On‐Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb–In0.75Ga0.25As‐Quantum‐Well–Nb Josephson Junctions

A superconducting hard gap in hybrid superconductor–semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non‐Abelian excitation). This requires the formation of homogeneous and barrier‐free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb–In0.75Ga0.25As‐quantum‐well–Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high‐quality and transparent contacts to the In0.75Ga0.25As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity‐induced superconductivity in the In0.75Ga0.25As‐quantum‐well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g‐factor and Rashba spin–orbit coupling in In0.75Ga0.25As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb–In0.75Ga0.25As–Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.

quantum wells make InGaAs a very attractive material in the field of topological quantum computing, electronics, spintronics, and photonics. [7] In addition to all these advantages, the ability to tune the indium composition allows the formation of highly transmissive metal-semiconductor interfaces which we discuss in this paper. We study the fabrication and low-temperature measurements of eight symmetric S-Sm-S planar and ballistic Josephson junctions on a chip containing an In 0.75 Ga 0.25 As quantum well in a heterostructure in which each junction consists of two identical niobium (Nb) superconducting electrodes in contact with a 2DEG that is formed ≈120 nm below the wafer's surface. Each junction is measured individually using a lock-in measurement technique. The measurements are carried out in a dilution fridge with a base temperature of 40 mK in a magnetic field of up to 9 T and the quantum transport of the junctions are measured below 800 mK. We observe large critical currents and a U-shape hard gap at low source-drain voltage bias V SD due to Andreev bound states at the S-Sm interfaces in four out of seven working junctions while the other three show evidence of a soft gap. The subharmonic energy gap structures (SGS) [8] are observed when the applied V SD satisfies the expression V = 2Δ/ne, where the Δ is the Nb superconducting gap energy (2Δ Nb ≈ 2.2 meV), n = 1, 2, 3, … is an integer, and e is the electron charge. The SGS are clearly observed that are strongly temperature and magnetic field dependent.
Results from the Experiments: Figure 1b shows a false color scanning electron microscopy (SEM) image of the on-chip Andreev device, consisting of eight symmetric and planar Nb-In 0.75 Ga 0.25 As-Nb Josephson junctions. In Figure 1c, the zoomed-in image of the junction 3 (J3) is shown and this junction will be discussed here in detail. All junctions are in the ballistic regime as the distance (shortest path where superconducting electrode's wave functions in each side could overlap) between the two Nb electrodes is 850 nm which is shorter than the corresponding elastic mean free path 2 e 1 e s e n µ π = − ≈ 2 µm. The differential resistance dV/dI versus V SD at 50 mK for four junctions with a hard superconducting gap are shown in Figure 2a. An excess current I exc flows through the junctions as a result of electron-and hole-like quasiparticles correlations (Andreev reflections) below the junction's T c ′ and for voltage biases within the superconducting gap. The dV/dI (V SD ) value is reduced in the gap region and a U-shape dip which is a signature of a hard gap [5] is observed for junction numbers 2, 3, 5, and 7, where supercurrents with critical currents of up to 2 µA are measured. However, the results for junction numbers 1, 4, and 6 are different and they show a soft gap signature [9,10] in which the junction resistance drops but dV/dI (V SD ) is not flat. The origin of the soft gap is not fully understood, however, this has so far been explained by the effect of inhomogeneities at the S-Sm interfaces together with quasiparticle broadening. [9] In our junctions, this difference may be due to a residue altering the wet etching process resulting in a tunneling barrier at the interface or variation in the etch depth so that the Nb trench in which the Nb sits is not deep enough in some areas. In this case, the resulting tunneling barrier leads to a reduction of the excess current with both normal and Andreev reflections competing together. These devices will be discussed in detail elsewhere. We could not measure quantum transport, neither a hard-nor soft-gap structure for junction number 8 because of a wire contact failure between the device and pad.
Temperature Dependence of Induced Superconductivity in In 0.75 Ga 0.25 As: The dV/dI (V SD ) curves for temperatures between 50 and 800 mK for junction number 3 are plotted in Figure 2b where the curves are shifted vertically upward by 0.5 kΩ for clarity.
