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Charge Detection in Gate-Defined Bilayer Graphene Quantum Dots Annika Kurzmann, Hiske Overweg, Marius Eich, Alessia Pally, Peter Rickhaus, Riccardo Pisoni, Yongjin Lee, Takashi Taniguchi, Kenji Watanabe, Thomas Ihn, and Klaus Ensslin Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b01617 • Publication Date (Web): 16 Jul 2019 Downloaded from pubs.acs.org on July 19, 2019
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Nano Letters
❈❤❛r❣❡ ❉❡t❡❝t✐♦♥ ✐♥ ●❛t❡✲❉❡✜♥❡❞ ❇✐❧❛②❡r ●r❛♣❤❡♥❡ ◗✉❛♥t✉♠ ❉♦ts ∗✱†
❆♥♥✐❦❛ ❑✉r③♠❛♥♥✱
†
P❡t❡r ❘✐❝❦❤❛✉s✱
†
❍✐s❦❡ ❖✈❡r✇❡❣✱
†
❘✐❝❝❛r❞♦ P✐s♦♥✐✱
‡
❚❛❦❛s❤✐ ❚❛♥✐❣✉❝❤✐✱
†❙♦❧✐❞
†
▼❛r✐✉s ❊✐❝❤✱
†
❨♦♥❣❥✐♥ ▲❡❡✱
†
❚❤♦♠❛s ■❤♥✱
†
❆❧❡ss✐❛ P❛❧❧②✱
‡
❑❡♥❥✐ ❲❛t❛♥❛❜❡✱
†
❛♥❞ ❑❧❛✉s ❊♥ss❧✐♥
❙t❛t❡ P❤②s✐❝s ▲❛❜♦r❛t♦r②✱ ❊❚❍ ❩ür✐❝❤✱ ❈❍✲✽✵✾✸ ❩ür✐❝❤✱ ❙✇✐t③❡r❧❛♥❞
‡◆❛t✐♦♥❛❧
■♥st✐t✉t❡ ❢♦r ▼❛t❡r✐❛❧ ❙❝✐❡♥❝❡✱ ✶✲✶ ◆❛♠✐❦✐✱ ❚s✉❦✉❜❛ ✸✵✺✲✵✵✹✹✱ ❏❛♣❛♥
❊✲♠❛✐❧✿ ❛♥♥✐❦❛❦❅♣❤②s✳❡t❤③✳❝❤
❆❜str❛❝t ❲❡ r❡♣♦rt ♦♥ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ✐♥ ❡❧❡❝tr♦st❛t✐❝❛❧❧②✲❞❡✜♥❡❞ q✉❛♥t✉♠ ❞♦t ❞❡✈✐❝❡s ✐♥ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ✉s✐♥❣ ❛♥ ✐♥t❡❣r❛t❡❞ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❚❤❡ ❞❡✈✐❝❡ ✐s ❢❛❜r✐❝❛t❡❞ ✇✐t❤♦✉t ❛♥② ❡t❝❤✐♥❣ ❛♥❞ ❢❡❛t✉r❡s ❛ ❣r❛♣❤✐t❡ ❜❛❝❦ ❣❛t❡✱ ❧❡❛❞✐♥❣ t♦ ❤✐❣❤ q✉❛❧✐t② q✉❛♥t✉♠ ❞♦ts✳ ❚❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r ✐s ❜❛s❡❞ ♦♥ ❛ s❡❝♦♥❞ q✉❛♥t✉♠ ❞♦t s❡♣❛r❛t❡❞ ❢r♦♠ t❤❡ ✜rst ❞♦t ❜② ❞❡♣❧❡t✐♦♥ ✉♥❞❡r♥❡❛t❤ ❛ ✶✺✵ ♥♠ ✇✐❞❡ ❣❛t❡✳ ❲❡ s❤♦✇ t❤❛t ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡s ✐♥ t❤❡ s❡♥s✐♥❣ ❞♦t ❛r❡ s❡♥s✐t✐✈❡ t♦ ✐♥❞✐✈✐❞✉❛❧ ❝❤❛r❣✐♥❣ ❡✈❡♥ts ♦♥ t❤❡ ♥❡❛r❜② q✉❛♥t✉♠ ❞♦t✳ ❚❤❡ ♣♦t❡♥t✐❛❧ ❝❤❛♥❣❡ ❞✉❡ t♦ s✐♥❣❧❡ ❡❧❡❝tr♦♥ ❝❤❛r❣✐♥❣ ❝❛✉s❡s ❛ st❡♣✲❧✐❦❡ ❝❤❛♥❣❡ ✭✉♣ t♦ ✼✼✪✮ ✐♥ t❤❡ ❝✉rr❡♥t t❤r♦✉❣❤ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ ❝❤❛r❣✐♥❣ st❛t❡s ♦❢ ❛ q✉❛♥t✉♠ ❞♦t ✇✐t❤ t✉♥❛❜❧❡ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs ❛♥❞ ♦❢ ❝♦✉♣❧❡❞ q✉❛♥t✉♠ ❞♦ts ❝❛♥ ❜❡ ❞❡t❡❝t❡❞✳
❑❡②✇♦r❞s ❇✐❧❛②❡r ❣r❛♣❤❡♥❡✱ q✉❛♥t✉♠ ❞♦t✱ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥✱ t✉♥♥❡❧✐♥❣✱ ♠✉❧t✐❞♦ts
✶
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
■♥tr♦❞✉❝t✐♦♥
