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Sebastian Heedt

Publications and source records attributed to Sebastian Heedt.

At least 19 recordsLinked to original sources

20 Second Parity Lifetime in an InAs--Pb Tetron Device

A central promise of topological quantum computing is that increasing the excitation gap improves device performance significantly. Here, we experimentally validate this principle in an InAs--Pb tetron device via interferometric single-shot parity measurements. By replacing aluminum with the higher-gap superconductor lead in our superconductor-semiconductor hybrid devices, we have improved the robustness of our topological phase. In addition, to enable fast and precise bring-up at scale, we have developed an rf measurement technique that resolves low-energy wire-end states and directly measures their energy splitting with $\mu\text{eV}$ precision. We employ this technique to bring up a device in a multi-tetron array and perform parity measurements of one of the tetron's hybrid nanowires (NWs). By controllably switching the wire parity, we observe $h/2e$-periodic bimodal shifts in the quantum capacitance of a quantum dot coupled to the hybrid nanowire in an interference loop. Further time-resolved measurements reveal a characteristic parity switching time of $\sim 20$ s with some instances reaching minute-scale. Such extremely long parity lifetimes are orders of magnitude longer than typical qubit operation times, which are on the order of $\mu\text{s}$. Finally, we discuss potential implications for the fidelity of Pauli measurements.

cond-mat.mes-hall

Shubnikov-de Haas Characterization of Superconductor-Semiconductor Heterostructures

Hybrid superconductor-semiconductor nanostructures are a central component for research spanning condensed matter physics and quantum information processing. Continued progress relies critically on the ability to characterize, control, and optimize several intrinsic material properties including spin-orbit coupling, band offsets, and disorder in a device-relevant stack that necessarily couples the electronic states of a superconducting metal film and a semiconductor. Here we report a new method to extract fundamental material parameters utilizing simple Shubnikov-de Haas (SdH) oscillation measurements in heterostructures in which metallic electronic states are coupled to a two-dimensional electron gas (2DEG) residing in an InAs quantum well beneath an aluminum thin film. Proper analysis of the full magnetoresistance data facilitates extraction of the quantum well carrier density, spin-orbit coupling strength, and both transport and quantum scattering times. Most importantly, the extracted scattering times in the 2DEG are impacted by the metal-semiconductor coupling strength allowing us to quickly gain information on proximity-induced superconducting gap without any fabrication or mK measurements. The wealth of information that is accessed with these simple measurements positions this methodology as an important tool for hybrid materials optimization.

cond-mat.mes-hall

Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device

We present a hardware realization and measurements of a tetron qubit device in a superconductor-semiconductor heterostructure. The device architecture contains two parallel superconducting nanowires, which support four Majorana zero modes (MZMs) when tuned into the topological phase, and a trivial superconducting backbone. Two distinct readout interferometers are formed by connecting the superconducting structure to a series of quantum dots. We perform single-shot interferometric measurements of the fermion parity for the two loops, designed to implement Pauli-$X$ and $Z$ measurements of the tetron. Performing repeated single-shot measurements yields two widely separated time scales $\tau_X = 14.5\pm 0.3 \, \mathrm{\mu s}$ and $\tau_Z = 12.4\pm 0.4\, \mathrm{ms}$ for parity switches observed in the $X$ and $Z$ measurement loops, which we attribute to intra-wire parity switches and external quasiparticle poisoning, respectively. We estimate assignment errors of $\mathrm{err}^X_a=16\%$ and $\mathrm{err}^Z_a=0.5\%$ for $X$ and $Z$ measurement-based operations, respectively.

cond-mat.mes-hall

Response to recent comments on Phys. Rev. B 107, 245423 (2023) and Subsection S4.3 of the Supp. Info. for Nature 638, 651-655 (2025)

The topological gap protocol (TGP) is a statistical test designed to identify a topological phase with high confidence and without human bias. It is used to determine a promising parameter regime for operating topological qubits. The protocol's key metric is the probability of incorrectly identifying a trivial region as topological, referred to as the false discovery rate (FDR). Two recent manuscripts [arXiv:2502.19560, arXiv:2503.08944] engage with the topological gap protocol and its use in Phys. Rev. B 107, 245423 (2023) and Subsection S4.3 of the Supplementary Information for Nature 638, 651-655 (2025), although they do not explicitly dispute the main results of either one. We demonstrate that the objections in arXiv:2502.19560 and arXiv:2503.08944 are unfounded, and we uphold the conclusions of Phys. Rev. B 107, 245423 (2023) and Nature 638, 651-655 (2025). Specifically, we show that no flaws have been identified in our estimate of the false discovery rate (FDR). We provide a point-by-point rebuttal of the comments in arXiv:2502.19560 and arXiv:2503.08944.

cond-mat.mes-hall

Roadmap to fault tolerant quantum computation using topological qubit arrays

We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap encompasses four generations of devices: a single-qubit device that enables a measurement-based qubit benchmarking protocol; a two-qubit device that uses measurement-based braiding to perform single-qubit Clifford operations; an eight-qubit device that can be used to show an improvement of a two-qubit operation when performed on logical qubits rather than directly on physical qubits; and a topological qubit array supporting lattice surgery demonstrations on two logical qubits. Devices that enable this path require a superconductor-semiconductor heterostructure that supports a topological phase, quantum dots and coupling between those quantum dots that can create the appropriate loops for interferometric measurements, and a microwave readout system that can perform fast, low-error single-shot measurements. We describe the key design components of these qubit devices, along with the associated protocols for demonstrations of single-qubit benchmarking, Clifford gate execution, quantum error detection, and quantum error correction, which differ greatly from those in more conventional qubits. Finally, we comment on implications and advantages of this architecture for utility-scale quantum computation.

quant-ph

Interferometric Single-Shot Parity Measurement in an InAs-Al Hybrid Device

The fusion of non-Abelian anyons or topological defects is a fundamental operation in measurement-only topological quantum computation. In topological superconductors, this operation amounts to a determination of the shared fermion parity of Majorana zero modes. As a step towards this, we implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined nanowire. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1 fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7 $\mu$s at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. These results are consistent with a measurement of the fermion parity encoded in a pair of Majorana zero modes that are separated by approximately 3 $\mu$m and subjected to a low rate of poisoning by non-equilibrium quasiparticles. The large capacitance shift and long poisoning time enable a parity measurement error probability of 1%.

cond-mat.mes-hall

Impact of junction length on supercurrent resilience against magnetic field in InSb-Al nanowire Josephson junctions

Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity by studying Josephson supercurrent. However, an external magnetic field generally suppresses the supercurrent through hybrid nanowire junctions and significantly limits the field range in which the supercurrent phenomena can be studied. In this work, we investigate the impact of the length of InSb-Al nanowire Josephson junctions on the supercurrent resilience against magnetic fields. We find that the critical parallel field of the supercurrent can be considerably enhanced by reducing the junction length. Particularly, in 30 nm-long junctions supercurrent can persist up to 1.3 T parallel field - approaching the critical field of the superconducting film. Furthermore, we embed such short junctions into a superconducting loop and obtain the supercurrent interference at a parallel field of 1 T. Our findings are highly relevant for multiple experiments on hybrid nanowires requiring a magnetic field-resilient supercurrent.

cond-mat.mes-hall

InAs-Al Hybrid Devices Passing the Topological Gap Protocol

We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes. The devices are fabricated from high-mobility two-dimensional electron gases in which quasi-one-dimensional wires are defined by electrostatic gates. These devices enable measurements of local and non-local transport properties and have been optimized via extensive simulations to ensure robustness against non-uniformity and disorder. Our main result is that several devices, fabricated according to the design's engineering specifications, have passed the topological gap protocol defined in Pikulin et al. [arXiv:2103.12217]. This protocol is a stringent test composed of a sequence of three-terminal local and non-local transport measurements performed while varying the magnetic field, semiconductor electron density, and junction transparencies. Passing the protocol indicates a high probability of detection of a topological phase hosting Majorana zero modes as determined by large-scale disorder simulations. Our experimental results are consistent with a quantum phase transition into a topological superconducting phase that extends over several hundred millitesla in magnetic field and several millivolts in gate voltage, corresponding to approximately one hundred micro-electron-volts in Zeeman energy and chemical potential in the semiconducting wire. These regions feature a closing and re-opening of the bulk gap, with simultaneous zero-bias conductance peaks at both ends of the devices that withstand changes in the junction transparencies. The extracted maximum topological gaps in our devices are 20-60 $\mu$eV. This demonstration is a prerequisite for experiments involving fusion and braiding of Majorana zero modes.

cond-mat.mes-hall

Parametric exploration of zero-energy modes in three-terminal InSb-Al nanowire devices

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field and junction transparencies. Identifying the lowest-energy state allows for the construction of lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes.

cond-mat.mes-hall

Protocol to identify a topological superconducting phase in a three-terminal device

We develop a protocol to determine the presence and extent of a topological phase with Majorana zero modes in a hybrid superconductor-semiconductor device. The protocol is based on conductance measurements in a three-terminal device with two normal leads and one superconducting lead. A radio-frequency technique acts as a proxy for the measurement of local conductance, allowing a rapid, systematic scan of the large experimental phase space of the device. Majorana zero modes cause zero bias conductance peaks at each end of the wire, so we identify promising regions of the phase space by filtering for this condition. To validate the presence of a topological phase, a subsequent measurement of the non-local conductance in these regions is used to detect a topological transition via the closing and reopening of the bulk energy gap. We define data analysis routines that allow for an automated and unbiased execution of the protocol. Our protocol is designed to screen out false positives, especially trivial Andreev bound states that mimic Majorana zero modes in local conductance. We apply the protocol to several examples of simulated data illustrating the detection of topological phases and the screening of false positives.

cond-mat.mes-hall

Single-shot fabrication of semiconducting-superconducting nanowire devices

Semiconducting-superconducting nanowires attract widespread interest owing to the possible presence of non-abelian Majorana zero modes, which hold promise for topological quantum computation. However, the search for Majorana signatures is challenging because reproducible hybrid devices with desired nanowire lengths and material parameters need to be reliably fabricated to perform systematic explorations in gate voltages and magnetic fields. Here, we exploit a fabrication platform based on shadow walls that enables the in-situ, selective and consecutive depositions of superconductors and normal metals to form normal-superconducting junctions. Crucially, this method allows to realize devices in a single shot, eliminating fabrication steps after the synthesis of the fragile semiconductor/superconductor interface. At the atomic level, all investigated devices reveal a sharp and defect-free semiconducting-superconducting interface and, correspondingly, we measure electrically a hard induced superconducting gap. While our advancement is of crucial importance for enhancing the yield of complex hybrid devices, it also offers a straightforward route to explore new material combinations for hybrid devices.

cond-mat.mes-hall

Shadow-wall lithography of ballistic superconductor-semiconductor quantum devices

The realization of a topological qubit calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of novel quantum devices and ultimately topological qubits while eliminating many fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables, in particular, the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.

cond-mat.mes-hall

Transmission phase read-out of a large quantum dot in a nanowire interferometer

Detecting the transmission phase of a quantum dot via interferometry can reveal the symmetry of the orbitals and details of electron transport. Crucially, interferometry will enable the read-out of topological qubits based on one-dimensional nanowires. However, measuring the transmission phase of a quantum dot in a nanowire has not yet been established. Here, we exploit recent breakthroughs in the growth of one-dimensional networks and demonstrate interferometric read-out in a nanowire-based architecture. In our two-path interferometer, we define a quantum dot in one branch and use the other path as a reference arm. We observe Fano resonances stemming from the interference between electrons that travel through the reference arm and undergo resonant tunnelling in the quantum dot. Between consecutive Fano peaks, the transmission phase exhibits phase lapses that are affected by the presence of multiple trajectories in the interferometer. These results provide critical insights for the design of future topological qubits.

cond-mat.mes-hall

Exfoliated hexagonal BN as gate dielectric for InSb nanowire quantum dots with improved gate hysteresis and charge noise

We characterize InSb quantum dots induced by bottom finger gates within a nanowire that is grown via the vapor-liquid-solid process. The gates are separated from the nanowire by an exfoliated 35\,nm thin hexagonal BN flake. We probe the Coulomb diamonds of the gate induced quantum dot exhibiting charging energies of $\sim 2.5\,\mathrm{meV}$ and orbital excitation energies up to $0.3\,\mathrm{meV}$. The gate hysteresis for sweeps covering 5 Coulomb diamonds reveals an energy hysteresis of only $60\mathrm{\mu eV}$ between upwards and downwards sweeps. Charge noise is studied via long-term measurements at the slope of a Coulomb peak revealing potential fluctuations of $\sim 1\,\mu \mathrm{eV}/\mathrm{\sqrt{Hz}}$ at 1\,Hz. This makes h-BN the dielectric with the currently lowest gate hysteresis and lowest low-frequency potential fluctuations reported for low-gap III-V nanowires. The extracted values are similar to state-of-the art quantum dots within Si/SiGe and Si/SiO${_2}$ systems.

cond-mat.mes-hall

Dresselhaus spin-orbit coupling in [111]-oriented semiconductor nanowires

The contribution of bulk inversion asymmetry to the total spin-orbit coupling is commonly neglected for group III-V nanowires grown in the generic [111] direction. We have solved the complete Hamiltonian of the circular nanowire accounting for bulk inversion asymmetry via exact numerical diagonalization. Three different symmetry classes of angular momentum states exist, which reflects the threefold rotation symmetry of the crystal lattice about the [111] axis. A particular group of angular momentum states contains degenerate modes which are strongly coupled via the Dresselhaus Hamiltonian, which results in a significant energy splitting with increasing momentum. Hence, under certain conditions Dresselhaus spin-orbit coupling is relevant for [111] InAs and [111] InSb nanowires. We demonstrate momentum-dependent energy splittings and the impact of Dresselhaus spin-orbit coupling on the dispersion relation. In view of possible spintronics applications relying on bulk inversion asymmetry we calculate the spin expectation values and the spin texture as a function of the Fermi energy. Finally, we investigate the effect of an axial magnetic field on the energy spectrum and on the corresponding spin polarization.

cond-mat.mes-hall

Parity transitions in the superconducting ground state of hybrid InSb-Al Coulomb islands

The number of electrons in small metallic or semiconducting islands is quantized. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting-semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS,and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e. compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.

cond-mat.supr-con

Magnetoconductance correction in zinc-blende semiconductor nanowires with spin-orbit coupling

We study the effects of spin-orbit coupling on the magnetoconductivity in diffusive cylindrical semiconductor nanowires. Following up on our former study on tubular semiconductor nanowires, we focus in this paper on nanowire systems where no surface accumulation layer is formed but instead the electron wave function extends over the entire cross section. We take into account the Dresselhaus spin-orbit coupling resulting from a zinc-blende lattice and the Rashba spin-orbit coupling, which is controlled by a lateral gate electrode. The spin relaxation rate due to Dresselhaus spin-orbit coupling is found to depend neither on the spin density component nor on the wire growth direction and is unaffected by the radial boundary. In contrast, the Rashba spin relaxation rate is strongly reduced for a wire radius that is smaller than the spin precession length. The derived model is fitted to the data of magnetoconductance measurements of a heavily doped back-gated InAs nanowire and transport parameters are extracted. At last, we compare our results to previous theoretical and experimental studies and discuss the occurring discrepancies.

cond-mat.mes-hall

Weak (anti)localization in tubular semiconductor nanowires with spin-orbit coupling

We compute analytically the weak (anti)localization correction to the Drude conductivity for electrons in tubular semiconductor systems of zinc blende type. We include linear Rashba and Dresselhaus spin-orbit coupling (SOC) and compare wires of standard growth directions $\langle100\rangle$, $\langle111\rangle$, and $\langle110\rangle$. The motion on the quasi-two-dimensional surface is considered diffusive in both directions: transversal as well as along the cylinder axis. It is shown that Dresselhaus and Rashba SOC similarly affect the spin relaxation rates. For the $\langle110\rangle$ growth direction, the long-lived spin states are of helical nature. We detect a crossover from weak localization to weak anti-localization depending on spin-orbit coupling strength as well as dephasing and scattering rate. The theory is fitted to experimental data of an undoped $\langle111\rangle$ InAs nanowire device which exhibits a top-gate-controlled crossover from positive to negative magnetoconductivity. Thereby, we extract transport parameters where we quantify the distinct types of SOC individually.

cond-mat.mes-hall