The current-voltage characteristics (IVC) of the junction is plotted in Figure 3a at various temperatures by integration of dV/dI (V SD ). A pronounced supercurrent and quantum transport between two Nb superconducting junctions are observed at zero magnetic field and at low temperatures between 50 and 500 mK. The largest critical current (I c ) was measured at the lowest temperature of 50 mK. As shown in Figure 3b for junctions 3 and 5, I c is suppressed as the temperature increases and totally disappeared above 600 and 300 mK for these two junctions, respectively. This is due to the relatively large distance between the two Nb electrodes (850 nm) and the normal state resistance of the junctions (R N ≈ 0.1-0.8 kΩ). However, we observed a flat dV/dI (V SD ) within Δ/e which suggests  interface fabrication with high transparency based on Blonder-Tinkham-Klapwijk (BTK) theory. [11] As shown in Figure 3c, the SGS structures correspond to Δ/2e (cyan dashed line), Δ/3e (light-green dashed line), and gap edge (light-pink dashed line) are observed for junction 3. The shape of the gap and SGS has been shown to be influenced by the ratio of L/ξ N , [6,[11][12][13] where ξ N is the Bardeen-Cooper-Schrieffer coherence length. The SGS consists of a set of pronounced maxima in dV/dI at V = 2Δ/ne if L/ξ N << 1, but the amplitude of the SGS decreases by increasing the ratio of L/ξ N . For L ≈ ξ N the peaks evolve into dips. To find the ratio between L and ξ N in our junction we shall point out that in our chip the heterostructure has a quantum well with 30 nm thickness formed ≈120 nm below the wafer's surface and sandwiched between InAlAs layers. Using Δ Nb = 1.1 meV and the equation ξ N = ℏν FN /πΔ Nb , the coherence length of the 2DEG is calculated as ξ N = 177 nm. However, because of the proximity effect a minigap is induced into the 2DEG and the Δ Nb will be replaced with a smaller value Δ ind = 1.76 k B T′ c ≈ 100 µeV which results in ξ N ≈ 2 µm. [6] Therefore we consider the junction with a hard gap to be a short ballistic junction (L/ξ N << 1). Thus the flat dV/dI (V SD ) observed within Δ Nb for four junctions are consistent with BTK theory [11] that predicts such an effect only for junctions with Z < 0.2 where Z is the dimensionless interface barrier strength.
From BTK theory: This results in a reduction of differential resistance within the energy gap. However, if the interface transparency is not good, T −1 = (1 + Z 2 ) < 1, part of the incident electrons are normal reflected and there will be competition between the Andreev and normal reflections which results in the increase of the resistance and formation of a zero-bias peak within the gap. This implies that there is a tunneling barrier formed at the S-Sm interfaces. In our experimental results, we did not observe a zero-bias peak in dV/dI (V) curve therefore we can estimate Z < 0.2 or T > 0.96 for our devices. [6,11] Both the hard gap and SGS are suppressed significantly at temperatures above 400 mK leading to a shift toward zero bias as shown in Figure 3d. Magnetic Field Dependence of Induced Superconductivity in In 0.75 Ga 0.25 As: As discussed above we have ballistic junctions with high-transparency superconducting electrodes in contact with a 2DEG where the coherent Andreev reflections and correlation of electrons and holes lead to bound states and therefore phase coherent supercurrents between the electrodes. The color coded plot of dV/dI as a function of applied perpendicular B and applied voltage V is shown in Figure 4a   shows Fraunhofer-like oscillation of I c as seen in Figure 4a for an area of small field between 0 < B ⊥ (mT) < 1, when no vortices penetrate the superconductor films. This happens as the applied perpendicular field swings the phase of the induced superconductivity in the 2DEG that was confined between Nb superconducting electrodes. The oscillation period of I c (B) changes continuously and nonmonotonically from Φ 0 to 2Φ 0 depending on the size and topology of the devices where Φ 0 = h/2e is the flux quantum. [14][15][16][17] In our device the oscillation of I c (B) slightly differs from the Fraunhofer pattern that shows a maximum in the supercurrent at zero applied-field and its oscillatory amplitude decays to zero by increasing the field. This is because we have a junction with a length of 850 nm at the shortest path (where the supercurrent is likely to observe) that increases to 26 µm at the end of the active region (where it is unlikely to observe the phase coherent quantum transport). Therefore, in each junction we have a small area of A = L × w = 3.4 µm 2 with induced superconductivity that is bounded to large areas of ≈100 µm 2 in each side of the junction where they are in the normal state. A similar result was also reported in 2DEG (hybrid NbN-GaAs-NbN) [6] as well as nanowire (hybrid Ti/Pb-InAs-Ti/Pb) [18] Josephson junction systems.