●r❛♣❤❡♥❡ ✐s ❛ ♣r♦♠✐s✐♥❣ ❝❛♥❞✐❞❛t❡ ❢♦r ❢✉t✉r❡ ♥❛♥♦✲❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s ✐♥❝❧✉❞✐♥❣ ❜✉✐❧❞✐♥❣ ❜❧♦❝❦s ❢♦r q✉❛♥t✉♠ ✐♥❢♦r♠❛t✐♦♥ ♣r♦❝❡ss✐♥❣✳ ❘❡❛s♦♥s ❛r❡ t❤❡ ❡①♣❡❝t❡❞ ❧♦♥❣ s♣✐♥ ❧✐❢❡t✐♠❡s ✶ ❛♥❞ ❤✐❣❤ ❝❛rr✐❡r ♠♦❜✐❧✐t✐❡s✳ ✷✕✹ ❊①♣❡r✐♠❡♥t❛❧❧② t❤❡s❡ s♣✐♥ ❧✐❢❡t✐♠❡s ❤❛✈❡ ♥♦t ❜❡❡♥ ❞❡♠♦♥str❛t❡❞ ②❡t✳ ❋♦r ♣r♦❣r❡ss ✐♥ t❤✐s ❞✐r❡❝t✐♦♥ ✺ ❛ ❞❡✈✐❝❡ ✐s ♥❡❡❞❡❞ t❤❛t ❛❧❧♦✇s t♦ ❝♦♥✜♥❡ ❝❤❛r❣❡s ❛♥❞ s✐♠✉❧t❛♥❡♦✉s❧② ♠❡❛s✉r❡ t❤❡✐r ❞②♥❛♠✐❝s ✐♥ ❛ t✐♠❡✲r❡s♦❧✈❡❞ ✇❛②✳ ❚❤✐s ✐s ♣♦ss✐❜❧❡ ✇✐t❤ ❛ ❝❤❛r❣❡ ❞❡t❡❝t♦r ✐♥ ❝❧♦s❡ ♣r♦①✐♠✐t② t♦ ❛ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦t ✭◗❉✮✳ ■♥ ●❛❆s ❜❛s❡❞ ❞❡✈✐❝❡s ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ◗❉s ❛♥❞ ◗P❈s ❛❧❧♦✇❡❞ t♦ ❞❡t❡❝t s♣✐♥✲q✉❜✐t st❛t❡s ✺✱✻ ❛♥❞ ♠♦❧❡❝✉❧❛r st❛t❡s ✐♥ ❝♦✉♣❧❡❞ ◗❉s✳ ✼ ❋✉rt❤❡r♠♦r❡✱ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ❝❛♥ ❜❡ ✉s❡❞ t♦ ✐♥✈❡st✐❣❛t❡ t✉♥♥❡❧✐♥❣ ❞②♥❛♠✐❝s ♦❢ ❝❤❛r❣❡s ✐♥ ❛ t✐♠❡✲r❡s♦❧✈❡❞ ✇❛② ✽✱✾ ❛♥❞ t♦ ♦❜t❛✐♥ t❤❡ ❢✉❧❧ ❝♦✉♥t✐♥❣ st❛t✐st✐❝s ♦❢ t❤❡ ❝❤❛r❣❡ ❝✉rr❡♥t ❛♥❞ t❤❡ ❝❤❛r❣❡ ♦❝❝✉♣❛t✐♦♥✳ ❘❡❝❡♥t ❡①♣❡r✐♠❡♥ts s❤♦✇ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ❛♥❞ ♠❡❛s✉r❡♠❡♥t ♦❢ q✉❛♥t✉♠ ❞♦ts ✶✵✕✶✷ ❛♥❞ q✉❛♥t✉♠ ♣♦✐♥t ❝♦♥t❛❝ts ✶✶✱✶✸✱✶✹ ✐♥ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✱ t❤❛t ❛r❡ ❝♦♠♣❛r❛❜❧❡ t♦ ●❛❆s ❞❡✈✐❝❡s✳ ❇✐❧❛②❡r ❣r❛♣❤❡♥❡ ♦✛❡rs t❤❡ ♣♦ss✐❜✐❧✐t② t♦ ❡❧❡❝tr♦st❛t✐❝❛❧❧② ❞❡✜♥❡ ♥❛♥♦str✉❝t✉r❡s ❜② ♦♣❡♥✐♥❣ ❛ ❜❛♥❞ ❣❛♣ t❤r♦✉❣❤ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛ ❞✐s♣❧❛❝❡♠❡♥t ✜❡❧❞ ♥♦r♠❛❧ t♦ t❤❡ ❜✐❧❛②❡r ♣❧❛♥❡✳ ✶✺✕✶✼ ❲✐t❤ ❛ s✉✐t❛❜❧❡ ❞❡s✐❣♥ ♦❢ t♦♣ ❛♥❞ ❜❛❝❦ ❣❛t❡ ❡❧❡❝tr♦❞❡s✱ ✐t ❛❧❧♦✇s ❢♦r ❡❧❡❝tr♦st❛t✐❝ ❝♦♥✜♥❡♠❡♥t ♦❢ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ❤✐❣❤ q✉❛❧✐t② ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ❞❡✈✐❝❡s✳ ❚❤❡s❡ ❞❡✈✐❝❡s ✉s❡ ❡♥❝❛♣s✉❧❛t✐♦♥ ✐♥ ❤❡①❛❣♦♥❛❧ ❜♦r♦♥ ♥✐tr✐❞❡ ✭❤❇◆✮✱ ✶✽ ❡❞❣❡ ❝♦♥t❛❝ts ✶✾ ❛♥❞ ❛ ❣r❛♣❤✐t❡ ❜❛❝❦ ❣❛t❡✱ ✶✵✕✶✷ t❤❛t s❝r❡❡♥s ❝❤❛r❣❡ ✐♠♣✉r✐t✐❡s tr❛♣♣❡❞ ✐♥ t❤❡ s✐❧✐❝♦♥ ♦①✐❞❡ s✉❜str❛t❡✳ ✷✵ ■♥ ♣r❡✈✐♦✉s ❡①♣❡r✐♠❡♥ts✱ ❡①❢♦❧✐❛t❡❞ ❣r❛♣❤❡♥❡ ✢❛❦❡s ❤❛✈❡ ❜❡❡♥ ❡t❝❤❡❞ t♦ ❢❛❜r✐❝❛t❡ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ ✷✶✕✷✸ s✐♥❣❧❡✲❡❧❡❝tr♦♥✲tr❛♥s✐st♦rs ✭❙❊❚s✮ ✷✹ ❛♥❞ q✉❛♥t✉♠ ❞♦ts ✷✺✱✷✻ ✇✐t❤ ❝❤❛r❣❡ ❞❡✲ t❡❝t♦r✳ ✷✼✕✸✶ ❆ ❞✐s❛❞✈❛♥t❛❣❡ ♦❢ t❤✐s ❢❛❜r✐❝❛t✐♦♥ ♠❡t❤♦❞ ❛r❡ ❝❤❛r❣❡ ❝❛rr✐❡r ❧♦❝❛❧✐③❛t✐♦♥s ❛t t❤❡ r♦✉❣❤ s❛♠♣❧❡ ❡❞❣❡s✱ t❤❛t ❝❛♥ ❧❡❛❞ t♦ tr❛♥s♠✐ss✐♦♥ r❡s♦♥❛♥❝❡s ❢r♦♠ t❤❡ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs ✇❤✐❝❤ ♠❛② ❞♦♠✐♥❛t❡ t❤❡ ❡♥t✐r❡ ❞❡✈✐❝❡ ❜❡❤❛✈✐♦r ✐♥ ❝❡rt❛✐♥ ♣❛r❛♠❡t❡r r❡❣✐♠❡s✳ ✸✷ ❍❡r❡✱ ✇❡ ✉s❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ✇✐t❤ ✐ts ❡❧❡❝tr♦st❛t✐❝❛❧❧② ✐♥❞✉❝❡❞ ❜❛♥❞ ❣❛♣ t♦ ❢❛❜r✐❝❛t❡ ❛ ❢✉❧❧② ❣❛t❡✲❞❡✜♥❡❞ ❞❡✈✐❝❡ ✇✐t❤ q✉❛♥t✉♠ ❞♦ts✱ t❤❛t ❛r❡ ❛❧s♦ ✉s❡❞ ❛s ❝❤❛r❣❡ ❞❡t❡❝t♦rs✳ ❚❤❡ q✉❛❧✐t② ♦❢ t❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts ❛♥❞ t❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ t❤❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ✷
ACS Paragon Plus Environment
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Nano Letters
♠❛t❝❤❡s t❤❛t ♦❢ t❤❡ tr❛❞✐t✐♦♥❛❧ s❡♠✐❝♦♥❞✉❝t♦rs ❙✐ ❛♥❞ ●❛❆s✳ ❆ ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ✐♥ ❞✐✛❡r❡♥t ❡t❝❤❡❞ ❞❡✈✐❝❡s ✇✐t❤ ♦✉r ❡❧❡❝tr♦st❛t✐❝❛❧❧② ❞❡✜♥❡❞ ❞❡✈✐❝❡ ✐s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✶✳ ❲❡ ♠❡❛s✉r❡ ❛ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ t❤❛t ❡①❝❡❡❞s t❤❡ ❜❡st ♣r❡✈✐♦✉s r❡s✉❧ts ❜② ♠♦r❡ t❤❛♥ ❛ ❢❛❝t♦r ♦❢ t✇♦✳ ❋✉rt❤❡r♠♦r❡✱ ❛ t✉♥❛❜❧❡ ❣❛t❡✲❞❡✜♥❡❞ q✉❛♥t✉♠ ❞♦t ✐s ✉s❡❞ ❛s ❝❤❛r❣❡ ❞❡t❡❝t♦r ✐♥st❡❛❞ ♦❢ ❛ r❛♥❞♦♠ r❡s♦♥❛♥❝❡ ✐♥ ❛ ♥❛♥♦ r✐❜❜♦♥✳ ❚❤❡ q✉❛❧✐t② ♦❢ ♦✉r ❞❡✈✐❝❡ ❛♥❞ t❤❡ ❣♦♦❞ ❝♦♥tr♦❧ ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r ♠❛❦❡s ✐t ✐♥t❡r❡st✐♥❣ ❢♦r ❢✉t✉r❡ ✐♥✈❡st✐❣❛t✐♦♥s ♦❢ t❤❡ s♣✐♥ ❛♥❞ ✈❛❧❧❡② ❝♦❤❡r❡♥❝❡ ❛♥❞ r❡❧❛①❛t✐♦♥ r❛t❡s✳ ❚❛❜❧❡ ✶✿ ❈♦♠♣❛r✐s♦♥ ♦❢ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ♠❡❛s✉r❡♠❡♥ts ✐♥ ❣r❛♣❤❡♥❡ ✐♥ t❤❡ ❧❛st ②❡❛rs✳ ❲❡ ❝♦♠♣❛r❡ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ❛s t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ❝❤❛♥❣❡ ∆G ✐♥ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r ✐♥ ❞❡✈✐❝❡s ✉s✐♥❣ ❞✐✛❡r❡♥t ❞❡t❡❝t♦rs ❛♥❞ ❢❛❜r✐❝❛t✐♦♥ ♠❡t❤♦❞s✳ P✉❜❧✐❝❛t✐♦♥ ∆G(e2 /h) ❋❛❜r✐❝❛t✐♦♥ ●ütt✐♥❣❡r ❡t ❛❧✳ ✭✷✵✵✽✮ ✷✽ 10−4 ❊t❝❤❡❞ ✷✾ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✵✮ < 0.1 ❊t❝❤❡❞ ❋r✐♥❣❡s ❡t ❛❧✳ ✭✷✵✶✶✮ ✸✵ ✵✳✵✵✺ ❊t❝❤❡❞ ✸✸ ●ütt✐♥❣❡r ❡t ❛❧✳ ✭✷✵✶✶✮ ✵✳✵✺ ❊t❝❤❡❞ ✸✶ ❱♦❧❦ ❡t ❛❧✳ ✭✷✵✶✸✮ ✵✳✵✵✷ ❊t❝❤❡❞ ❚❤✐s ✇♦r❦ ✭✷✵✶✾✮ ✵✳✷ ●❛t❡✲❞❡✜♥❡❞
❉❡t❡❝t♦r ❘❡s♦♥❛♥❝❡ ✐♥ ❛ ♥❛♥♦r✐❜❜♦♥ ❙❊❚ ❘❡s♦♥❛♥❝❡ ✐♥ ❛ ♥❛♥♦r✐❜❜♦♥ ❘❡s♦♥❛♥❝❡ ✐♥ ❛ ♥❛♥♦r✐❜❜♦♥ ❘❡s♦♥❛♥❝❡ ✐♥ ❛ ♥❛♥♦r✐❜❜♦♥ ◗✉❛♥t✉♠ ❞♦t r❡s♦♥❛♥❝❡
❈❤❛r❛❝t❡r✐③❛t✐♦♥ ❚❤❡ ✈❛♥✲❞❡r✲❲❛❛❧s ❤❡t❡r♦str✉❝t✉r❡ ❤❛s ❜❡❡♥ ❢❛❜r✐❝❛t❡❞ ✉s✐♥❣ t❤❡ ❞r② tr❛♥s❢❡r ♠❡t❤♦❞✳ ✶✽ ❆ s❝❤❡♠❛t✐❝ ♦❢ t❤❡ st❛❝❦ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✶❛✳ ■t ❝♦♥s✐sts ✭❢r♦♠ ❜♦tt♦♠ t♦ t♦♣✮ ♦❢ ❛ ❣r❛♣❤✐t❡ ❜❛❝❦ ❣❛t❡ ✭❣r❡②✮✱ ❛ ❜♦tt♦♠ ❤❡①❛❣♦♥❛❧ ❜♦r♦♥ ♥✐tr✐❞❡ ✭❤❇◆✮ ✢❛❦❡ ✭✸✸ ♥♠ t❤✐❝❦✱ ❧✐❣❤t ❜❧✉❡ ✐♥ ❋✐❣✉r❡ ✶❛✮✱ t❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ✢❛❦❡ ✭❞❛r❦ r❡❞✮ ❛♥❞ ❛ t♦♣ ❤❇◆ ✢❛❦❡ ✭✸✺ ♥♠ t❤✐❝❦✱ ❧✐❣❤t ❜❧✉❡✮✳ ❚❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ✢❛❦❡ ✐s ❡❧❡❝tr✐❝❛❧❧② ❝♦♥t❛❝t❡❞ ✉s✐♥❣ ❡❞❣❡ ❝♦♥t❛❝ts ✶✾ ❛♥❞ ♠❡t❛❧ ❞❡♣♦s✐t✐♦♥ ✭❈r✴❆✉✮✳ ■♥ ❛ ♥❡①t st❡♣ t❤❡ ❈r✴❆✉ ✭✺ ♥♠✴✷✵ ♥♠ ❢♦r t❤❡ s♠❛❧❧ str✉❝t✉r❡s ❛♥❞ ✶✵ ♥♠✴✻✵ ♥♠ ❢♦r t❤❡ ❝♦♥♥❡❝t✐♦♥s t♦ t❤❡ ❜♦♥❞ ♣❛❞s✮ s♣❧✐t ❣❛t❡s ❛♥❞ ♠✐❞❞❧❡ ❣❛t❡ ✭❙● ❛♥❞ ▼●✱ ❣r❡② ✐♥ ❋✐❣✉r❡ ✶❜✮ ❛r❡ ❞❡♣♦s✐t❡❞ ♦♥ t♦♣ ♦❢ t❤❡ st❛❝❦✳ ❚❤❡ ♠✐❞❞❧❡ ❣❛t❡ ✐s ✶✺✵ ♥♠ ✇✐❞❡ ❛♥❞ s❡♣❛r❛t❡❞ ❢r♦♠ t❤❡ s♣❧✐t ❣❛t❡s ❜② ✶✵✵ ♥♠ ♦♥ ❜♦t❤ s✐❞❡s✱ ❢♦r♠✐♥❣ t✇♦ ❝❤❛♥♥❡❧s ✭❜❧❛❝❦ ✐♥ ❋✐❣✉r❡ ✶❜✮✳ ❆♥ ✐♥s✉❧❛t✐♥❣ ✸✵ ♥♠ t❤✐❝❦ ❆❧2 ❖3 ❧❛②❡r s❡♣❛r❛t❡s t❤❡ s♣❧✐t ❣❛t❡s ❛♥❞ t❤❡ ❈r✴❆✉ ✸
ACS Paragon Plus Environment
Nano Letters
c
a
finger gate Al3O2
n
split gate
p
n middle gate
E hBN Bilayer graphene source
Graphite back gate
dot
d
b
QD2
MG
QD1
QD2
0.4
l2 ne
5
an
Ch
drain
0.2 0
3
2
1
0.0
el1
ann
-0.2
Ch
∂IQD1/∂VSD1(e2/h)
hBN
EF
VSD1 (mV)
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Page 4 of 21
-5 SG
-9.2
-9.4
-9.0 VQD1 (V)
-8.8
-8.6
-0.4
❋✐❣✉r❡ ✶✿ ✭❛✮ ❙❝❤❡♠❛t✐❝ ♣✐❝t✉r❡ ♦❢ t❤❡ ❞✐✛❡r❡♥t ❧❛②❡rs ✐♥ t❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ❞❡✈✐❝❡✳ ✭❜✮ ❋❛❧s❡✲❝♦❧♦r ❛t♦♠✐❝ ❢♦r❝❡ ♠✐❝r♦s❝♦♣❡ ✭❆❋▼✮ ✐♠❛❣❡ ♦❢ t❤❡ ❡❧❡❝tr♦st❛t✐❝❛❧❧②✲❞❡✜♥❡❞ ❞❡✈✐❝❡✳ ❇② ✉s✐♥❣ t❤❡ s♣❧✐t ❣❛t❡s ❙● ✭❣r❛②✮ ✐♥ ❛❞❞✐t✐♦♥ t♦ t❤❡ ♠✐❞❞❧❡ ❣❛t❡ ▼● ✭❣r❛②✮ t✇♦ ❝♦♥❞✉❝t✐♥❣ ❝❤❛♥♥❡❧s ✭❝❤❛♥♥❡❧ ✶ ❛♥❞ ❝❤❛♥♥❡❧ ✷✱ ❜❧❛❝❦✮ ❛r❡ ❝r❡❛t❡❞✳ ❚❤❡ ✜♥❣❡r ❣❛t❡s ✭❜❧✉❡ ❛♥❞ r❡❞✮ ❛❝r♦ss t❤❡ ❝❤❛♥♥❡❧s ♣r♦❞✉❝❡ q✉❛♥t✉♠ ❞♦ts ❛♥❞ ❝❤❛r❣❡ ❞❡t❡❝t♦rs ✐♥ t❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✳ ✭❝✮ ❙❝❤❡♠❛t✐❝ ♣✐❝t✉r❡ ♦❢ t❤❡ ❜❛♥❞ str✉❝t✉r❡ ❛t ❞✐✛❡r❡♥t ❧❛t❡r❛❧ ♣♦s✐t✐♦♥s ❛❧♦♥❣ t❤❡ ❝✉rr❡♥t ❞✐r❡❝t✐♦♥ ✭r❡❞ ❛♥❞ ❜❧✉❡ ❛rr♦✇s ✐♥ ✭❜✮✮ ✐♥ t❤❡ ❝❤❛♥♥❡❧✳ ❚❤❡ ❞❛s❤❡❞ ❧✐♥❡ ✐s t❤❡ ❡q✉✐❧✐❜r✐✉♠ ❡❧❡❝tr♦❝❤❡♠✐❝❛❧ ♣♦t❡♥t✐❛❧ ❛❧♦♥❣ t❤❡ ❞✐r❡❝t✐♦♥ ♦❢ ❝✉rr❡♥t ✢♦✇✳ ✭❞✮ ▼❡❛s✉r❡♠❡♥t ♦❢ ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡ ❞✐❛♠♦♥❞s ♦❢ q✉❛♥t✉♠ ❞♦t ✶ ✭◗❉✶✮✱ ✇❤❡♥ t❤❡ ✜rst t❤r❡❡ ❤♦❧❡s ❛r❡ ❝❤❛r❣❡❞ ✐♥t♦ t❤❡ ❞♦t✳
✹
ACS Paragon Plus Environment
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Nano Letters
✭t❤✐❝❦♥❡ss s✐♠✐❧❛r t♦ ❙●s✮ ✜♥❣❡r ❣❛t❡s ✭❜❧✉❡ ❛♥❞ r❡❞ ✐♥ ❋✐❣✉r❡ ✶❜✮✳ ❚❤❡ ✇✐❞❡r ✜♥❣❡r ❣❛t❡s ❤❛✈❡ ❛ ✇✐❞t❤ ♦❢ ✶✷✵ ♥♠✱ t❤❡ ♥❛rr♦✇ ♦♥❡ ✐s ✷✵ ♥♠ ✇✐❞❡✳ ❚❤❡✐r ❧❛t❡r❛❧ s❡♣❛r❛t✐♦♥ ✐s ✾✵ ♥♠✳ ❆ q✉❛♥t✉♠ ❞♦t ❝❛♥ ❜❡ ❢♦r♠❡❞ ❜❡❧♦✇ ❡❛❝❤ ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡s ✭t✇♦ q✉❛♥t✉♠ ❞♦ts ✐♥ ❝❤❛♥♥❡❧ ✶ ❛♥❞ t❤r❡❡ ❞♦ts ✐♥ ❝❤❛♥♥❡❧ ✷✮✳ ❚❤❡ ❛t♦♠✐❝ ❢♦r❝❡ ♠✐❝r♦s❝♦♣❡ ✐♠❛❣❡ ✐♥ ❋✐❣✉r❡ ✶❜ s❤♦✇s t❤❡ ❧❛t❡r❛❧ ❧❛②♦✉t ♦❢ t❤❡ t✇♦ t♦♣ ❣❛t❡ ❧❛②❡rs ✇✐t❤ s♣❧✐t ❣❛t❡s ✭❣r❛②✮✱ ♠✐❞❞❧❡ ❣❛t❡ ✭❣r❛②✮✱ ✜♥❣❡r ❣❛t❡s ✭❜❧✉❡ ❛♥❞ r❡❞✮ ❛♥❞ t❤❡ ❖❤♠✐❝ ❝♦♥t❛❝ts ✭②❡❧❧♦✇✮✳ ❚❤❡ ❣r❛♣❤✐t❡ ❜❛❝❦ ❣❛t❡ ❛♥❞ t❤❡ s♣❧✐t ❣❛t❡s ❝❛♥ ❜❡ ✉s❡❞ t♦ ✭✐✮ ♦♣❡♥ ❛ ❜❛♥❞ ❣❛♣ ❜❡❧♦✇ t❤❡ ❣❛t❡s✱ ❛♥❞ ✭✐✐✮ t✉♥❡ t❤❡ ❋❡r♠✐ ❡♥❡r❣② ✐♥t♦ t❤❡ ❜❛♥❞ ❣❛♣✱ ✇❤✐❝❤ r❡♥❞❡rs t❤❡s❡ r❡❣✐♦♥s ✐♥s✉❧❛t✐♥❣✳ ◆✲t②♣❡ ❝❤❛♥♥❡❧s ✇✐t❤ ❛ ❧✐t❤♦❣r❛♣❤✐❝ ✇✐❞t❤ ♦❢ 100 ♥♠ ❛r❡ ❢♦r♠❡❞ ❜❡t✇❡❡♥ t❤❡ ❣❛t❡s ✭s❡❡ ❋✐❣✉r❡ ✶❝ ❜❧✉❡ ♥✲❞♦♣❡❞ r❡❣✐♦♥s✮ ❜② ❛♣♣❧②✐♥❣ ❛ ♣♦s✐t✐✈❡ ✈♦❧t❛❣❡ t♦ t❤❡ ❣r❛♣❤✐t❡ ❜❛❝❦ ❣❛t❡ ✭V❇● = 3 ❱✮ ❛♥❞ ❛ ♥❡❣❛t✐✈❡ ✈♦❧t❛❣❡ t♦ t❤❡ s♣❧✐t ❣❛t❡s ✭V❙● = −3.5 ❱✮✳ ❚❤❡ ▼● ✐s ✉s❡❞ t♦ s❡♣❛r❛t❡ t❤❡ ❝❤❛♥♥❡❧s✱ ✇❤❡r❡ ❛ ❣❛t❡ ✇✐❞t❤ ♦❢ 150 ♥♠ ✐s ♥❡❡❞❡❞ t♦ ❛✈♦✐❞ ❧❡❛❦❛❣❡ ❝✉rr❡♥ts ❜❡t✇❡❡♥ t❤❡♠✳ ❙❡♣❛r❛t❡ s♦✉r❝❡✲❞r❛✐♥ ❜✐❛s ✈♦❧t❛❣❡s V❙❉ ❛r❡ ❛♣♣❧✐❡❞ t♦ ❡❛❝❤ ❝❤❛♥♥❡❧ ✉s✐♥❣ ♣❛✐rs ♦❢ ♦❤♠✐❝ ❝♦♥t❛❝ts ✭❋✐❣✉r❡ ✶❜✮✳ ❯s✐♥❣ ♦♥❡ ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡s t❤❡ ❋❡r♠✐✲❡♥❡r❣② ✐♥ t❤❡ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ r❡❣✐♦♥ ❜❡❧♦✇ t❤❡ ✜♥❣❡r ❣❛t❡ ❝❛♥ ❜❡ t✉♥❡❞ ✐♥t♦ t❤❡ ❜❛♥❞ ❣❛♣ ✭♣✐♥❝❤✲♦✛✮ ♦r ✐♥t♦ t❤❡ ♣✲r❡❣✐♦♥ ✭❋✐❣✉r❡ ✶❝ r❡❞✮✱ ✇❤❡r❡ ❛ ◗❉ ❝♦♥✜♥✐♥❣ ❤♦❧❡s ✐s ❢♦r♠❡❞✳ ❚❤❡ ❜❛♥❞ str✉❝t✉r❡ ✐s s❦❡t❝❤❡❞ ✐♥ ❋✐❣✉r❡ ✶❝ ✭❧♦✇❡r ♣❛♥❡❧✮ ✇✐t❤ s♦✉r❝❡ ❛♥❞ ❞r❛✐♥ ❝♦♥t❛❝ts ✐♥ t❤❡ ♥✲r❡❣✐♦♥s ❛♥❞ t❤❡ ❤♦❧❡ ◗❉ ❜❡❧♦✇ t❤❡ ✜♥❣❡r ❣❛t❡✳ ❇❡t✇❡❡♥ t❤❡ ♥✲ ❛♥❞ ♣✲r❡❣✐♦♥s t❤❡ ❋❡r♠✐✲❡♥❡r❣② ✭❛t t❤❡ ❡❞❣❡s ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡✱ s❡❡ ❋✐❣✉r❡ ✶❝✮ ❧✐❡s ✐♥ t❤❡ ❜❛♥❞ ❣❛♣✱ ❤❡♥❝❡ ♥❛t✉r❛❧ t✉♥♥❡❧ ❜❛rr✐❡rs ❢♦r t❤❡ q✉❛♥t✉♠ ❞♦t ❛r❡ ❢♦r♠❡❞✳ ✶✷ ❊❛❝❤ q✉❛♥t✉♠ ❞♦t ✇✐t❤ ✐ts s❤❛r♣ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡s ✐s ❛❧s♦ ❛ s❡♥s✐t✐✈❡ ❞❡t❡❝t♦r ❢♦r s✐♥❣❧❡ ❝❤❛r❣❡s ✐♥ ❛♥② ♦t❤❡r ◗❉ ♥❡❛r❜②✳ ❚❤❡ r❡s♦♥❛♥❝❡s ♦❢ t❤❡ ◗❉s ❛r❡ ❡✈❡♥ ♠♦r❡ s❡♥s✐t✐✈❡ t❤❛♥ ❛ ◗P❈✱ ❞✉❡ t♦ t❤❡ st❡❡♣❡r s❧♦♣❡ ♦❢ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ✈❡rs✉s ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡✳ ❆❧❧ ♠❡❛s✉r❡♠❡♥ts ♣r❡s❡♥t❡❞ ❤❡r❡ ✇❡r❡ ♣❡r❢♦r♠❡❞ ✐♥ ❛ ❞✐❧✉t✐♦♥ r❡❢r✐❣❡r❛t♦r ✇✐t❤ ❛♥ ❡❧❡❝✲ tr♦♥✐❝ ❜❛s❡ t❡♠♣❡r❛t✉r❡ ♦❢ ✻✵ ♠❑ ✐♥ ❛ t✇♦✲t❡r♠✐♥❛❧ ❉❈ s❡t✉♣ ✇✐t❤ ❛ ❜✐❛s ✈♦❧t❛❣❡ ❛♣♣❧✐❡❞ ❜❡t✇❡❡♥ s♦✉r❝❡ ❛♥❞ ❞r❛✐♥✱ ❛♥❞ t❤❡ ❞r❛✐♥ ❝♦♥t❛❝t ❣r♦✉♥❞❡❞✳ ❚❤❡ ✐♥t❡❣r❛t✐♦♥ t✐♠❡ ❢♦r ❝✉rr❡♥t ♠❡❛s✉r❡♠❡♥ts ✇❛s s❡t t♦ ✷✵ ♠s✳ ✺
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
❋✐❣✉r❡ ✶❞ s❤♦✇s ❛ ♠❡❛s✉r❡♠❡♥t ♦❢ ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡ ❞✐❛♠♦♥❞s ♦❢ ◗❉✶ ❢♦r♠❡❞ ✉♥❞❡r✲ ♥❡❛t❤ t❤❡ ❧❡❢t r❡❞✲❝♦❧♦r❡❞ ✜♥❣❡r ❣❛t❡ ✐♥ ❝❤❛♥♥❡❧ ✶ ✭s❡❡ ❋✐❣✉r❡ ✶❜✮✳ ❲❡ ♠❡❛s✉r❡ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ❝✉rr❡♥t ∂I◗❉✶ /∂V❙❉✶ ✐♥ ❝❤❛♥♥❡❧ ✶ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✶ ❢♦r♠✐♥❣ ◗❉✶ ❛♥❞ t❤❡ ❉❈ s♦✉r❝❡✲❞r❛✐♥ ❜✐❛s V❙❉✶ ✳ ■♥ t❤❡ ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡ ❞✐❛♠♦♥❞s ✇❡ s❡❡ s✐♥❣❧❡ ❤♦❧❡s ❝❤❛r❣✐♥❣ ✐♥t♦ t❤❡ q✉❛♥t✉♠ ❞♦t ❛t V◗❉✶ = −8.95 ❱, −9.17 ❱, −9.36 ❱ ❢♦r V❙❉ ≈ 0 ❱✳ ❋r♦♠ t❤❡ ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡ ❞✐❛♠♦♥❞s ❛ ❝❤❛r❣✐♥❣ ❡♥❡r❣② ♦❢ ❛❜♦✉t E❝❤ = 5 ♠❡❱ ❛♥❞ ❛ ✜♥❣❡r ❣❛t❡ ❧❡✈❡r ❛r♠ α = 0.02 ❝❛♥ ❜❡ ❞❡t❡r♠✐♥❡❞✳
❘❡s✉❧ts ❛♥❞ ❞✐s❝✉ss✐♦♥ ❋♦r t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ❡①♣❡r✐♠❡♥t s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✷✱ ◗❉✶ ✐♥ ❝❤❛♥♥❡❧ ✶ ✐s ✉s❡❞ ❛s s❡♥s✐♥❣ ❞♦t✳ ❆ s♦✉r❝❡✲❞r❛✐♥ ❜✐❛s ♦❢ 100 µ❱ ✭♦♣t✐♠✐③❡❞ ❢♦r t❤❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧✮ ✐s ❛♣♣❧✐❡❞ ❛❝r♦ss t❤❡ s❡♥s✐♥❣ ❞♦t ❛♥❞ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✶ ✐s ❝❤♦s❡♥ s♦ t❤❛t s❡q✉❡♥t✐❛❧ t✉♥♥❡❧✐♥❣ t❤r♦✉❣❤ ◗❉✶ ✐s ♣♦ss✐❜❧❡ ❛♥❞ ❛ ❝✉rr❡♥t ✐s ♠❡❛s✉r❡❞✳ ❆t t❤✐s ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ t❤❡ q✉❛♥t✉♠ ❞♦t ✐s ❛ s❡♥s✐t✐✈❡ ❞❡t❡❝t♦r ❢♦r ❝❤❛♥❣❡s ♦❢ t❤❡ ❝❤❛r❣❡ ❝♦♥✜❣✉r❛t✐♦♥ ✐♥ ✐ts ❡♥✈✐r♦♥♠❡♥t✳ ❆ s♠❛❧❧ ❝❤❛♥❣❡ ✐♥ t❤❡ ❡❧❡❝tr♦st❛t✐❝ ❡♥✈✐r♦♥♠❡♥t ♦❢ t❤❡ ❞♦t ❧❡❛❞s t♦ ❛ s❤✐❢t ♦❢ t❤❡ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡ ✐♥ ❡♥❡r❣② ✭♦r ❡q✉✐✈❛❧❡♥t❧②✱ ✐♥ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✷ ✮ ❛♥❞ t❤❡r❡❢♦r❡ t♦ ❛ ❝❤❛♥❣❡ ✐♥ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ G◗❉✶ t❤r♦✉❣❤ ❝❤❛♥♥❡❧ ✶✳ ❆ s❡❝♦♥❞ ♣✲t②♣❡ q✉❛♥t✉♠ ❞♦t ✭s✐❣♥❛❧ ❞♦t ◗❉✷✮ ✐s ❢♦r♠❡❞ ❜❡❧♦✇ t❤❡ ❧❡❢t ❜❧✉❡ ❣❛t❡ ✐♥ ❝❤❛♥♥❡❧ ✷ ✭❋✐❣✉r❡ ✶❛✮✱ ❜② t✉♥✐♥❣ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✷ ✳ ❚❤❡ ❧✐♥❡❛r ❝♦♥❞✉❝t❛♥❝❡ G◗❉✷ t❤r♦✉❣❤ ❝❤❛♥♥❡❧ ✷ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✷❛ ✉♣♣❡r ♣❛♥❡❧✱ ✇❤❡r❡ t❤❡ ❣❛t❡ ✈♦❧t❛❣❡s V◗❉✶ ❛♥❞ V◗❉✷ ❛r❡ ❝❤❛♥❣❡❞ ❛♥❞ ❛ s♦✉r❝❡✲❞r❛✐♥ ✈♦❧t❛❣❡ ♦❢ V❙❉ = 100 µ❱ ❛❝r♦ss t❤❡ s✐❣♥❛❧ ❞♦t ✐s ❛♣♣❧✐❡❞✳ ❇② ❝❤❛♥❣✐♥❣ V◗❉✷ ✇❡ s❝❛♥ ❛❝r♦ss ♦♥❡ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡ ♦❢ ◗❉✶ ✭❞❡t❡❝t♦r ❞♦t✮ ❛♥❞ ♠❡❛s✉r❡ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ G◗❉✶ ✐♥ ❝❤❛♥♥❡❧ ✶ ❛♥❞ G◗❉✷ ❝❤❛♥♥❡❧ ✷ ❛t t❤❡ s❛♠❡ t✐♠❡✳ ❚❤❡ ✉♣♣❡r ♣❛♥❡❧ ✐♥ ❋✐❣✉r❡ ✷❛ s❤♦✇s r❡❣✉❧❛r❧② s♣❛❝❡❞ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡s ✐♥ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ t❤❡ s✐❣♥❛❧ ❞♦t✱ ✇❤✐❝❤ s❧✐❣❤t❧② s❤✐❢t ❜② ❝❤❛♥❣✐♥❣ V◗❉✶ ✳ ❚❤❡s❡ r❡s♦♥❛♥❝❡s ❛r❡ ♦❜s❡r✈❡❞ t❤r♦✉❣❤ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ✐♥ t❤❡ ❧♦✇❡r ♣❛♥❡❧ ♦❢ ❋✐❣✉r❡ ✷❛✳ ✻
ACS Paragon Plus Environment
Page 6 of 21
0.04
Signal dot
-9.09
b
GQD2 (e2/h)
VQD1 (V)
a
-9.10
0.03
0.02
-9.11
0.1
GQD1 (e2/h)
0.2 -9.10
GQD1 (e2/h)
Sensor dot
-9.09
Signal dot
0.02 0.01 0.00 0.3
0.00 VQD1 (V)
ΔGQD1
0.2
Sensor dot ΔVQD2
0.1
-9.11 -8.0
-7.8
-7.6 -7.4 VQD2 (V) c
-7.2
-7.0
0.0 -8.0
0.0
-7.8
-7.6 -7.4 VQD2 (V)
-7.2
-7.0
104
SNR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
GQD2 (e2/h)
Page 7 of 21
103 100 10 10
100 103 Bandwidth (Hz)
104
❋✐❣✉r❡ ✷✿ ✭❛✮ ❈♦♥❞✉❝t❛♥❝❡ G◗❉✷ ♦❢ t❤❡ s✐❣♥❛❧ ❞♦t ✭◗❉✷✮ ✭✉♣♣❡r ♣❛♥❡❧✮ ❛♥❞ ❝♦♥❞✉❝t❛♥❝❡ G◗❉✶ ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦t ✭❧♦✇❡r ♣❛♥❡❧✮ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡s V◗❉✷ ❛♥❞ V◗❉✶ ❢♦r ❛ ✜①❡❞ ❜❛❝❦ ❣❛t❡ ✭V❇● = 3 ❱✮ ❛♥❞ s♣❧✐t ❣❛t❡ ✈♦❧t❛❣❡ ✭V❙● ≈ −3.5 ❱✮✳ ❯♣♣❡r ♣❛♥❡❧✿ ❚❤❡ ❧✐♥❡s s♣❛❝❡❞ ✇✐t❤ ❛ ♣❡r✐♦❞✐❝✐t② ♦❢ ✵✳✵✾ ❱ ✐♥ V◗❉✷ ❛r❡ ❞✉❡ t♦ ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡ r❡s♦♥❛♥❝❡s✳ ❚❤❡ ❧♦✇❡r ♣❛♥❡❧ s❤♦✇s t❤❡ s✐♠✉❧t❛♥❡♦✉s❧②✲❛❝q✉✐r❡❞ ♠❡❛s✉r❡♠❡♥t ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r ❝♦♥❞✉❝t❛♥❝❡ G◗❉✶ ✳ ❲❡ ♦❜s❡r✈❡ ❢❡❛t✉r❡s ❛❧✐❣♥❡❞ ✇✐t❤ t❤❡ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡s ✐♥ t❤❡ ✉♣♣❡r ♣❛♥❡❧ ✭❤✐❣❤❧✐❣❤t❡❞ ✇✐t❤ ✈❡rt✐❝❛❧ ❞❛s❤❡❞ ❣r❛② ❧✐♥❡✮ ❛♥❞ t✐❧t❡❞ ❧✐♥❡s r❡s✉❧t✐♥❣ ❢r♦♠ t❤❡ ❝r♦ss ❝❛♣❛❝✐t❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ s❡♥s✐♥❣ ❞♦t ❛♥❞ V◗❉✷ ✭❤✐❣❤❧✐❣❤t❡❞ ✇✐t❤ ❞✐❛❣♦♥❛❧ ❞❛s❤❡❞ ❣r❛② ❧✐♥❡✮✳ ❚❤❡ ❞❛s❤❡❞ ❜❧❛❝❦ ❧✐♥❡s ✐♥ t❤❡ ✉♣♣❡r ❛♥❞ ❧♦✇❡r ♣❛♥❡❧ ✐♥❞✐❝❛t❡ t❤❡ ❧✐♥❡ ❝✉ts ✐♥ ❜✱ r❡s♣❡❝t✐✈❡❧②✳ ✭❝✮ ❙◆❘ ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ❢♦r ❞✐✛❡r❡♥t ♠❡❛s✉r❡♠❡♥t s②st❡♠ ❜❛♥❞✇✐❞t❤✳
✼
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
❆ ❧✐♥❡✲❝✉t ✐♥ V◗❉✶ ❞✐r❡❝t✐♦♥ s❤♦✇s ❛ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡ ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦t ✭◗❉✶✮✱ t❤❛t s❤✐❢ts t♦ ♠♦r❡ ♥❡❣❛t✐✈❡ VQD1 ✱ ✇❤❡♥ VQD2 ✐s ✐♥❝r❡❛s❡❞✳ ❚❤❡ ❞✐❛❣♦♥❛❧ s❤✐❢t ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦ts r❡s♦♥❛♥❝❡ ✭♠❛r❦❡❞ ❜② ❞✐❛❣♦♥❛❧ ❞❛s❤❡❞ ❧✐♥❡✮ ✐s ❞✉❡ t♦ t❤❡ ❝r♦ss ❝❛♣❛❝✐t❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ s❡♥s✐♥❣ ❞♦t ❛♥❞ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ ❞❡✜♥✐♥❣ t❤❡ s✐❣♥❛❧ ❞♦t✳ ❋r♦♠ t❤✐s s❤✐❢t ❛ r❛t✐♦ ❜❡t✇❡❡♥ t❤❡ ❧❡✈❡r ❛r♠ ♦❢ t❤❡ ❜❧✉❡ ❣❛t❡ ✭V◗❉✷ ✮ ♦♥ t❤❡ s❡♥s♦r ❞♦t ❛♥❞ t❤❡ r❡❞ ❣❛t❡ ✭V◗❉✶ ✮ ♦♥ t❤❡ s❡♥s♦r ❞♦t αV◗❉✷ −◗❉✶ /αV◗❉✶ ✲◗❉✶ = 0.07 ✐s ❝❛❧❝✉❧❛t❡❞✳ ❲❡ ✐❞❡♥t✐❢② s✐♥❣❧❡ ❝❤❛r❣✐♥❣ ❡✈❡♥ts ✐♥ t❤❡ s✐❣♥❛❧ ❞♦t ❛s ❛❜r✉♣t s❤✐❢ts ♦❢ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ r❡s♦♥❛♥❝❡ ✐♥ t❤❡ s❡♥s✐♥❣ ❞♦t ✭♠❛r❦❡❞ ✇✐t❤ ✈❡rt✐❝❛❧ ❞❛s❤❡❞ ❧✐♥❡✮✱ ❛❧✐❣♥❡❞ ✇✐t❤ t❤❡ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡s ♦❢ t❤❡ s✐❣♥❛❧ ❞♦t ✭s❡❡ ✈❡rt✐❝❛❧ ❞❛s❤❡❞ ❧✐♥❡s✮✳ ▲✐♥❡ ❝✉ts ❢r♦♠ ❋✐❣✉r❡ ✷❛ ❛t V◗❉✶ = 9.1 ❱ ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✷❜✳ ❘❡❣✉❧❛r❧② s♣❛❝❡❞ ❝♦♥❞✉❝t❛♥❝❡ r❡s♦♥❛♥❝❡s ❛r❡ ♦❜s❡r✈❡❞ ✐♥
❋✐❣✉r❡ ✷❜ ✭✉♣♣❡r ♣❛♥❡❧✮✱ ✇❤❡♥ s❡q✉❡♥t✐❛❧ t✉♥♥❡❧✐♥❣ t❤r♦✉❣❤ t❤❡ s✐❣♥❛❧ ❞♦t ✐s ♣♦ss✐❜❧❡✳ ❚❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝♦♥❞✉❝t❛♥❝❡ G◗❉✶ ♠❡❛s✉r❡❞ s✐♠✉❧t❛♥❡♦✉s❧② ✐♥ t❤❡ ❞❡t❡❝t♦r ❝❤❛♥♥❡❧ ✐s s❤♦✇♥ ✐♥ t❤❡ ❧♦✇❡r ♣❛♥❡❧ ✐♥ ❋✐❣✉r❡ ✷❜✳ ❲❡ ♦❜s❡r✈❡ ❛ ❜r♦❛❞❡♥❡❞ r❡s♦♥❛♥❝❡ ✇✐t❤ ