Zero Bias Conductance Peak in Dirac Semimetal-Superconductor Devices

Majorana zero modes (MZMs), a building block for topological quantum computer, can appear at the interface between a superconductor and a topological material. One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements. In this Letter, we report observation of such a large, nearly quantized ZBCP in junction structures of normal metal(Ti/Au)-Dirac semimetal (Cd3As2)-conventional superconductor (Al). Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs. We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zilberman more than 50 years ago [JETP 28, 1272 (1969)]. Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multi-terminal semiconductor or topological insulator/semimetal setup. We thus in this Letter provide criteria for identifying when the ZBCP is definitely not caused by an MZM.

Topological quantum computation (QC) [1,2] has emerged as a promising approach to QC due to its enhanced tolerance to errors which are induced by inevitable coupling to the environment.In this scheme, a quantum bit (qubit) would be constructed out of four Majorana quasiparticles (MQPs) [3], with a gate performed by moving one MQP around another, or braiding MQPs.Because the braiding is topological and non-local, Majorana-based qubits would be intrinsically robust against local decoherence sources and thereby enable fault-tolerant QC.
Until 2008, the search for MQPs in solid-state systems focused on the exotic 5/2 fractional quantum Hall state [4,5], for which the earlier theoretical framework of TQC was developed [2].
However, concrete evidence of such quantum Hall non-Abelian anyons has not been established.
The advent of topological insulators has prompted new proposals for realizing Majorana quasiparticles via the superconducting proximity effect [6,7].In these systems, the Majorana quasiparticles are predicted to appear as topological defects, namely Majorana zero modes (MZMs), at the superconductor-magnet interface or π-Josephson junction at the surface of a topological insulator.Soon after this pioneering theoretical work, it was realized that MZMs could also be realized in a semiconductor system in combination with a strong spin-orbit coupling, an external magnetic field, and the superconducting proximity effect [8][9][10].One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements.ZBCPs have been observed in InSb and InAs nanowire systems [11][12][13][14][15][16][17] and ferromagnetic atom chains [18].However, the origin of the observed ZBCPs in these experiments remains debated [19][20][21].As such, more experiments are imperative to establish MZMs in other topological quantum material systems beyond semiconducting nanowires.In the following, we will present results in a Dirac semimetal (DSM) [22,23] cadmium-arsenide (Cd3As2) that show a large, nearly quantized ZBCP in junction structures of normal metal (titanium/gold Ti/Au) -Cd3As2 -conventional superconductor (aluminum Al).Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs.We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zil'berman more than 50 years ago [24].Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multi-terminal semiconductor or topological insulator/semimetal setup.We thus in this Letter provide criteria for identifying when the ZBCP is definitely not caused by an MZM.
A scanning electron microscopy image of one device is shown in Fig. 1a.A total of five junctions are fabricated in this device and they share the same Ti/Au electrode.The distance between two nearby junctions is ~ 1.5 µm in the device shown in Fig. 1a, but is larger in other devices.In our experiment, only the right most junction is measured, and the four remaining Al contact leads are open.The distance between the T/Au and Al electrodes is about 80 nm.Fig. 1b shows the temperature (T) dependence of the resistance of this tunneling junction device.The superconducting transition temperature of Al electrode is at ~ 1.2K (not shown).The sharp drop at T ~ 0.7K is due to the onset of the proximity effect induced bulk superconductivity in Cd3As2.
Metal-superconductor junction device structures have been extensively utilized in the past for studying superconductivity [29].When such a device is biased above the superconducting gap, the device is in the normal state, the current(I)-voltage(V) relationship is ohmic, and a constant differential conductance (dI/dV) is measured.When the device bias is reduced and the incident electron from the normal metal is within the superconducting energy gap, the electron can form a Cooper pair with another electron in the metal, and this Cooper pair then tunnels into the superconductor.Due to this process, a hole with the opposite spin and velocity but equal absolute momentum is reflected to the metal.This process, known as Andreev reflection (AR), is schematically depicted in Figure 1c.If the interface quality is high, the conductance within superconducting energy gap becomes twice the normal conductance [29], and this is commonly dubbed perfect AR (PAR).Figure 1d shows a clear example of PAR observed in our device at T = 0.39K, where the normalized differential conductance dI/dV is plotted as a function of d.c.voltage bias (Vdc) across the junction, and normalization is defined relative to the normal state conductance, GN ≈ 0.0128 Ω -1 .At high |Vdc|, the device is in the normal state and the conductance is constant, as expected.As |Vdc| decreases, moving into the superconducting gap, the conductance assumes a value of 2GN.One can argue that the observed PAR is a signature of Klein tunneling in the Cd3As2 surface state [30].The observation of this PAR also demonstrates 1) the formation of a hard gap induced by the proximity effect and 2) the absence of backscattering in the normal region.
As the junction is further cooled down, a large ZBCP is observed.The normalized conductance at the base temperature of T = 21 mK and zero magnetic field is shown in Fig. 2a.
Overall, the curve is very similar to that in Fig. 1d, except at Vdc = 0V, where a large, sharp peak is observed.Notably, the value of this peak is 4 times that of the normal conductance value.To further examine the origin of this ZBCP, its temperature dependence is mapped out. Figure 2b shows the dI/dV curves as a function of Vdc at various temperatures.In Fig. 2c, the value of ZBCP is plotted versus T. At low temperatures, the amplitude is almost constant around 4 GN.It then starts decreasing at T > 0.1K and eventually disappears around T ~ 0.4K.Lorentzian fitting to each temperature curve is performed, from which the full width at half maximum (FWHM) of the ZBCP is obtained.In Figure 2d, we show the resulting temperature dependence of the FWHM.It is nearly constant at ~ 3µV in the low temperature regime, where the amplitude of ZBCP is also constant.the FWHM starts increasing above 0.1K, where the ZBCP amplitude also starts decreasing.The FWHM increases sharply for T > 0.3K.
Below, we try to explain the data by considering two alternative mechanisms for ZBCP formation: 1) the existence of MZMs at the interface between a superconductor and a quantum spin Hall insulator stack/Dirac semimetal [28,[31][32][33] and 2) a supercurrent mechanism that may give rise to the observed large ZBCP [24].Our detailed theoretical modeling will show that the latter origin is the one most likely to apply.
For the first mechanism, it is known that Fermi arc surface states of a Dirac semimetal can be viewed equivalently as a momentum-space stack of many identical two-dimensional quantum spin Hall insulator (QSHI) layers [33].In other words, according to the theoretical work [33], in the presence of momentum conservation our junction structure could be viewed as a collection of many identical copies of Ti/Au-2D QSHI-Al junction devices.At low temperatures, MZMs can form at the interface between the QSHI edge channels and the superconductor [31,32], and in the presence of backscattering they contribute to a large, quantized ZBCP.However, our detailed examinations cast doubts over this mechanism.First, the width of ZBCP is too narrow, being even smaller than the measurement temperature (indicated by the red dash line in Fig. 2d), while the width of MZM ZBCPs cannot be smaller than 3.5KBT [34] This thus excludes a non-interacting electron explanation for the data.Second, magnetic backscattering is required to obtain localized MZMs that give rise to ZBCP.In the absence of magnetic scattering the weak antilocalization (WAL) effect in Cd3As2 should produce a zero-bias conductance dip [34].This is inconsistent with the experimental observation.
Next, we consider the supercurrent mechanism analyzed according to Ivanchenko and Zil'berman (IZ) [24].First, where does the supercurrent in our setup arise?We assume good ohmic contact between the Al and Ti/Au electrodes in each of the NS (normal metal-superconductor) junctions below the superconducting gap.Then two nearby Al electrodes, if they are phase coherent, can support supercurrents and additional current path (as shown by the green arrows in Fig. 1a) besides the direct NS one (as shown by the red arrow in Fig. 1a) is available.Thermal fluctuations and circuitry move the maximum of the supercurrent from the zero bias.In this case the supercurrent peak in I-V characteristics shows up a ZBCP in dI/dV.The large distance between the superconducting electrodes suppresses the supercurrent making the observed amplitude of ZBCP comparable to GN.
In the following, we use the IZ formula [24] to quantitatively fit our measured differential conductance curves and extract parameters of our system.For this purpose, we first obtain I-V curves by integrating the differential conductance.Fig. 3a shows the result at T = 21mK.The fitting range is limited within the Andreev reflection regime.Next, the linear contribution due to AR within the superconducting gap is subtracted from the I-V curve as it is due to a parallel conductance channel.The obtained data, shown in Fig. 3b, represents the contribution from the supercurrent between two Al electrodes.The circuit diagram in Fig. 3c is an effective description for the experimental setup.Here, VB is the voltage source, V the voltage that is plotted on the xaxis in Fig. 3a-b, R1 the junction resistance, and R2 the lump resistance in the measurement circuit.
We neglect the capacitance C of the junction in the fitting.This is justified because of a large separation of Al electrodes.
The equations for the I-V curve fitting are then given as follows [24]: Here, In(x) is the modified Bessel function of complex order, ∆(0) = 50 µeV is the topological superconductivity gap, and I0 the total critical current of the supercurrent quanta.The BCS temperature dependence of ∆(T)/∆(0) is the first order expansion around T = 0.In Figs.3d-g, we show the fitting at four selected temperatures.It agrees well with the experimental data at low temperatures, e.g., at T = 21, 65, and 203 mK.Fitting fails at higher temperatures, for example at T = 350 mK, where the temperature becomes comparable to the induced superconducting gap and quasiparticle contributions to current likely disturb the fitting.In Fig. 3h, the maximal current extracted from the fitting at each temperature is plotted.
The good agreement between the theoretical fitting and experimental data strongly supports that the ZBCP is due to the supercurrent between two separated Al electrodes.Moreover, because of this supercurrent origin, the FWHM width of ZBCP can be smaller than the measurement temperature, as the width of the ZBCP is determined by the circuit parameters, not intrinsic temperature broadening.This explains the puzzle seen in Fig. 2d.
The parameters obtained from the above fitting are I0 = 34.8nA,R1 = 58.6Ω, and R2 = 88.4Ω. R1 is close to the normal-state resistance across the Ti/Au-Al junction, which is about 78 Ω.
Based on these fitting parameters, we can estimate the number of spin-resolved supercurrent quanta in our device.First, we calculate the critical current ∆I0 of a single supercurrent quantum.
Notably, the supercurrent mechanism also explains the peculiar magnetic (B) field dependence of the ZBCP we observed.In Figure 4, the measured dI/dV is plotted as a function of magnetic field and Vdc, respectively.The ZBCP in our device is extremely sensitive to the magnetic fields and disappears at a magnetic field merely larger than 1.3 mT. Figure 4b shows the extracted experimental values of ZBCP at different temperatures demonstrating a clear oscillating pattern.
For example, at the base T of 21 mK, the amplitude decreases from 4GN at B = 0T to ~ 2GN at 0.5 mT.It then increases to 3GN at 0.75 mT, before it drops to zero again at higher magnetic fields.
Since the critical magnet field of the superconducting Al electrodes is ~ 40 mT, much larger than 1.3 mT, the disappearance cannot be due to the loss of the superconductivity in Al.Furthermore, this small period cannot be caused by the magnetic flux across the Ti/Au-Al junction area.In fact, considering the area of the junction is S ~ 4 × 10 −7 m 2 , magnetic flux quantum is inserted into the junction at  =   = 52 mT, much larger than the observed 0.5 mT.Here  = 2.067 × 10 −15 Wb is magnetic flux quantum.Thus, interference across this junction can be excluded as the source of the ZBCP oscillations.On the other hand, under the supercurrent model, the effective junction area should be the one between the two adjacent junction devices, which is about 4 µm 2 .Consequently, the Fraunhofer period is ~ 0.5mT, consistent with the experimental observation.
Finally, one remark is in order before we conclude.The IZ model was conventionally used for short Josephson junctions.In our case, however, it still applies to a device where the two Al electrodes are separated by ~ 10 µm, as shown in Fig. 5a.In this device, the normal metal contacts are made of Ni/Au.The differential conductance between the Ni/Au and Al electrodes for the middle junction is shown in Fig. 5b.Overall, it is similar to that in the first device already discussed, with both exhibiting a perfect AR and a large ZBCP.Applying the IZ fitting yields again a good agreement, as shown in Fig. 5c for the 98 mK data and in Fig. 5d for the extracted I0.
However, unlike the first specimen where the separation between two adjacent junctions is comparable to the Al superconducting coherence length (ξAl ~ 1µm) and/or Cd3As2 phase coherence length (lφ ~ 0.6 µm) [36], the separation of Al electrodes in this device is now ~10 µm, much longer than ξAl and lφ.Thus, it is totally surprising that the supercurrent appears to still exist over such a large distance.In the following, we discuss three possibilities to resolve this apparent difficulty in our interpretation.First, lφ entering the WAL measurements [36] is different from lφ relevant for the Aharonov-Bohm-like interference necessary for the Fraunhofer patter [37].
Second, the supercurrent is proportional to the transmission (to the power of 2) through the channels connecting the superconductors.In our device with large Al electrodes, there can exist a tail of the channel transmission distribution responsible for the supercurrent.Third, it is possible that existence of supercurrent is determined by the electron pairing coherence length, which might be very long in the topological surface states in Cd3As2 due to the suppressed backscattering.
Finally, the Josephson effect over such a long distance seems to indicate relative decoupling of the surface and bulk states which can be used for potential applications of the material.
In summary, we report observation of a large ZBCP in tunnel junctions made of normal metal (Ti/Au) -Dirac semimetal (Cd3As2) -conventional superconductor (Al).Our detailed analyses suggest that this large ZBCP probably is due to the existence of a supercurrent between two farseparated superconducting Al electrodes.Our results thus call for extreme caution when assigning a large ZBCP to the MZM origin, especially when the width of the ZBCP is below 3.5KBT.2).This approach, however, relies on fine-tuning of parameters.First, disorder needs to be strong, since backscattering between surface modes of opposite momenta is forbiddenby TRS.
On the other hand, disorder has to be weak enough to allow coupling of the normal lead to the localized MZMs.Despite extensive numerical simulations we were unable to identify a parameter regime that supports localized MZMs in the presence of TRS, thus rejecting the naïve hypothesis.The results of an exemplary quantum transport simulation are presented in Fig. S2.
Here, a normal lead  with six propagating modes and a superconducting lead  connect to the The work at Sandia National Labs was supported by a Laboratory Directed Research and Development project.Device fabrication was performed at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science.Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.This paper describes objective technical results and analysis.Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.Work at UT Dallas was supported by ARO under Grant No. W911NF-18-1-0416 and NSF under Grant No. DMR-1921581.Work at UBC was supported by NSERC and CIFAR.

Figures and Figure Captions
Figures and Figure Captions

Figure 1 .
Figure 1.Andreev reflection and zero-bias conductance peak.(a), an SEM picture of the device.(b), Temperature dependence of the junction resistance.(c) A schematic diagram showing the Andreev reflection.(d) the normalized differential conductance dI/dV versus the d.c.bias across the junction (Vdc) measured in our device at T = 0.39K at zero magnetic field.The conductance around the zero bias is twice as much as that in normal state indicating a highly transparent interface between superconductor and Cd3As2.

Figure 2 .
Figure 2. Temperature dependence of ZBP.A) dI/dV at base temperature T = 21 mK.A zero-

Figure 3 :
Figure 3: (a) the I-V curve at T = 21 mK, obtained by integrating the corresponding dI/dV curve.

Figure 4 .
Figure 4. Magnetic field dependence of ZBCP.a, 2D color plot of dI/dV as a function of

Figure 5 : 2 ℎ
Figure 5: (a) SEM image of another device where the tunnel junctions are separated by ~ 10 µm.
scattering region  with dimensions   =   = 15 and   = 800.The scattering region hosts chemical potential disorder generated from the box distribution �−  2 ,  2 �.Instead of a

Figure S 2
Figure S 2 Zero bias conductance minimum from Weak Localization.The scattering region  has dimension   =   = 15 and   = 800.Disorder is simulated by a random chemical potential drawn from the box distribution �−  2 ,  2 �.