Charge-sensing of a GeSi coreshell nanowire double quantum dot using a high-impedance superconducting resonator

2025-09-29 2 0 3.37MB 7 页 10玖币

侵权投诉

Charge-sensing of a Ge/Si core/shell nanowire double quantum dot using a

high-impedance superconducting resonator

J. H. Ungerer,1, 2, ∗P. Chevalier Kwon,1, ∗T. Patlatiuk,1J. Ridderbos,1, 3 A. Kononov,1

D. Sarmah,1E. P. A. M. Bakkers,4, 5 D. Zumb¨uhl,1, 2 and C. Sch¨onenberger1, 2, †

1Department of Physics, University of Basel, Klingelbergstrasse 82 CH-4056, Switzerland

2Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82 CH-4056, Switzerland

3MESA+ Institute for Nanotechnology, University of Twente,

P.O. Box 217, 7500 AE Enschede, The Netherlands

4Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

5Department of Applied Physics, TU Eindhoven,

Den Dolech 2, 5612 AZ Eindhoven, The Netherlands

(Dated: December 6, 2022)

Spin qubits in germanium are a promising contender for scalable quantum computers. Reading

out of the spin and charge conﬁguration of quantum dots formed in Ge/Si core/shell nanowires is

typically performed by measuring the current through the nanowire. Here, we demonstrate a more

versatile approach on investigating the charge conﬁguration of these quantum dots. We employ

a high-impedance, magnetic-ﬁeld resilient superconducting resonator based on NbTiN and couple

it to a double quantum dot in a Ge/Si nanowire. This allows us to dispersively detect charging

eﬀects, even in the regime where the nanowire is fully pinched oﬀ and no direct current is present.

Furthermore, by increasing the electro-chemical potential far beyond the nanowire pinch-oﬀ, we

observe indications for depleting the last hole in the quantum dot by using the second quantum dot

as a charge sensor. This work opens the door for dispersive readout and future spin-photon coupling

in this system.

I. INTRODUCTION

The interest in group-IV semiconductor spin qubits

is large because of their small footprint, a low concen-

tration of nuclear spins and available knowledge about

their production in semiconductor industry [1–5]. By

integrating on-chip superconducting resonators, strong

spin-photon coupling has been demonstrated for spins

of conﬁned electrons in a Si two-dimensional electron

gas [6, 7]. Hole spins may oﬀer the additional advan-

tages of improved relaxation and decoherence times as

they lack a valley degeneracy and exhibit a reduced wave-

function overlap with nuclear spins [8, 9]. Especially,

holes in one-dimensional Si or Ge nanowires [10–12] are

of a special interest because they posses strong spin-orbit

interaction [13–15]. The spin-orbit interaction poten-

tially simpliﬁes qubit control and coupling to resonators

by electric-dipole spin resonance (EDSR) [16, 17]. It

thereby releases the need of implementing micromagnets

and hence facilitates scaling-up.

Recently, the coherent manipulation of a hole-spin

qubit in a gate-deﬁned double quantum dot (DQD) in

a Ge/Si core/shell nanowire has been demonstrated [18].

However, in these experiments both the charge and the

spin-state of the double quantum dot were determined

by direct current measurements. This technique limits

the capability of determining the total number of holes

present in the nanowire. Furthermore, it requires long

∗These authors contributed equally to the work.

†www.nanoelectronics.unibas.ch

integration times and severely limits the maximum cycle

length in pulsed-gate experiments.

Rather than measuring the current through the Ge/Si

core/shell nanowire double quantum dot, pioneering

works have employed another quantum dot to determine

changes in the charge-occupancy of the DQD and to per-

form spin readout [19, 20].

feedline

resonator

dc lines

100 nm

100 μm

a) b)

FIG. 1. Device overview. a) Schematic of hybrid resonator

architecture. NbTiN is shown in dark blue, the Si substrate is

shown white. The feedline on the left is used for reading out

the notch-type coplanar-waveguide half-wave resonator which

is dc biased at its voltage node in the center. Additional dc

lines are used for sending current through the nanowire and

applying gate voltages on all bottom gates. b) False colored

scanning electron micrograph of a similar device with Ge/Si

nanowire lying on top of bottom gates covered with HfO2.

The gate colored red is connected to the resonator. c) Trans-

mission (phase and magnitude) through the feedline as a func-

tion of frequency close to the resonator frequency. The solid

blue curve indicates a ﬁt from which we extract the resonance

frequency and estimate the quality factor (see main text).

arXiv:2211.00763v2 [cond-mat.mes-hall] 3 Dec 2022

A diﬀerent approach for measuring the DQD is real-

ized by probing a resonator coupled to the source contact

of a DQD [21–23]. This approach is further simpliﬁed by

connecting the resonator to a plunger gate, performing

gate-dispersive sensing [24]. This technique has enabled

measurements of the relaxation and dephasing times of

hole spins in a Ge/Si core/shell nanowire DQD using a

lumped-element resonator [25]. First attempts of cou-

pling Ge/Si nanowires to on-chip superconducting res-

onators were based on low-impedance resonators with a

weak charge-photon coupling and in a regime of many

holes present in the nanowire [26].

In this work, we extend the existing measurements

by coupling one of the two quantum dots to a high-

impedance superconducting resonator, see Fig. 1. The

used coupling scheme allows us to detect charging in the

other dot by means of capacitive charge sensing [27–30].

