ABSTRACT Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana

modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally

investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state

in the island is lowered to zero energy yielding persistent 1_e_-periodic Coulomb blockade conductance peaks (_e_ is the elementary charge). In this condition, conductance through the

MAJORANA-HOSTED SUPERCONDUCTING ISLAND Article Open access 05 November 2022 ENHANCED MAJORANA STABILITY IN A THREE-SITE KITAEV CHAIN Article Open access 31 March 2025 CORRELATION BETWEEN TWO

DISTANT QUASIPARTICLES IN SEPARATE SUPERCONDUCTING ISLANDS MEDIATED BY A SINGLE SPIN Article Open access 24 April 2024 INTRODUCTION Initial experiments reporting signatures of Majorana zero

modes (MZMs) in hybrid superconductor–semiconductor nanowires focussed on zero-bias conductance peaks (ZBPs) using local tunneling spectroscopy1,2,3,4. Subsequently, Majorana islands

provided additional evidence of MZMs based on nearly 1_e_-spaced Coulomb blockade (CB) peaks5, and indicated a Rashba-like spin–orbit coupling with the spin–orbit field lying in-plane,

perpendicular to the wire axis6. Under some circumstances, these signatures can be mimicked by trivial modes7,8,9, motivating a new generation of experiments that explicitly probe non-local

properties, which are more difficult to mimic. For instance, non-locality of MZMs was recently investigated by measuring the energy splitting induced by the interaction of a quantum dot and

a zero-energy state in a hybrid nanowire10. Non-locality can also be accessed by interferometric measurements of a Majorana island, where CB couples separated MZMs and fixes fermion

parity11,12,13,14,15. In the topological regime, a Majorana island can coherently transfer a single-electron between its two ends through MZMs11,12. To demonstrate the effect, a Majorana

island can be embedded in the arm of an Aharonov–Bohm (AB) interferometer. If single-electron transport in both the reference arm and the Majorana island is coherent, conductance through the

interferometer is expected to show oscillations with a flux period _h_/_e_11,16. In addition, interferometry offers a way to distinguish between localized trivial modes and MZMs12,14. This

technique was used to investigate coherent transport in semiconductor quantum dots17,18,19,20. In this work, we study coherent single-electron transport through a Majorana island with an AB

interferometer. At high magnetic fields, we observe 1_e_ periodic CB peaks due to a discrete zero-energy state. In this case, we observe the conductance through the interferometer to

oscillate periodically for a flux _h_/_e_ piercing the AB ring, while oscillations are suppressed when the island shows a 2_e_ periodicity or is in the normal state. The observation of

conductance oscillations in the 1_e_ regime indicates coherent single-electron transport through the Majorana island, as predicted for electron teleportation mediated by MZMs11. RESULTS

MAJORANA ISLAND INTERFEROMETER Devices were fabricated using an InAs two-dimensional electron gas (2DEG) heterostructure covered by 8 nm of epitaxially grown Al21. The bare 2DEG (without Al)

showed a phase coherence length of _l__ϕ_ ~ 4 μm (see Supplementary Fig. 1). Figure 1a shows a micrograph of device 1 with a 1.2 μm long and 0.1 μm wide superconducting Al stripe formed by

wet etching. Ti/Au top-gates were evaporated on top of a 25 nm HfO2 dielectric grown by atomic layer deposition. We studied two lithographically similar interferometers with circumferences

_L_loop of 5.6 μm for device 1 and 5 μm for device 2. Applying a negative voltage, _V_pg, to the central gate serves two purposes. It depletes the 2DEG surrounding the Al wire to form both

the Majorana island and the AB ring center and also adjusts the chemical potential and charge occupancy of the island. Energizing all exterior gates confines the 2DEG into an AB

interferometer by connecting the Majorana island to a normal conducting reference arm. The resistance of the reference arm was independently tuned by a negative gate voltage _V_c. A

source-drain bias voltage (_V_sd) was applied to one lead and the resulting current and four-terminal voltage was recorded. The in-plane magnetic fields _B_∥ and _B_t, and perpendicular

field, _B_⊥, were controlled by a three-axis vector magnet. At low temperatures, tunneling of single electrons onto a Majorana island with a superconducting gap _Δ_ is suppressed by CB,

except at charge degeneracies. When the lowest sub-gap state energy, _E_0, exceeds the charging energy _E_c, ground-state degeneracies only occur between even-occupied states, resulting in

2_e_-periodic CB conductance peaks22. Odd-occupied ground states are lowered into the accessible spectrum by a Zeeman field, resulting in even–odd CB peak spacing when 0 < _E_0 < _E_c.

The difference in peak spacings between even and odd states, _S_ = _S_e − _S_o, is proportional to _E_05 (see Fig. 1b). For well-separated MZMs, _E_0 tends exponentially toward zero,

yielding 1_e_ periodic CB peaks with a discrete zero-bias state at consecutive charge degeneracy point5,23. Both observations are necessary for a MZM interpretation. When MZMs are not widely

separated, CB peak spacings oscillate with field and chemical potential5,6,7. CB SPECTROSCOPY We first investigated the Majorana island without interferometry by depleting a segment of the

reference arm (see Fig. 1a). Figure 1b shows zero-bias differential conductance _G_ = d_I_/d_V_ of the island as a function of parallel magnetic field _B_∥ and gate voltage _V_pg, which

controls the electron occupancy and chemical potential of the island. CB peaks are 2_e_ periodic at zero field and split around 2 T, becoming 1_e_ periodic as the sub-gap state moves toward

zero energy (see Fig. 3a for peak spacing analysis). Performing CB spectroscopy, that is, measuring _G_ as a function of both source-drain bias _V_sd and _V_pg reveals Coulomb diamonds (Fig.

 1c–f). At low _B_∥, diamonds are 2_e_ periodic with distinct negative differential conductance (Fig. 1c), which transition to an even–odd peak spacing difference at moderate fields (Fig. 

1d), similar to previous work on superconducting Coulomb islands5,6,22,24,25,26,27. At high fields, the 1_e_ periodic diamonds show a discrete ZBP for consecutive charge degeneracy points

that is well separated from the superconducting gap (Fig. 1e). This sub-gap feature remained at zero bias until the superconducting gap closure, and persists for 3 mV in _V_pg, corresponding

to an energy range of 0.8 meV. For systems with strong spin–orbit interaction, a helical gap of _g__μ_B_B_∥ is expected, where _μ_B and _g_ are the Bohr magneton and electron _g_-factor,

respectively. We estimate a helical gap of ~0.6 meV at _B_∥ = 2.5 T for a _g_-factor of 4, comparable to the span of the ZBP in _V_pg. The stability of the zero-bias state in both magnetic

field and in chemical potential is consistent with the MZM picture (see Supplementary Fig. 2)5, however, the observation of coherent single-electron transport is needed to draw conclusions

about non-locality. Below, we additionally show that the zero-bias state is sensitive to rotations of the in-plane field. The magnitude of _B_∥ where 1_e_ periodicity is observed is in

agreement with ZBPs measured in tunneling spectroscopy in InAs 2DEGs3. In contrast, as a function of _B_t the peak spacing showed an oscillating even–odd periodicity, and no consecutive ZBPs

were observed (see Supplementary Fig. 3d–f), as expected for extended modes in the wire6,9,28. The normal state 1_e_ regime of the Majorana island appears above _B_∥ ~ 3 T with _E_c = 80 

μeV (Fig. 1f), where no discrete ZBPs are observed (see Supplementary Figs. 2 and 3a–c). INTERFEROMETRY AND COHERENT SINGLE-ELECTRON TRANSPORT The reference arm of the AB interferometer was

connected to the Majorana island by tuning _V_c from −8 to −3 V while _V_pg was compensated. This lifted the overall conductance by opening a path through the reference arm (see Fig. 2a-d).

Fig. 2e–h shows the conductance Δ_G_ through the full interferometer (with smooth background subtracted; see “Methods” section) as a function of _B_⊥ and gate voltage _V_pg, which control

the flux in the interferometer and occupancy of the island, respectively. Figure 2e shows small oscillations in Δ_G_(_B_⊥) at _B_∥ = 0 T for the 2_e_ periodic peaks. For _B_∥ = 2.2 T, where

the peak spacing is even–odd (Fig. 2f), the conductance showed moderate oscillations with a period Δ_B_⊥ = 1.5 mT. This periodicity corresponds to a single flux quantum _h_/_e_ threading an

area of  ~2.7 μm2, consistent with the ring center area defined by _V_pg. This indicates coherent 1_e_ transport through both the reference arm and the Majorana island. At _B_∥ = 2.7 T, the

CB peak spacing is uniformly 1_e_, and oscillation amplitude is maximal (see Fig. 2g). When the Majorana island is driven normal, _B_∥ > 3 T, conductance oscillations are reduced,

becoming comparable to the low field oscillations (Fig. 2h). The appearance of strong _h_/_e_ periodic conductance oscillations in the 1_e_ regime of the island is a key experimental

signature of electron teleportation. The strength and periodicity of the oscillations are examined more quantitatively using Fourier power spectrum (PS) analysis (see “Methods” section). In