To find the amount of flux penetrating the junction area A we should also note the flux crowding. [15,18] This comes from the expelled flux that is pushed into this area due to the screening currents in each Nb electrodes because of the Meissner state in low fields. Figure 4a shows an oscillation of ΔB ≈ 0.8 mT which approximately corresponds to an area of ≈ΔΦ/ΔB ≈ 2.5 µm 2 . This is however smaller than the area of the 2DEG between Nb electrodes at closest approach which is ≈3.4 µm 2 . This does not fit with the expected enhancement of field due to field focusing. [18] The applied magnetic field here is far from the critical filed of Nb so the system is expected to be in full Meissner regime. The following reasons may explain this deviation: i) dephasing from the normal 2DEG regions either side of the junction which reduces the junction's area considerably, and ii) a small amount of static magnetic disorder, and in the 2DEG there is a region formed that acts as quantum dots with an odd number of electrons. [9] Figure 4b shows the zero-bias differential resistance as a function of the applied parallel and perpendicular magnetic fields. It has been found that in order to get an S-Sm device into a topological regime the condition gµ Β Β > Δ ind should be satisfied [19] when the main superconductor sustains its gap. Here, g is the Lande g factor and µ Β is the Bohr magneton. We can extract the critical field B c * ≈ 500 mT from Figure 4b where the induced gap in the In 0.75 Ga 0.25 As 2DEG is totally suppressed for both field directions. This critical field is significantly smaller than the critical field of the Nb superconductor ≈3 T. If we assume that B c * is due to the Zeeman energy surpassing the induced superconductivity gap, i.e., gµ Β Β = Δ ind , our system with Δ ind ≈ 100 µeV will have a g-factor ≈3.4. This is consistent with the earlier report [20] and the recent experimental measurements of the g-factor in In 0.75 Ga 0.25 As based devices. [21] Our results together with the large g-factor and Rashba spin-orbit coupling in In 0.75 Ga 0.25 As quantum wells, which indeed can be varied by the indium composition, suggest that the Nb-2DEG-Nb system could be an excellent candidate to realize hybrid topological superconducting devices and to possible detection of Majorana modes. Detection of Majorana modes however in a 2D systems is not straightforward as it needs the careful imaging of magnetic vortices' cores or other topological defects  in the device which could be located anywhere. [22] Design and fabrication of gated Nb-In 0.75 Ga 0.25 As-Nb junctions and formation of 1D systems may help to facilitate the detection of these modes in our devices. In S-Sm devices containing gated 1D channels, the g-factor in In 0.75 Ga 0.25 As can be increased from ≈3.6 for wide wires (nearly 2D) to >6 for narrow wires [20] so would allow lower B-field observation of Majorana modes. Further development of such devices, i.e., scaling the number of junctions up to 256, [23] provides the possibility for realizing real quantum devices applicable for quantum technology.
We have experimentally demonstrated the successful fabrication of several symmetric, planar, and ballistic Josephson junctions on a chip and performed cryogenic measurements of these devices as a function of temperature and magnetic field. We have shown that proximity induced superconductivity in the In 0.75 Ga 0.25 As quantum well 2DEG results in detection of a hard gap and SGS on dV/dI (V SD ) characteristics of four out of seven junctions on a chip with critical current values of up to 0.2 µA. We could experimentally prove the formation of highly transparent interfaces between Nb and a 2DEG in an InGaAs wafer with an Andreev transmission probability of >0.96. Our result opens a new road toward hybrid topological quantum systems and helps pave the way for the development of on-chip Andreev devices for realizing the next generation of quantum processors.

Experimental Section
The In 0.75 Ga 0.25 As/In 0.75 Al 0.25 As/GaAs quantum wells [7] used in this study were grown by MBE. The wafer as shown in Figure 1a from the bottom to the surface comprises a 500 µm GaAs substrate, 50, 75, and 250 nm buffer layers of GaAs, AlAs, and GaAs, a 1300 nm InAlAs step-graded buffer layer, a 250 nm InAlAs buffer layer, a 30 nm 2DEG consisting of an In 0.75 Ga 0.25 As quantum well with electron density n s = 2.24 × 10 11 (cm −2 ) and mobility µ e = 2.5 × 10 5 (cm 2 V −1 s −1 ) in the dark and n s = 2.28 × 10 11 (cm −2 ) and µ e = 2.58 × 10 5 (cm 2 V −1 s −1 ) after illumination. The 2DEG quantum well is covered by a 60 nm In 0.75 Al 0.25 As spacer, 15 nm of n-type modulation doped In 0.75 Al 0.25 As, and a 45 nm In 0.75 Al 0.25 As layer followed by a 2 nm InGaAs cap layer. [7] Using photolithography and wet etching, in which a sulfuric acid solution of compositions H 2 SO 4 , H 2 O 2 , and H 2 O was used, we created an active region (a raised area referred to as mesa structure) with length l′ = 1440 and w′ = 160 µm in the middle of our chip where all the eight identical junctions are patterned and fabricated (see Figure 1b).
To make junctions, after photolithography patterning we removed the top InGaAs and InAlAs layers in the patterned area using wet etching. The etch produces a 120-140 nm deep trench in this area which is the depth of the In 0.75 Ga 0.25 As quantum well. This was followed by deposition of a ≈130 nm Nb film (about three times larger than the London penetration depth of Nb, 40 nm) to make high-quality superconducting contacts to the 2DEG, using DC magnetron sputtering in an Ar plasma. The sample was kept at 50 °C during this process. According to the design, each junction has a length of L = 850 nm at the shortest path which increases to 26 µm at the edge of the active region and a width of w = 4 µm as shown in Figure 1c. The ohmic contacts were made of gold/germanium/nickel (AuGeNi) to get a low resistance and good chemical bond (adhesion) to the semiconductor substrate and placed 100 µm away from the S-Sm interface to reduce any influence of the normal electrons on the S-Sm interface. Not all of the ohmic pads were used for source-drain bias measurements in this study. Gold wire of diameter 20 µm was used for the bond wires. The quantum transport measurements were performed by using a standard lock-in technique by superimposing a small ac-signal at a frequency of 70 Hz and an amplitude of 5 µV to the junction dc bias voltage and measuring the ac-current.