Radio-Frequency Methods for Majorana-Based Quantum Devices: Fast Charge Sensing and Phase-Diagram Mapping

Razmadze, Davydas; Sabonis, Deividas; Malinowski, Filip K.; Ménard, Gerbold; Pauka, Sebastian; Nguyễn, Hồng Quang; Zanten, D. M. T. van; O’Farrell, Eoin; Suter, Judith; Krogstrup, Peter; Kuemmeth, Ferdinand; Marcus, C. M.

doi:10.1103/physrevapplied.11.064011

Cited by 31 publications

(31 citation statements)

References 41 publications

(57 reference statements)

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“…To avoid the capacitive cross talk between the V RP and the sensor plunger V SP we apply an out of phase compensating saw-tooth ramp at the same frequency on V SP while taking a charge stability diagram. The fast measurement setup used here is equivalent to the one presented in [12]. Supplementary Figure 3.…”

Section: Measurement Techniquesmentioning

confidence: 99%

“…Charge of the right island is measured using a capacitively coupled segment of the same nanowire (see Fig. 1a) configured as single electron transistors (SET) [1] and embedded in an on-chip RLC resonant circuit [11,12].Charge stability diagrams of the double island at several axial magnetic fields are shown in Fig. 1e-g. Sharp arXiv:1902.00797v1 [cond-mat.mes-hall]…”

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confidence: 99%

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Photon-assisted tunnelling of zero modes in a Majorana wire

Zanten¹,

Sabonis²,

Suter³

et al. 2020

Nat. Phys.

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Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes (MZMs) at their ends, and networks of such structures can produce topologically protected qubits. In a double-island geometry where each segment hosts a pair of MZMs, inter-pair coupling mixes the charge parity of the islands and opens an energy gap between the even and odd charge states at the inter-island charge degeneracy. Here, we report on the spectroscopic measurement of such an energy gap in an InAs/Al double-island device by tracking the position of the microwave-induced quasiparticle (qp) transitions using a radio-frequency (rf ) charge sensor. In zero magnetic field, photon assisted tunneling (PAT) of Cooper pairs gives rise to resonant lines in the 2e-2e periodic charge stability diagram.In the presence of a magnetic field aligned along the nanowire, resonance lines are observed parallel to the inter-island charge degeneracy of the 1e-1e periodic charge stability diagram, where the 1e periodicity results from a zero-energy subgap state that emerges in magnetic field. Resonant lines in the charge stability diagram indicate coherent photon assisted tunneling of singleelectron states, changing the parity of the two islands. The dependence of resonant frequency on detuning indicates a sizable (GHz-scale) hybridization of zero modes across the junction separating islands.In a mesoscopic superconducting island, the presence of a single unpaired electron comes at an energy cost δ determined by the lowest quasiparticle state. As a consequence, the odd-parity charge states are elevated in energy. The total energy of a charge state with N electrons is E N = E C (N − n g ) 2 + δ mod(N, 2), where E C is the single-electron charging energy and n g is the gateinduced charge. For δ > E C (Fig. 1a), the island ground states are of even charge parity only, and the island occupation changes in steps of 2e as n g is changed [1]. When * These authors contributed equally to this work † email: marcus@nbi.ku.dk the island is weakly coupled to a superconducting reservoir the coherent exchange of Cooper pairs, characterized by Josephson energy E J , mixes ground states of equal parity, resulting in an anti-crossing (blue lines in Fig. 1a). This superposition of even-parity charge states is the basis of conventional superconducting qubits [2]. In a topological superconducting island, nonoverlapping Majorana zero modes comprise a zero-energy qp state denoted a Majorana bound state (MBS). Since δ = 0 in this case, the island charge occupation changes with regular steps of width 1e. Overlap between MZMs within the island leads to δ = 0. Consequently, the width of Coulomb valleys with even parity will either increase or decrease depending on the sign of δ [3], as recently demonstrated experimentally [4][5][6]. In contrast to the intra-island coupling of MZMs, the wave function overlap with an exterior MZM, characterized by E M , leaves δ unchanged but mixes states of different parity (see Fig. 1c). The ground states of the i...

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Section: Measurement Techniquesmentioning

confidence: 99%

mentioning

confidence: 99%

Photon-assisted tunnelling of zero modes in a Majorana wire

Zanten¹,

Sabonis²,

Suter³

et al. 2020

Nat. Phys.

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“…Finally, in case the resonator is attached to the device source it can be repurposed for rf conductance measurements [5,16,17]. When the source-drain resistance is finite, it introduces dissipation in the resonant circuit, mapping the channel conductance to the internal quality factor of the resonator.…”

Section: Fig 1 (A)mentioning

confidence: 99%

“…2(a) illustrates a small change of the resonance frequency compared to the resonator linewidth. To independently measure the gate capacitance with a different method, we form a quantum dot by setting the gate voltages V L,R to a tunneling regime (∼150 mV), and V G ≈ 4 V. Coulomb peaks versus V G are measured by means of rf-conductance [5,16,17], using the same resonator that was used for the direct capacitance measurement [Fig. 2(c)].…”

Section: Validationmentioning

confidence: 99%

Radio-frequency C-V measurements with sub-attofarad sensitivity

Malinowski¹,

Lin²,

Jong³

et al. 2021

Preprint

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We demonstrate the use of radio-frequency (rf) resonators to measure the capacitance of nanoscale semiconducting devices in field-effect transistor configurations. The rf resonator is attached to the gate or the lead of the device. Consequently, tuning the carrier density in the conducting channel of the device affects the resonance frequency, quantitatively reflecting its capacitance. We test the measurement method on InSb and InAs nanowires at dilution-refrigerator temperatures. The measured capacitances are consistent with those inferred from the periodicity of the Coulomb blockade of quantum dots realized in the same devices. In an implementation of the resonator using an off-chip superconducting spiral inductor we find sensitivity values reaching down to 75 zF/ √ Hz at 1 kHz measurement bandwidth, and noise down to 0.45 aF at 1 Hz bandwidth. We estimate the sensitivity of the method for a number of other implementations. In particular we predict typical sensitivity of about 40 zF/ √ Hz at room temperature with a resonator comprised of off-the-shelf components. Of several proposed applications, we demonstrate two: the capacitance measurement of several identical 80 nm-wide gates with a single resonator, and the field-effect mobility measurement of an individual nanowire with the gate capacitance measured in-situ.

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“…[7] and charge sensing followed Ref. [17]. Measurements were performed in a dilution refrigerator with a 6-1-1 T vector magnet.…”

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confidence: 99%

Comparing tunneling spectroscopy and charge sensing of Andreev bound states in a semiconductor-superconductor hybrid nanowire structure

Sabonis,

van Zanten,

Suter

et al. 2021

Preprint

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Transport studies of Andreev bound states (ABSs) are complicated by the interplay of charging effects and superconductivity. Here, we compare transport approaches to ABS spectroscopy in a semiconductor-superconductor island to a charge-sensing approach based on an integrated radio-frequency single-electron transistor. Consistency of the methods demonstrates that fast, noninvasive charge sensing allows accurate quantitative measurement of ABSs while eluding some complexities of transport.

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Radio-Frequency Methods for Majorana-Based Quantum Devices: Fast Charge Sensing and Phase-Diagram Mapping

Cited by 31 publications

References 41 publications

Photon-assisted tunnelling of zero modes in a Majorana wire

Photon-assisted tunnelling of zero modes in a Majorana wire

Radio-frequency C-V measurements with sub-attofarad sensitivity

Comparing tunneling spectroscopy and charge sensing of Andreev bound states in a semiconductor-superconductor hybrid nanowire structure

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