mathrm{\Gamma }\approx 0.025{\mathrm{\Delta }}_{\mathrm{p}}$. The magenta lines show a comparison with the model developed in Ref. [14] with a broadening parameter $\mathrm{\Gamma }<0.015{\mathrm{\Delta }}_{\mathrm{p}}$. The value of ${\mathrm{\Delta }}_{\mathrm{p}}$ in both models is $70$µeV. In (a) we have abandoned the normalization of the data on $R_N$ at high voltages and in the normal state. Instead, we have chosen to take the conductance value at the edge of the gray zone. The precise value is a bit arbitrary but should be close to this value. The curves are offset for better visibility. (b) Conductance of device 1 normalized with the normal-state resistance $R_N$ above the critical temperature $T>T_c$ at $30\mathrm{mK}$. The gray area indicates the voltage range where we assume an equilibrium proximity-induced superconducting state. The dashed lines show fits using Eq. (1) for three different $Z_{\mathrm{m}}$ parameters and a broadening of $0.7{\mathrm{\Delta }}_{\mathrm{Nb}}$.

Figure 5

(a) Gate dependence of normalized conductance of device 2 at $B=0\mathrm{T}$ from 1 to $-4\mathrm{V}$. The black bar indicates how the height of the central peak is evaluated in (b). (b) Normal-state resistance $R_N$ versus gate voltage (black) and size of the peak (red) defined as indicated in (a) by the black bar for $V_g=0$. (c) Normal-state conductance versus zero-bias conductance.