Electrostatic control of quasiparticle poisoning in a hybrid semiconductor-superconductor island
H. Q. Nguyen, D. Sabonis, D. Razmadze, E. T. Mannila, V. F. Maisi, D. M. T. van Zanten, E. C. T. O'Farrell, P. Krogstrup, F. Kuemmeth, J. P. Pekola, C. M. Marcus
The performance of superconducting devices is often degraded by the uncontrolled appearance and disappearance of quasiparticles, a process known as poisoning. We demonstrate electrostatic control of quasiparticle poisoning in the form of single-charge tunneling across a fixed barrier onto a Coulomb island in an InAs/Al hybrid nanowire. High-bandwidth charge sensing was used to monitor charge occupancy of the island across Coulomb blockade peaks, where tunneling rates were maximal, and Coulomb valleys, where tunneling was absent. Electrostatic gates changed on-peak tunneling rates by two orders of magnitude for a barrier with fixed normal-state resistance, which we attribute to gate dependence of the size and softness of the induced superconducting gap on the island, corroborated by separate density-of-states measurements. Temperature and magnetic field dependence of tunneling rates are also investigated.
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 μs) and sets a bound for a weakly coupled island (> 10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the r…
We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that when the coupling of the spin is of the order of the superconducting gap two almost degenerate subgap states are formed. By computing the Berry phase that is associated with the superconducting phase rotations in this model, we prove that these subgap states are characterized by a different charge and demonstrate that the switching between these states has the same effect as quasiparticle poisoning (unpoisoning) of the island. We also …
We study single-electron charging events in an Al/InAs nanowire hybrid system with deliberately introduced gapless regions. The occupancy of a Coulomb island is detected using a nearby radio-frequency quantum dot as a charge sensor. We demonstrate that a 1 micron gapped segment of the wire can be used to efficiently suppress single electron poisoning of the gapless region and therefore protect the parity of the island while maintaining good electrical contact with a normal lead. In the absence of protection by charging energy, the 1e switching rate can be reduced below 200 per second. In the s…
Qubits based on Majorana zero modes are a promising path towards topological quantum computing. Such qubits, though, are susceptible to quasiparticle poisoning which does not have to be small by topological argument. We study the main sources of the quasiparticle poisoning relevant for realistic devices -- non-equilibrium above-gap quasiparticles and equilibrium localized subgap states. Depending on the parameters of the system and the architecture of the qubit either of these sources can dominate the qubit decoherence. However, we find in contrast to naive estimates that in moderately disorde…
We study a hybrid device defined in an InAs nanowire with an epitaxial Al shell that consists of a quantum dot in contact with a superconducting island. The device is electrically floating, prohibiting transport measurements, but providing access to states that would otherwise be highly excited and unstable. Radio-frequency reflectometry with lumped-element resonators couples capacitatively to the quantum dot, and detects the presence of discrete subgap states. We perform a detailed study of the case with no island states, but with quantum-dot-induced subgap states controlled by the tunnel cou…
We demonstrate the operation of a differential single Cooper-pair box, a charge qubit consisting of two aluminum islands, isolated from ground, coupled by a pair of small-area Josephson junctions, and read out with a superconducting differential radio-frequency single electron transistor. We have tested four devices, all of which show evidence of quasiparticle poisoning. The devices are characterized with microwave spectroscopy and temperature dependence studies, and Coulomb staircases are shown to be e-periodic in all samples. However, coherent control is still possible with non-adiabatic vol…
We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers Qubit". All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic field…
We characterize in-situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends are consistent with a sub-gap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.
We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known relaxation algorithm for solving the Poisson equation in two dimensions is generalized to 3D. In addition,all charges on the system, free as well as induced charges,are determined accurately and self-consistently to satisfy the desired boundary conditions. This allows the straightforward calculation of the potential on the outer boundary using the free space electr…
We propose a novel method for suppression of quasiparticle poisoning in Al Coulomb blockade devices. The method is based on creation of a proper energy gap profile along the device. In contrast to the previously used techniques, the energy gap is controlled by the film thickness. Our transport measurements confirm that the quasiparticle poisoning is suppressed and clear 2$e$ periodicity is observed only when the island is made much thinner than the leads. This result is consistent with the existing model and provides a simple method to suppress quasiparticle poisoning.
We present measurements of one-dimensional superconductor-semiconductor Coulomb islands, fabricated by gate confinement of a two-dimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without sub-gap states, Coulomb blockade reveals Cooper-pair mediated transport. When sub-gap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti) crossings in (parallel) transverse magnetic field indicating Rashba-type spin-orbit coupling. Overall …
We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all …
We study the low temperature thermodynamic properties of a superconducting double-island qubit. For an odd number of electrons in the device, the ground state corresponds to the intrinsic quasiparticle bound to the tunneling contact. The ground state is separated from the continuum of excited states by a finite gap of order of the Josephson energy E_J. The presence of the bound quasiparticle state results in a nonmonotonic temperature dependence of the width of the transition region between Coulomb blockade plateaus. The minimum width occurs at the ionization temperature of the bound state, T_…
We have experimentally demonstrated pumping of Cooper pairs in a single-island mesoscopic structure. The island was connected to leads through SQUID (Superconducting Quantum Interference Device) loops. Synchronized flux and voltage signals were applied whereby the Josephson energies of the SQUIDs and the gate charge were tuned adiabatically. From the current-voltage characteristics one can see that the pumped current increases in 1e steps which is due to quasiparticle poisoning on the measurement time scale, but we argue that the transport of charge is due to Cooper pairs.
We study electronic transport through metallic multi-island Coulomb-blockade systems. Based on a diagrammatic real-time approach, we develop a computer algorithm that generates and calculates all transport contributions up to second order in the tunnel-coupling strengths for arbitrary multi-island systems. This comprises sequential and cotunneling, as well as terms corresponding to a renormalization of charging energies and tunneling conductances. Multi-island cotunneling processes with energy transfer between different island are taken into account. To illustrate our approach we analyze the c…
We demonstrate single-shot readout of quantum states of the Josephson charge qubit. The quantum bits are transformed into and stored as classical bits (charge quanta) in a dynamic memory cell - a superconducting island. The transformation of state |1> (differing form state |0> by an extra Cooper pair) is a result of a controllable quasiparticle tunneling to the island. The charge is then detected by a conventional single-electron transistor, electrostatically decoupled from the qubit. We study relaxation dynamics in the system and obtain the readout efficiency of 87% and 93% for |1> and |0> st…
CIC nanoGUNE-BRTA（巴斯克纳米材料研究中心）；Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（材料物理中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Ikerbasque, Basque Foundation for Science（伊克拉巴斯克科学基金会）
We investigated insulating Cu$_2$N islands grown on Cu(100) by means of combined scanning tunneling microscopy and atomic force microscopy with two vastly different tips: a bare metal tip and a CO-terminated tip. We use scanning tunneling microscopy data as proposed by Choi et al. [T. Choi et al., PRB 78, 035430 (2008).] to unambiguously identify atomic positions. Atomic force microscopy images taken with the two different tips show an inverted contrast over Cu$_2$N. The observed force contrast can be explained with an electrostatic model, where the two tips have dipole moments of opposite dir…
We study by first-principles calculations a densely packed island of organic molecules (F4TCNQ) adsorbed on graphene. We find that with electron doping the island naturally forms a p-n junction in the graphene sheet. For example, a doping level of ~ 3 * 10^{13} electrons per cm^2 results in a p-n junction with 800 meV electrostatic potential barrier. Unlike in a conventional p-n junction in graphene, in the case of the junction formed by an adsorbed organic molecular island we expect that the Klein tunneling is inhibited, even without an applied external magnetic field. Here Klein tunneling is…
Hybrid semiconductor/superconductor devices constitute an important platform for a wide range of applications, from quantum computing to topological-state-based architectures. Here, we demonstrate full modulation of the interference pattern in a superconducting interference device with two parallel islands of ballistic InAs quantum wells separated by a trench, by acting independently on two side-gates. This so far unexplored geometry enables us to tune the device with high precision from a SQUID-like to a Fraunhofer-like behavior simply by electrostatic gating, without the need for an addition…
Fluctuation of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots are studied within a model based on the electrostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energies depend also on an external magnetic field. In contrast with a single island quantum dot, where the spacing distribution is close to Gaussian, here the distribution has a peak at small spacing value. The fluctuations are mainly due to charging effects. The model can explain the occ…
We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron{transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the inter-island tunneling is considered constant, e.g. determined by the thickness of an insulating layer. A representative array of 3x3 quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matr…
We incorporate an Al-AlO_x-Al single-electron transistor as the gate of a narrow (~100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET). Near the MOSFET channel conductance threshold, we observe oscillations in the conductance associated with Coulomb blockade in the channel, revealing the formation of a Si single-electron transistor. Abrupt steps present in sweeps of the Al transistor conductance versus gate voltage are correlated with single-electron charging events in the Si transistor, and vice versa. Analysis of these correlations using a simple electrostatic model demonstrat…
This article is concerned with statistics of addition spectra for systems of identical charged particles. A classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots. It is based on the electrostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energy depend also on an external magnetic field. | In contrast with a single island quantum dot where the spacing distribution between conductance peaks …
An all-superconductor charge qubit enabling a radio-frequency readout of its quantum state is described. The core element of the setup is a superconducting loop which includes the single-Cooper-pair (Bloch) transistor. This circuit has two functions: First, it operates as a charge qubit with magnetic control of Josephson coupling and electrostatic control of the charge on the transistor island. Secondly, it acts as the transducer of the rf electrometer, which probes the qubit state by measuring the Josephson inductance of the transistor. The evaluation of the basic parameters of this device sh…
We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the…
We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $χ_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adj…
We investigate low-temperature and low-voltage-bias charge transport in a superconducting Al single electron transistor in a dissipating environment, realized as on-chip high-ohmic Cr microstrips. In our samples with relatively large charging energy values Ec > EJ, where EJ is the energy of the Josephson coupling, two transport mechanisms were found to be dominating, both based on discrete tunneling of individual Cooper pairs: Depending on the gate voltage Vg, either sequential tunneling of pairs via the transistor island (in the open state of the transistor around the points Qg = CgVg = e mod…
We present investigations of Josephson charge-phase qubits inductively coupled to a radio-frequency driven tank-circuit enabling the readout of the states by measuring the Josephson inductance of the qubit. The circuits including junctions with linear dimensions of 60 nm and 80 nm are fabricated from Nb trilayer and allowing the determination of relevant sample parameters at liquid helium temperature. The observed partial suppression of the circulating supercurrent at 4.2 K is explained in the framework of a quantum statistical model. We have probed the ground-state properties of qubit structu…
An Al-AlO_x-Al single-electron transistor (SET) acting as the gate of a narrow (~ 100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET) can induce a vertically aligned Si SET at the Si/SiO_2 interface near the MOSFET channel conductance threshold. By using such a vertically coupled Al and Si SET system, we have detected a single-charge defect which is tunnel-coupled to the Si SET. By solving a simple electrostatic model, the fractions of each coupling capacitance associated with the defect are extracted. The results reveal that the defect is not a large puddle or metal island, but…