Fig. 2i–l, the PS of Δ_G_(_B_⊥) are shown. Increasing _B_∥ leads to a peak appearing around _f_ = 0.65 mT−1, the frequency expected for AB interference. The PS is maximized in the 1_e_

regime. To quantify the oscillations amplitude, \(\langle \tilde{A}\rangle\), we average the integrated PS (see “Methods” section). We next correlate the _B_∥ dependence of the oscillations

amplitude, \(\langle \tilde{A}\rangle (B_\parallel )\), with the _B_∥ dependence of the lowest sub-gap state, _E_0(_B_∥), of the island. The sub-gap energy is found from the difference

between even and odd CB peak spacings, averaged separately, 〈_S_〉 = 〈_S_e〉−〈_S_o〉 (see Fig. 1b). In Fig. 3a, 〈_S_〉 remains constant as a function of _B_∥ (indicating 2_e_ transport) until a

sub-gap state moves below _E_c, reaching zero at 2.2 T without overshoot (as expected for well separated MZMs in a long wire5,23). At low fields, where the CB periodicity is 2_e_, the

oscillation amplitude \(\langle \tilde{A}\rangle\) is small (Fig. 3b). When 〈_S_〉 approaches zero at high fields (_B_∥ > 2 T), \(\langle \tilde{A}\rangle\) exhibits a sharp increase that

coincides with the 2_e_ to 1_e_ transition. Above 3 T, the device is in the normal state and \(\langle \tilde{A}\rangle\) returned to the low value found in the 2_e_ regime. This comparison

shows that the oscillation amplitude is correlated with the energy of the lowest subgap state, and is maximal in the 1_e_ superconducting regime, as expected for electron teleportation.  

Figure 3c, d shows a similar study for device 2. In Fig. 3c, 〈_S_〉 shows strong even–odd below 1 T, fluctuates around 〈_S_〉 = 0 between 1 and 2 T, then settles to 1_e_ (〈_S_〉 = 0) above 2 T.

CB spectroscopy reveals a discrete state that oscillates around zero bias in both _B_∥ and _V_pg without forming a stable 1_e_ periodic zero-bias peak (see Supplementary Fig. 5). These

oscillations about zero energy are compatible with hybridized Majorana modes due to wavefunction overlap resulting from the finite island length9,28. This overlap causes an energy splitting

that oscillates both in field and chemical potential5,6,27. Figure 3d shows that phase coherent transport first appears above 1 T and \(\langle \tilde{A}\rangle\) gradually increases until

reaching a maximum amplitude for 1_e_ peak spacing at 2.1 T, before diminishing in the normal state. In comparison to device 1, phase coherent transport appears when 〈_S_〉 oscillations about

zero, suggesting that hybridized Majorana modes characterized by an extended wavefunction may also contribute to coherent transport. The absence of energy oscillations may distinguish

non-local MZMs from hybridized Majorana modes (see Fig. 3a, c). We attribute the reduced oscillation amplitude in device 1 to result from the longer loop length _L_loop > _l__ϕ_, leading

to increased dephasing in the reference arm. We observe that conductance oscillations measured on opposite sides of a CB peak in the 1_e_ regime are out of phase (see yellow ticks in the

insets of Fig. 3) indicating a transmission phase shift of _π_ is acquired when the parity of the island is flipped. This demonstrates interferometric detection of island parity, which

offers a way to detect MZM parity as proposed by several recent topological qubit schemes13,29,30. In some cases, we found that the the phase shift is restored through the CB valley, such

that the same sides of adjacent CB peaks have the same phase. What determines whether there is phase recovery in the CB valley is not currently understood (see Supplementary Fig. 

6)15,18,19,20. The angular dependence of the in-plane magnetic field is investigated by fixing the field magnitude _B_r = 2.5 T and rotating the field by an angle _α_ (see Fig. 1).

Theoretically, a rotation of the in-plane field towards the Rashba field direction is expected to close the topological gap31. Figure 4a shows 1_e_ periodic Coulomb diamonds at _B_∥ = 2.5 T

with a discrete ZBP at each charge degeneracy point (similar to Fig. 1e). Rotating by an angle _α_ = 5° lifted the discrete state from zero energy, leading to even-odd peak spacing; at _α_ =

 10°, 1_e_ periodicity is recovered, though without a discrete ZBP. The observed sensitivity of the zero-energy state to in-plane field rotation is consistent with MZMs31. Small rotations

(∣_α_∣ < 7.5°) reduced the oscillation amplitude, \(\langle \tilde{A}\rangle\), as expected for even–odd periodicity (see Fig. 3). However, at larger angles (∣_α_∣ > 10°) where the

discrete ZBP is absent, a strong interference signal is observed (Fig. 4d). The observation of coherent transport in the absence of a discrete zero-energy state suggests trivial extended

modes are also phase coherent over the length of the island. Therefore, the additional information provided by bias spectroscopy is needed to distinguish teleportation from other coherent

transport mechanisms, as shown in Fig. 4a–c. We further studied the effect of different magnetic field directions. The results are shown in Supplementary Fig. 7. In summary, all three axes

showed coherent transport, with oscillation amplitude first increasing as 〈_S_〉 approached zero. This shows that the oscillation amplitude is dictated by the energy _E_0 in all field

directions and indicates that interference is not unique to a parallel magnetic field. Finally, we comment on the physical mechanism that correlates the oscillation amplitude to the energy

of _E_0. At low fields, the Majorana island favors an even parity where transport of electrons occurs as two sequential tunneling events on either end of the island22,25. The two electrons

acquire the condensate phase when forming a Cooper pair, which suppresses single-electron coherence. At moderate fields, a discrete sub-gap state is brought below _E_c and a single-electron

transport channel is opened, allowing coherent resonant tunneling through the Majorana island. When the discrete state is brought to zero-energy, the contribution of coherent transport is

increased due to electron teleportation. Finally, in the normal state, we interpret the reduction in interference signal to reflect the short coherence length in the diffusive Al wire. In

conclusion, we report signatures of single-electron teleportation via non-local MZMs using AB interference in combination with spectroscopy of a discrete zero-energy state. Our results also

reveal that coherent transport by topologically trivial modes extending over the full length of the Majorana island are allowed. These extended trivial modes may be precursors of topological

states in a finite length system that could transition into non-local MZMs by adjusting experimental parameters28. We have shown that interferometry accompanying bias spectroscopy revealing

stable 1_e_ periodic CB in magnetic field and chemical potential can discriminate non-local MZMs from extended modes (that display characteristic energy oscillations). Increasing the wire

length to greatly exceed the diffusive coherence length \(\xi =\sqrt{{\xi }_{0}\,{l}_{e}} \sim 1\) μm (for _Δ_ = 75 μeV at _B_∥ = 2.5 T), where _ξ_0 is the clean coherence length and _l_e ~ 

300 nm is the semiconducting mean free path will suppress 1_e_ transport via trivial extended modes32. The observation of coherent transport through the island rules out localized ABS at the

ends of the wire as the source of the studied zero-bias state. Indeed, transport flips the parity of localized modes and suppresses interference, while transport through MZMs preserves

island parity and coherent transport12,14. These localized modes could have been a possible interpretation of the previously observed ZBPs in single-end tunneling experiments8,9. These

results suggest that InAs–Al 2DEGs are a promising route towards more complex experiments related to the braiding or fusion of MZMs. We have established coherent transport and parity readout

from the transmission phase shifts in Majorana islands, two key results for future topological qubit networks13,29,30. Future devices will take advantage of improved material quality to

allow for increased wire lengths to suppress coherent trivial quasiparticle transport, allowing MZM contributions to be better separated from other potential contributions. METHODS WAFER

STRUCTURE The devices were fabricated on wafers grown by molecular beam epitaxy on a InP substrate. The wafer stack consists of a 1 μm graded In1−_x_Al_x_As insulating buffer, a 4 nm

In0.81Ga0.19As bottom barrier, a 5 nm InAs quantum well, and a top barrier consisting of 5 nm In0.9Al0.1As for device 1 and 10 nm In0.81Ga0.19As for device 2. A 7 nm film of epitaxial Al was

then grown in situ without breaking the vacuum of the chamber. The InAs 2DEGs were characterized with a Hall bar geometry (Al removed), which showed a peak mobility of _μ_ = 17,000 cm2 V−1 

s−1 for an electron density of _n_ = 1.7 × 1012 cm−2 and _n_ = 7.5 × 1011 cm−2 for devices 1 and 2, respectively. DEVICE FABRICATION Devices were fabricated using standard electron beam

lithography techniques. The devices were electrically isolated by etching mesa structures by first removing the top Al film with Al etchant Transene D, followed by a deep III–V chemical wet

etch H2O:C6H8O7:H3PO4:H2O2 (220:55:3:3). Next, the Al film on the mesa was selectively etched with Al etchant Transene D to produce the Al strip. A 25 nm-thick layer of insulating HfO2 was

grown by atomic layer deposition at a temperature of 90 °C over the entire sample. Top gates of Ti/Au (5/25 nm) were then evaporated and connected to bonding pads with leads of Ti/Au (5/250 

nm). MEASUREMENTS Electrical measurements were performed by standard lock-in techniques at 166 Hz by applying the sum of a variable dc bias voltage _V_sd and an ac excitation voltage of 3–10