We map the charge-stability diagram using both, direct

current measurements and resonator spectroscopy. Fur-

thermore, we gate the nanowire to a regime of low hole

occupancy where no direct current through the nanowire

can be observed (pinch-oﬀ). In this regime, the resonator

spectroscopy signal reveals the presence of several more

holes in the investigated dot. Finally, by further increas-

ing the gate voltages, we ﬁnd indications of the depletion

of the last hole in the investigated dot.

II. DEVICE DESCRIPTION

An overview of the device under investigation is shown

in Fig. 1a) and b). The device consists of a hybrid

resonator-nanowire architecture. A notch-type half-wave

(λ/2) resonator with a central frequency fr≈3.1 GHz

is deﬁned in a NbTiN ﬁlm of thickness ∼10 nm, cen-

ter conductor width of ∼370 nm and a distance between

center conductor and ground plane of ∼35 µm. The

resonator is capacitively coupled at a voltage anti-node

to a feedline which is used for resonator readout. At

the middle of the center conductor (voltage node), the

resonator is dc biased. In front of the dc bias pad, a

meandered inductor ensures suﬃcient frequency detun-

ing between the λ/2 mode and a second, quarter-wave

mode that forms due to the T-shaped section of the res-

onator. Thereby, microwave-leakage through the dc bias

line is reduced [31]. The resonator’s second voltage anti-

node is galvanically connected to one out of ﬁve bottom

gates. The bottom gates are fabricated by Ti/Pd sand-

wiched by ALD-grown HfO2and have a width of approx-

imately 25 nm. The gate pitch is 50 nm. On top of the

bottom gates a Ge/Si core/shell nanowire is determin-

istically placed using a micromanipulator, see Fig. 1 b).

All presented measurements are performed in a dilution

refrigerator at a base temperature of 35 mK.

The transmission S21 through the feedline in proximity

to the notch-type resonator as a function of frequency f

is given by [32, 33]

S21(f) = aeiαe−2πifτ h1−eiΦ/(1+Qc/Qloss )

1+2i(f/fr−1)/(1/Qc+1/Qloss )i,

where a,αand τaccount for the microwave propaga-

tion through the wiring in the cryostat and the resonance

is described by its resonance frequency fr, the coupling

quality factor Qcand the loss quality factor Qloss. The

term eiΦaccounts for the Fano shape of the observed res-

onance arising from impedance mismatches in the feed-

line coupled to the resonator [34].

We identify the resonance of the superconducting res-

onator at around 3.1 GHz by considering its tempera-

ture dependence. The measured transmission (phase

and magnitude) through the feedline around resonance is

shown on Fig. 1c). The signal is superimposed on a large

standing-wave background (see Fig. A.1 in the appendix.)

which we attribute to an impedance mismatch between

the feedline and the 50-Ohm environment of the cryostat.

Despite the large ﬂuctuations in the transmission mag-

nitude, we are able to ﬁt the phase of the transmission

(solid, blue curve in Fig. 1c) and extract the resonance

frequency fr= 3.111 GHz, and estimate the Q factors

Qc≈600 and Qloss ≈600. The uncertainity in these val-

ues originates from the large standing wave background.

We perform a ﬁnite-element simulation of the res-

onator using Sonnet and recover the resonance frequency

of the central mode of the resonator half-wave mode

when taking into account a sheet kinetic inductance of

70 pH/. Together with the stray line capacitance of

75 pF/m, this corresponds to a resonator impedance

of 1.6 kΩ, much larger than the standard 50 Ω, hence

improving the coupling strength between resonator and

double quantum dot [35, 36]. We attribute the rather low

Qloss to microwave leakage from the resonator to the dc

lines via capacitive coupling through the set of bottom

gates [37]. Indeed, using Sonnet, we estimate the mutual

capacitance between two neighbouring bottom gates to

be Cgg ≈800 aF. In future works, the mutual capacitance

can likely be decreased with an optimised gate geometry

and the resulting microwave leakage might be further re-

duced via improved ﬁltering of the dc lines [31, 38].

III. CHARGE SENSING

Due to the Fermi level pinning stemming from the stag-

gered Si/Ge band-gap alignment, the Ge/Si core/shell

nanowire is a hole conductor. Therefore, by applying

positive gate voltages, we deﬁne the barrier potentials on

the gates g1, g3and g5. This gives rise to the conﬁnement

potential of two quantum dots whose electrochemical po-

tentials are tuned by the gates g2and g4[39].

In the following, we investigate two diﬀerent conﬁne-

ment conﬁgurations. The ﬁrst conﬁguration is schemati-

cally depicted in Figure 2a). Here, two fairly symmetric

quantum dots, the left (L) and the right (R), are formed

between the gates g1 and g3 and between the gates g3

and g5. In this conﬁguration, each dot couples to its re-

spective neighbors as shown on the sketch in Figure 2a).

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Charge-sensingofaGe/Sicore/shellnanowiredoublequantumdotusingahigh-impedancesuperconductingresonatorJ.H.Ungerer,1,2,P.ChevalierKwon,1,T.Patlatiuk,1J.Ridderbos,1,3A.Kononov,1D.Sarmah,1E.P.A.M.Bakkers,4,5D.Zumbuhl,1,2andC.Schonenberger1,2,y1DepartmentofPhysics,UniversityofBasel,Klingelbergstrasse8...

展开>> 收起<<

Charge-sensing of a GeSi coreshell nanowire double quantum dot using a high-impedance superconducting resonator.pdf

共7页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Charge-sensing of a GeSi coreshell nanowire double quantum dot using a high-impedance superconducting resonator

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: