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Non-Majorana states yield nearly quantized conductance in proximatized nanowires


Semiconductor nanowires with proximity-induced superconductivity are leading contenders for manifesting Majorana fermions in condensed matter1,2,3,4,5. However, unambiguous detection of these quasiparticles is controversial6, and one proposed method is to show that the peak in the conductance at zero applied bias is quantized to the value of 2e2/h (refs. 7,8,9,10). This has been reported previously11, but only by probing one end of the device. Yet, if peaks come from Majorana modes, they should be observed at both ends simultaneously. Here we fabricate devices that feature tunnel probes on both ends of a nanowire and observe peaks that are close to the quantized value. These peaks evolve with the tunnel barrier strength and magnetic field in a way that is consistent with Majorana zero modes. However, we only find nearly quantized zero-bias peaks localized to one end of the nanowire, while conductance dips are observed for the same parameters at the other end. We also identify delocalized states near zero magnetic field and at higher electron density, which is not in the basic Majorana regime. These results enable us to lay out procedures for assessing the non-locality of subgap wavefunctions and provide a classification of nanowire bound states based on their localization.

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Fig. 1: Three-terminal nanowire device and basic characterizations.
Fig. 2: Nearly quantized ZBCP on the left side.
Fig. 3: Absence of zero-bias peak on the right side.
Fig. 4: Localized and delocalized states.
Fig. 5: Accidentally correlated ZBCPs from both sides.

Data availability

An extended curated data ontology including all data within this paper and data on other three-terminal devices is provided on Zenodo ( An interactive Jupyter notebook containing data in this paper is on GitHub (


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We thank S. Gazibegovic for assistance with growing nanowires. This work was supported by NSF PIRE-1743717, NSF DMR-1906325, ONR and ARO.

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Authors and Affiliations



G.B. and E.P.A.M.B. provided the nanowires. P.Y. and J.C. fabricated the devices. P.Y. and M.G. performed the measurements. P.Y., K.Z., V.M. and S.M.F. analysed the results and wrote the manuscript, with contributions from all of the authors.

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Correspondence to S. M. Frolov.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Three terminal measurement setups, extended data of the tunnel barrier gate dependence of the ZBCP and the effect of the contact resistance.

a, Schematics of the device and measurement setups. Red arrows indicate the direction of dc current flow for positive bias. The source-drain voltage is applied through the superconducting contact, current and differential conductance are measured simultaneously at two normal contacts. The two wider tunnel gates are connected together as T3. b, Simplified measurement circuit diagram representing all elements of the circuit as resistors. Rfilters is the resistance of RC filters and Rim is the input impedance of the current amplifier. Dashed box indicates on chip elements. The nanowire segment in contact with NbTiN is a multi-terminal conductor which can be fully characterized by a resistance tensor, R\({\,}_{{\rm{Nanowire}}}\), which is the resistance of the nanowire segment between the normal contacts. Semiconductor-normal metal contact resistances are indicated by R\({\,}_{{\rm{L}}^{\prime} }\) and R\({\,}_{{\rm{R}}^{\prime} }\). The exact values of contact resistances are unknown, but they can be estimated from saturation current at positive gate voltages. c and d, Differential conductance GL and GR as functions of TL voltage and source-drain voltage from the same dataset as Fig. 2(d). The gate settings are S-gate = -0.17 V and TR = -0.105 V. e, Zero bias linecuts from panel c with different R\(^{\prime}\) subtracted. When 0, 1 kΩ, 2 kΩ, 3 kΩ, 4 kΩ, 5 kΩ are subtracted (from bottom to top), the conductance plateau increases from 0.8*2e2/h to 1.1*2e2/h. f, Bias linecuts at TL= -0.05 V (yellow dashed line) from panel c and panel d show the shape of the ZBCP on the left side and absence of clear ZBCP on the right side.

Extended Data Fig. 2 Additional zero field tunnel barrier data and induced gaps.

a and b, Barrier gate scans from the left and right sides respectively, while S-gate is set to 1 V. The two sides show similar barrier gate dependence and overall transparency. Note the left side reaches 3*2e2/h at saturated regime, indicating a possible contact resistance of 3-4 kΩ. c, Pinch off traces at Vbias = 10 meV from panel a and panel b. d and e, Differential conductance GL and GR as functions of S-gate voltage and source-drain voltage, while TL = -0.015 V and TR = -0.075 V. While the barrier gates are set near the pinch off regime, the two sides have very similar induced gaps. f, Bias linecuts at S-gate = -0.75 V (yellow dashed lines) from panel d and panel e. The left side has a gap with Δ = 800 μeV and the gap on the right side is about 760 μeV. The error bar for the gap estimation is 40 μeV.

Extended Data Fig. 3 Magnetic field angle dependence of the ZBCP and subgap states on both sides.

a and b, Differential conductance GL and GR as functions of field angle and source-drain voltage when TR = -0.105 V, TL= -0.04 V and S-gate = -0.18 V. Note the contact resistance of 4 kΩ is subtracted for the left side. The field is parallel to the nanowire and perpendicular to the spin-orbit field when the field angle is zero. On the left side, the ZBCP only exists and reaches 2e2/h within a small angle around zero degree. On the right side, the subgap states are asymmetrical in field angle. Most importantly, no ZBCP is observed in the range -20 degree to 20 degree. c, Bias linecuts at 0, 4, -16 degree field angle from panel a. The ZBCP splits into two peaks when the field angle deviates from 0 degree. d, Zero bias linecuts from panel a and panel b show distinct behavior on the two sides: the zero bias conductance on the left side peaks at zero degree while the zero bias conductance on the right side remains almost unchanged.

Extended Data Fig. 4 Evolution of ZBCPs in magnetic fields.

a-j, Source-drain voltage vs. S-gate scans of the same regime of Extended Data Fig. 7(c)(d) at different fields. The gate settings are TL = -0.045 V and TR = -0.105 V. On the left side, subgap states and ZBCPs appear around B = 0.3 T. The height of the ZBCPs reaches 2e2/h at 1 T (panel g) and 1.3 T (panel i). The contact resistance of 4 kΩ is subtracted for the left side. On the right side, subgap states develop at higher fields. Most importantly, no ZBCP is observed on the right side within the field range investigated. k, Zero bias linecuts taken from Extended Data Fig. 7(e), and panels a, g, i show conductance increase with increasing magnetic field and reach 2e2/h at 1 T and 1.3 T.

Extended Data Fig. 5 Effect of TR on the left-side-only ZBCP in Fig. 3 and effect of T3.

a and b, Differential conductance GL and GR as functions of TR voltage and S-gate voltage at zero field and zero bias when TL is set to -0.04 V. This is the regime where we find the nearly quantized ZBCP on the left side in Fig. 2. The two sides show distinct states, which confirms the finding that there are only localized states in this regime. c and d, Differential conductance GL and GR as functions of source-drain voltage and TR voltage at 1 T. While the TR pinch off the right side, the ZBCP on the left side remains unchanged with conductance close to 2e2/h. Notably, there are also states near zero bias on the right side when TR is below -0.05 V. However, they never form a ZBCP. The two wider barrier gates are connected and controlled by a single voltage T3. For all other measurements in this paper, T3 is set to above 1.5 V to facilitate high transparency. Here we present the effect of T3. e and f, Differential conductance GL and GR as functions of S-gate voltage and T3 voltage at zero bias and zero magnetic field, while S-gate = 1 V, TL = -0.15 V and TR = 0.1 V. The resonances we observed in S-gate scans show no considerable gate dependence of T3, indicating the associated wavefunctions live far away from T3. T3 also tune different sets of resonances on the left and the right side, which can also be seen in the source-drain voltage vs.T3 scans (panel g and h).The gate settings are S-gate = 1 V, TL= -0.1 V and TR= 0.075 V. Those states show no considerable gate dependence on S-gate, indicating the existence of more dots above T3.

Extended Data Fig. 6 Magnetic field dependence of the subgap states for different S-gate voltages.

Magnetic field dependence of the subgap states for different S-gate voltages. Apart from the nearly quantized ZBCP at S-gate = -0.17 V (Fig. 2(a)), we also found similar ZBCPs at S-gate = -0.09 V, S-gate = -0.16 V and S-gate = -0.3 V (panels a, c and g). Only when S-gate = -0.235 V (panel e), the ZBCP is lower than 2e2/h. The tunnel gate settings are TL = -0.045 V and TR = -0.105 V. The contact resistance of 4 kΩ is subtracted for all the left side scans. On the right side, no correlated ZBCP is observed at any of these S-gate voltages.

Extended Data Fig. 7 Delocalized states vs. localized states in different S-gate regimes.

a and b, Zero bias differential conductance GL and GR as functions of TR voltage and S-gate voltage (0 V to 0.5 V) at zero magnetic field, while TL is set to -0.13 V. On the left side (panel a), delocalized states S1-S4 exhibit GR dependence, manifesting their non-local property. On the contrary, the localized state L1 shows no GR dependence as it does not change with varying GR voltage. On the right side (panel b), delocalized states S1-S4 appear at the same positions with the same gate dependence as on the left side, while their magnitudes are different on the two sides. The localized state L1 is missing on the right side, which is reasonable as this state is localized near the left side. Similarly, the localized state R1 only appears on the right side. c and d, Zero bias differential conductance GL and GR as functions of TL voltage and S-gate voltage (-0.5 V to 0 V) at B = 0 T, while TR is set to -0.15 V. This is the regime where we find ZBCPs close to quantization on the left side in Fig. 2. While there are three apparent resonances (labeled as L2, L3, L4) on the left side along the black dashed line, no similar features are observed on the right side. These scans confirm the low probability of having well separated Majorana bound states in that region, given the variety of localized and uncorrelated states within the nanowire. e and f, Source-drain voltage vs. S-gate scans along the black dashed line in panel c and panel d showing the resonances on the left side and the absence of similar features on the right side.

Extended Data Fig. 8 Extended data for regime in Fig. 5.

We have shown ZBCPs onset at similar fields on the left and right sides when S-gate is set to 0.6 V (Fig. 5). As mentioned in the main text, that correlation is not robust against variation in S-gate. In Extended Data Figs. 8 and 9 we present more data around S-gate = 0.6 V. a and b, differential conductance GL and GR as functions of TL voltage and S-gate voltage at zero field while bias is set to zero and TR = 0.09 V. The two sides show delocalized states S5 and S6, which can be seen from the two sides simultaneously and have the same gate dependence. Yellow (red) dots indicate the gate setting for Extended Data Fig. 9 (Fig. 5). c, S-gate linecuts from panel a and panel b at TL = -0.15 V. Yellow (red) dashed lines indicate the S-gate setting for Extended Data Fig. 9 (Fig. 5).

Extended Data Fig. 9 Extended data for ZBCPs in Fig. 5.

Here we present more magnetic field scans around the regime of Fig. 5 when TL = -0.15 V and TR = 0.09 V. The S-gate settings are indicated by the yellow and red dots in Extended Data Fig. 8. As shown in the left panels, the onset fields of the ZBCPs on the left side change to higher fields when S-gate is reduced. And the ZBCPs also exhibits splitting features at S-gate = 0.55 V and S-gate = 0.5 V. On the right side, however, the ZBCP onset and splitting do not generally match the left side manifestations.

Extended Data Fig. 10 Nearly-quantized ZBCP in another S-gate regime.

a and b, Differential conductance GL and GR as functions of bias voltage and magnetic field when S-gate = 1 V, TL = -0.25 V and TR = 0.05 V. This is a regime with a more positive S-gate setting than that explored in Figs. 1-3. On the left side, a ZBCP appears around B = 0.6 T and reaches 2e2/h around 0.85 T. The contact resistance of 4 kΩ is subtracted for the left side again. While there are some subgap states on the right side around similar fields, no prominent ZBCP is observed. c, Magnetic field linecuts at Vbias = 0 and Vbias = 1.5 meV from panel a. d, Bias linecuts at B= 0, 0.4 T and 0.85 T from panel a.

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Yu, P., Chen, J., Gomanko, M. et al. Non-Majorana states yield nearly quantized conductance in proximatized nanowires. Nat. Phys. 17, 482–488 (2021).

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