 μV applied to one of the top ohmic contacts as shown in Fig. 1a. The resulting current across the device was recorded by grounding a bottom ohmic via a low-impedance current-to-voltage

converter, and the four terminal voltage was measured by an ac voltage amplifier with an input impedance of 500 MΩ. All measurements were taken in a dilution refrigerator with a base

temperature of 20 mK and an electron temperature of 40 mK estimated by the temperature dependence saturation of ZBP conductance3. DATA ANALYSIS To highlight the oscillating components of the

differential conductance _G_(_B_⊥), a smooth background was subtracted with a low-degree polynomial Savitzky–Golay filter resulting in Δ_G_33. Analysis of the oscillations was performed by

first performing a fast Fourier transform _F_(_f_) of Δ_G_(_B_⊥) using a Hanning window then calculating the power spectral density _P__S_(_f_) = ∣_F_(_f_)∣2. The oscillation amplitude

\(\langle \tilde{A}\rangle\) was obtained by averaging integrated power spectra. The integration was limited to a band in frequency between _f_1 = 0.55 mT−1 and _f_2 = 0.75 mT−1, spanning

the range of a single flux quantum _Φ_0 = _h_/_e_ through the area _A_ defined by either the central gate (_A_1 = 2.25 μm2) or the exterior gates (_A_2 = 3.1 μm2), where _f_ = _A_/_Φ_0 (see

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Corporation, the Danish National Research Foundation, and the Villum Foundation. F.N. acknowledges support from European Research Commission, Grant No. 804273. We thank Karsten Flensberg,

Joshua Folk, Michael Hell, Andrew Higginbotham, Torsten Karzig, Panagiotis Kotetes, Martin Leijnse, Tommy Li, Alice Mahoney, and Ady Stern for useful discussions. AUTHOR INFORMATION Author

notes * F. Nichele Present address: IBM Research - Zurich, Sumerstrasse 4, 8803, Rschlikon, Switzerland * These authors contributed equally: A. M. Whiticar, A. Fornieri. AUTHORS AND

AFFILIATIONS * Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen and Microsoft Quantum Lab Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark A. M.

Whiticar, A. Fornieri, E. C. T. O’Farrell, A. C. C. Drachmann, C. M. Marcus & F. Nichele * Department of Physics and Astronomy and Microsoft Quantum Lab Purdue, Purdue University, West

Lafayette, IN, 47907, USA T. Wang, C. Thomas, S. Gronin, R. Kallaher, G. C. Gardner & M. J. Manfra * Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA T.

Wang, C. Thomas, S. Gronin, R. Kallaher, G. C. Gardner & M. J. Manfra * School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA M. J. Manfra * School of

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CONTRIBUTIONS T.W., C.T., S.G., R.K., G.C.G. and M.J.M. developed and grew the InAs/Al heterostructure. A.M.W. and A.F. designed and fabricated the devices. A.M.W. and A.F. performed the

measurements. Data analysis was done by A.M.W. and A.F with input from C.M.M. and F.N. C.M.M. and F.N. conceived the experiment. A.M.W. and A.F. interpreted the data with input from

E.C.T.O., A.C.C.D., C.M.M. and F.N. The manuscript was written by A.M.W., A.F., C.M.M. and F.N. with suggestions from all other authors. CORRESPONDING AUTHORS Correspondence to C. M. Marcus

or F. Nichele. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PEER REVIEW INFORMATION _Nature Communications_ thanks Ramón Aguado

and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional claims in

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http://creativecommons.org/licenses/by/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Whiticar, A.M., Fornieri, A., O’Farrell, E.C.T. _et al._ Coherent transport through

a Majorana island in an Aharonov–Bohm interferometer. _Nat Commun_ 11, 3212 (2020). https://doi.org/10.1038/s41467-020-16988-x Download citation * Received: 09 March 2020 * Accepted: 17 May

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