Josephson Radiation from Gapless Andreev Bound States in HgTe-Based Topological Junctions

Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency $f_J$ rather than conventional emission at $f_J$. Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency $f_J/2$. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the $f_J/2$ line, much shorter than for the $f_J$ line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.

Popular Summary

Long sought in high-energy physics, Majorana particles (particles that are their own antiparticles) can emerge in condensed matter systems and are promising candidates for future fault-tolerant quantum computation. They have therefore generated immense experimental and theoretical investigations. To engineer Majorana particles, one may use a topological insulator (a material that behaves as an insulator in its interior but as a conductor on its surface) in combination with superconducting and ferromagnetic materials. Though this recipe is well known, major experimental challenges have hampered the unambiguous demonstration of the existence of Majorana particles and of their properties. We address one of these hurdles by studying superconductivity and electrical currents in the topological insulator mercury telluride (HgTe).

One of the challenges is how to induce superconductivity at the interface between the superconductor and the topological insulator. Insight into this superconductivity can be gained by studying a device known as a Josephson junction, where two superconductors are coupled by a thin insulating barrier. This creates a supercurrent, an electrical current that can flow indefinitely. Special features of this current can reveal properties of the underlying superconductivity. Importantly, the supercurrent in a topological junction is predicted to oscillate at half of the frequency of a nontopological junction. We observe this fractional Josephson effect in a junction formed by connecting superconducting electrodes of aluminum to an HgTe quantum well.

This result establishes HgTe as a propitious platform to create and manipulate Majorana excitations, a prerequisite for a scalable fault-tolerant topological quantum computation.

Figure 1

Voltage bias and measurement setups. (a) The spectrum of Andreev bound states in a topological Josephson junction hosts a $4\pi$-periodic gapless Andreev doublet (dark blue) around zero energy, and other gapped Andreev modes (bulk or edge modes, depicted in light blue). Coupling to the continuum (gray area), other Andreev states, and possible relaxation mechanisms are pictured as red arrows. The exact spectrum is not known, and depends on parameters such as length of the junction and Fermi energy. (b) On the colored SEM picture, the mesa is visible in blue, the Al leads in violet, and the gate is indicated in yellow. A shunt resistance $R_S$ enables a stable voltage bias across the junction. The measurement of the voltage across the junction and across $R_I$ directly yields $V$ and $I$. The rf signal is coupled to the amplification scheme via a bias $T$. (c) The rf signal is amplified by a cryogenic HEMT amplifier (with additional room-temperature amplification). A directional coupler can be used to send a rf excitation signal (backwards) for characterization purposes (see SM [16]).

Figure 2

Emission spectra. (a)–(c) $I\text{−}V$ curves (red lines) and emission spectrum (blue lines) for a nontopological weak link (a) and a quantum spin Hall weak link [(b) at $V_g=-0.55\mathrm{V}$ and (c) at $V_g=-1.4\mathrm{V}$]. The radiation is collected at fixed detection frequency $f_d\simeq 3\mathrm{GHz}$ when sweeping the bias. Gray dashed lines indicate the expected values of $2f_J$ (innermost) and $f_J$ and $f_J/2$ (outermost lines). (d)–(f) Two-dimensional plot of the power collected from the devices, as a function of voltage $V$ and detection frequency $f_d$ [(d) in the nontopological weak link and (e) and (f) in the topological weak link for, respectively, $V_g=-0.55\mathrm{V}$ and $V_g=-1.4\mathrm{V}$). White lines indicate the expected resonance lines at $2f_J$ (innermost) and $f_J$ and $f_J/2$ (outermost). For better visibility, the data are normalized to their maximum for each frequency. In (e), additional features for frequencies $f_d\ge 5\mathrm{GHz}$ are visible, which can be traced back to resonant features in the electromagnetic environment of the junction. Their influence is examined in Sec. III of SM [16].

Figure 3

Resistively shunted junction simulations. (a) Simulated $I\text{−}V$ curve (blue) compared with measured data at $V_g=-0.55\mathrm{V}$. The simulations are performed for $R_I=R_S=24\mathrm{\Omega }$, $R_n=130\mathrm{\Omega }$, $I_{4\pi }=100\mathrm{nA}$, and $I_c=240\mathrm{nA}$. (b) Simulated Fourier transform of the voltage $V$ in the junction, as a function of detection frequency $f_d$ and voltage $V$, for the same simulation parameters as in (a). A good qualitative agreement is found with Fig. 2. In particular, the predominance of the emission at $f_J/2$ for low voltages (below $12\mu \mathrm{V}$) is well reproduced.

Figure 4

Gate dependence. (a),(b) 2D maps of the normalized amplitude $A$ as a function of bias voltage $V$ and gate voltage $V_g$ for detection frequency $f_d=2.98$ and 5.5 GHz, respectively. In (b), a resonant feature in the electromagnetic environment is visible as a split peak between $V_g=-0.5$ and $-0.8\mathrm{V}$, whose position is altered by the change in $V_g$ (see Sec. III of SM [16]). (c) The ratio of the intensity of the $4\pi$- to the $2\pi$-periodic amplitudes $⟨r⟩=⟨A_{4\pi }/A_{2\pi }⟩$ (averaged over frequency in the 2–10 GHZ range) (as a red line) and the critical current (as a blue line) are plotted as a function of gate voltage $V_g$. After rescaling of the critical current measured in Ref. [18], the emission features can be compared with previous observations on the Shapiro response.