Microwave optomechanics with a carbon nanotube ... and some news - - PowerPoint PPT Presentation

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

Microwave optomechanics with a carbon nanotube

... and some news about MoS2 too ...

Andreas K. H¨ uttel University of Regensburg

current affiliation: Aalto University, Espoo, Finland

IWEPNM 2020, Kirchberg in Tirol, 13 March 2020

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

suspended carbon nanotubes: NEMS and quantum transport

nanotube metal

• D. R. Schmid et al., PRB 91, 155439 (2015), K. J. G. G¨
• tz et al., PRL 120, 246802 (2018), M. Marga´

nska et al., PRL 122, 086802 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

low-temperature transport: Coulomb blockade

tunnel barriers between contacts and nanotube; low temperature kBT ≪ e2/C: quantum dot all following measurements at Tbase 10mK (unless noted)

d s

source dot gate

N el.

drain

Vg Vsd I d s

Vg Coulomb blockade

d s

single electron tunneling Vg dI dVsd

Vsd≈0 (linear response regime)

CB N-1 el. CB N el. CB N+1 el. SET SET SET

schematic drawing

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

clean transport spectrum, shell effects

• K. J. G. G¨
• tz et al., PRL 120, 246802 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

driven transversal vibrations, “the old-fashioned way”

• transport spectroscopy setup plus rf irradiation
• mechanical resonance visible in time-averaged

current

I (pA) I (nA) f (MHz)

• 64.5 dBm

f (MHz)

• 17.8 dBm

Q=140670 2 1 100 300 500 88 87 86 293.41 293.42 293.43 293.44

(different device)

• A. K. H¨

uttel et al., Nano Lett. 9, 2547 (2009)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

how about doing microwave optomechanics with a nanotube?

• C. A. Regal

, Nature Physics , 555 (2008) et al. 4

10 µm x 6 mm

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

highly active field of research

g zg mass

• M. Aspelmeyer et al., Rev. Mod. Phys. 86, 1391 (2014)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

how about doing microwave optomechanics with a nanotube?

• C. A. Regal

, Nature Physics , 555 (2008) et al. 4

10 µm x 6 mm

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

dispersive optomechanical coupling

moving element modulates CPW resonator capacitance

↔

• ptical cavity with moving mirror

microwave drive LC circuit vibrating capacitor

ˆ

Hint = −¯ hg0 ˆ a†ˆ a

ˆ

b + ˆ b† g0

= ∂ωcav ∂x

• x=0

xzpf

= ωcav

2Ccav

∂Ccav ∂x

• x=0

xzpf

• M. Aspelmeyer et al., Rev. Mod. Phys. 86, 1391 (2014)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

numbers for dispersive coupling?

carbon nanotube graphene drum aluminum beam

• V. Singh et al. (2014)
• C. A. Regal et al. (2008)

mass m 10−20 kg 2× 10−15 kg resonance frequency fmech 503MHz 36MHz 2.3MHz quality factor Qmech 104 105 105 zero point fluct. xzpf 2pm 30 fm 40 fm cavity frequency fcav 5.7GHz 5.9GHz 5GHz cavity Q Qcav 437 25000 10000 cavity occupation ncav 6.75× 104 (6.75× 104) (6.75× 104) coupling capacitance Cg 2.6aF 580aF capacitance sensitivity

∂Cg/∂x

1pF/m 170pF/m zero-photon coupling g0 2.9mHz 0.83Hz 0.15Hz dispersive coupling g0Qcav/fcav 2× 10−10 3× 10−6 3× 10−7 sideband cooling rate

κopt(∝ ncav) ∼ 10−7 Hz

0.77Hz 12mHz A single-wall carbon nanotube is a great mechanical resonator, but is also annoyingly small.

• S. Blien et al., Nature Comm. 11, 1636 (2020); V. Singh et al., Nat. Nano 9, 820 (2014); C. A. Regal et al., Nat. Phys. 4, 555 (2008)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

we built it anyway (geometry is not everything!)

1 mm

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

nanotube deposition area

100 µm

• gate finger connected to cavity
• isolation layer (cross-linked PMMA)
• long resistive meanders as RF block
• four gold electrodes

(source, drain, and two for cutting)

• deep-etched areas to allow fork deposition
• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

nanotube growth on commercial quartz tuning forks

4 . 8 m m 100 µm 1 µm

nanotube

nominally 1nm Co sputter-deposited as catalyst; growth in high gas flow

details: S. Blien et al., PSSb 255, 1800118 (2018)

• S. Blien et al., PSSb 255, 1800118 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

nanotube deposition

1 µm

fork CNT electrodes

1 2 3 4

lower fork, detect contact electrically, burn outer segments with current, retract fork

details: S. Blien et al., PSSb 255, 1800118 (2018)

• S. Blien et al., PSSb 255, 1800118 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

now this is cooled to 10mK

1.8 K 4 K 300 K 700 mK 100 mK 10 mK

port 1 port 2

• 20 dB
• 10 dB
• 10 dB
• 20 dB
• 3 dB
• 10 dB

+30 dB VNA microwave source HEMT + 30dB V +30 dB filter filter

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

• ptomechanically induced (in)transparency (I)

1 mm

V

bias

V

gate

Idc VNA 1 2 drive

probe drive

f

probe drive

fmech f f

cavity reson.

fmech

• strong drive at fdrive = fcav − fmech (red sideband)
• probe transmission with weak signal fprobe near

fcav

• when fprobe − fdrive = fmech:

interaction with mechanics −

→ signal loss

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

• ptomechanically induced (in)transparency (II)
• 32,0
• 31,5
• 31,0

dB

• 30.7
• 30.65
• 30.6

5.7424 5.7426

• 32,0
• 31,5
• 31,0

dB

• 31.05
• 31

5.7406 5.7408

5.740 5.742

(GHz) fprobe = 5.23989 GHz fdrive = 5.23809 GHz fdrive

• clear OMIT feature for

fprobe − fdrive = fmech

• intransparency due to specific cavity /

detection arrangement

• would not be visible with

g0 ∼ 10mHz (even at high drive power)

• obviously something was

missing in the theory

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

• ptomechanically induced (in)transparency (III) – now with gate!

5.74240 5.74245

• 1.191
• 1.189
• 1.187

V (V)

g

(GHz) 20 10 50

• 1.191
• 1.189
• 1.187

V (V)

g

• 31
• 30.8

(dB) |S21|2 /2π

p

ω g (kHz) /2π g (Hz)

0/2π

75 100

• we trace the OMIT signal over a

sharp CB oscillation

• “dip” position

↔

fmech(Vg)

• depth, width of “dip”

↔

• ptomechanical coupling g
• fit each trace, extract g(Vg)
• large on flanks of SET peak

g ≃ 20kHz g0 = g/√ncav ≃ 95Hz

• in Coulomb blockade & at de-

generacy point zero / no signal

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

another type of capacitance

• Capacitance “seen” by the coplanar resonator:

CCNT = e ∂ Qg

∂Vg = ··· = e Cg

CΣ

∂ N ∂Vg + const.

• The nanotube moves

− →

Cg changes by δCg

− →

the Coulomb oscillations shift in Vg

• We define an effective gate voltage modulation equivalent to the motion:

Cg δV eff

g

= Vg δCg

• This results in

∂CCNT ∂x = ∂CCNT ∂V eff

g

∂V eff

g

∂x = ··· = e ∂ 2 N ∂V 2

g

Vg CΣ

∂Cg ∂x

amplification factor!

• S. Blien et al., Nature Comm. 11, 1636 (2020); similar concepts in articles of E. Laird, M. Sillanp¨

a¨ a, T. Duty

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

Coulomb blockade enhancement of coupling

N(Vg): tunneling through

Lorenz-broadened level, width Γ

∂CCNT ∂x = e ∂ 2 N ∂V 2

g

Vg CΣ

∂Cg ∂x

g0 = ωcav 2Ccav

∂CCNT ∂x

• x=0

xzpf insert device values ...

1 1 5 10 20 20 80

• 1.19
• 1.188
• 1.186

Vg (V) g/2π (kHz) dI/dV (a.u.) <N> C (aF)

CNT

• 1.19
• 1.188
• 1.186

Vg (V) g (Hz)

0/2π

30 100

d dVg

∝

d dVg

∝

charge q-capacitance coupling

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

Coulomb blockade enhancement of coupling

N(Vg): tunneling through

Lorenz-broadened level, width Γ

∂CCNT ∂x = e ∂ 2 N ∂V 2

g

Vg CΣ

∂Cg ∂x

g0 = ωcav 2Ccav

∂CCNT ∂x

• x=0

xzpf insert device values ...

1 1 5 10 20 20 80

• 1.19
• 1.188
• 1.186

Vg (V) g/2π (kHz) dI/dV (a.u.) <N> C (aF)

CNT

• 1.19
• 1.188
• 1.186

Vg (V) g (Hz)

0/2π

30 100

d dVg

∝

d dVg

∝ x 5.77

• S. Blien et al., Nature Comm. 11, 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

numbers for dispersive coupling?

carbon nanotube graphene drum aluminum beam

• V. Singh et al. (2014)
• C. A. Regal et al. (2008)

mass m 5× 10−21 kg 2× 10−15 kg resonance frequency fmech 503MHz 36MHz 2.3MHz quality factor Qmech 104 105 105 zero point fluct. xzpf 2pm 30 fm 40 fm cavity frequency fcav 5.74GHz 5.9GHz 5GHz cavity Q Qcav 497 25000 10000 cavity occupation ncav 6.75× 104 (6.75× 104) (6.75× 104) coupling capacitance Cg 10aF 580aF zero-photon coupling g0 95Hz 0.83Hz 0.15Hz dispersive coupling g0Qcav/fcav 8× 10−6 3× 10−6 3× 10−7

• sideb. cooling rate

κopt(∝ ncav)

211Hz 0.77Hz 12mHz Suddenly this is much more interesting (even for our low ncav and Qcav).

• S. Blien et al., Nature Comm. 11, 1636 (2020); V. Singh et al., Nat. Nano 9, 820 (2014); C. A. Regal et al., Nat. Phys. 4, 555 (2008)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

• utlook
• first optomechanical system with electronic quantum confinement
• improve coplanar cavity parameters, coupling, amplification
• re-arrange attenuators, better HEMT amplifier, insert a JPA
• simulate and optimize cavity geometry
• improve dc cable filtering
• ...
• g κm,κcav reachable, C ∼ nth reachable

− →

quantum control of motion!

• good cavity limit: cooling, heating, temperature readout, energy balance with single electron tunneling!

(note that kBTbase hfmech)

• bad cavity limit: conductance measurement with 100 MHz bandwidth
• quantum state transfer, mechanical quantum information processing

... and much more ...

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

And now for something completely different.

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

And now for something completely different.

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

let’s go TMDC!

• first synthesis of WS2 and MoS2 multiwall

nanotubes in 1992 by R. Tenne

• all chiralities semiconducting
• band gap decreases with radius
• intrinsic superconductivity,

e.g., in WS2 nanotubes via ionic gating:

• F. Qin et al., Nat. Comm. 8, 14465 (2017)
• F. Qin et al., Nano Letters 18, 6789 (2018)
• we get spatial confinement for free!
• no previous work on quantum dots and low

temperature transport spectroscopy

• R. Tenne et al., Nature 360, 444 (1992); G. Seifert et al., PRL 85, 146 (2000)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

TMDC nanotube growth (group M. Remˇ skar, Ljubljana)

100nm

• two-zone furnace
• iodine-assisted chemical transport reaction
• M. Remˇ

skar et al., APL 69, 351 (1996)

• slow, near-equilibrium growth
• near defect-free nanostructures
• mixture of 2d and 1d morphologies
• individual multiwall tubes
• diameter from ∼ 10nm up to several µm
• length up to several millimeters
• S. Reinhardt et al., pssRRL 13, 1900251 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

MoS2 nanotube device, T = 300K

• 2

2

• 20

20 I (nA) VBias

Gate = -30V

VGate = 0V VGate = 30V 1

• 20

20 I (nA) VBias = 10mV

Lch=1μm Au contacts

VGate

• n-type field effect
• linear I(V) characteristics
• Ron ≈ 15MΩ
• Fermi-level pinning to conduction band
• not perfect yet, but promising

metal MoS2

Eg e-

• S. Reinhardt et al., pssRRL 13, 1900251 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

stability diagram, T = 0.3K (1) ΔE

• 2

2

G (V)

• 9

9 VSD (mV)

• 4 e2/h)

doesn’t look that nice yet, but...

• S. Reinhardt et al., pssRRL 13, 1900251 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

stability diagram, T = 0.3K (2)

ΔE

• 2

2

G (V)

• 9

9 VSD (mV)

• 4 e2/h)

0.55

G (V)

• 10

10 VSD (mV)

• 4 e2/h)
• large scale: disordered system of quantum dots
• zoom: highly regular Coulomb oscillations
• trap states at the metal contacts!

capacitances confirm this

• S. Reinhardt et al., pssRRL 13, 1900251 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

excitation lines!

• 4
• 3

VG (V)

• 8

8 VSD (mV) 8 dI/dV (10-4 e2/h) ΔE

• 3.2
• 3

VG (V) 2 7 VSD (mV) 3 dI/dV (10-4 e2/h)

• excitation lines visible in conductance,

∆E ∼ 500µeV

• expected mean level spacing for a chaotic

quantum dot (assuming r = 10nm, l = 450nm):

∆E = ¯

h2π m∗A ∼ 10µeV

• 1D geometry, large Nel −

→ large ∆E?

• band structure calculations and 2d

magnetotransport data exist

• no theory on confinement spectrum yet
• many more measurements needed
• S. Reinhardt et al., pssRRL 13, 1900251 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

thanks

Stefan Blien Patrick Steger Niklas H¨ uttner Richard Graaf Simon Reinhardt Christian B¨ auml Luka Pirker

• Prof. Maja Remˇ

skar

Thomas Huber

• Dr. Ondrej Vavra
• Dr. Andreas Pfeffer
• Prof. Dieter Weiss
• Prof. Christoph Strunk
• Prof. Eva Weig
• Prof. Florian Marquardt
• Prof. Yaroslav Blanter
• Prof. Pertti Hakonen

... and many others

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks

thank you! — questions?

5.74240 5.74245

• 1.191
• 1.189
• 1.187

V (V)

g

(GHz) 20 10 50

• 1.191
• 1.189
• 1.187

V (V)

g

• 31
• 30.8

(dB) |S21|2 /2π

p

ω g (kHz) /2π g (Hz)

0/2π

75 100

Microwave optomechanics: S. Blien et al., Nature Comm. 11, 1636 (2020) MoS2 nanotubes: S. Reinhardt et al., pssRRL 13, 1900251 (2019)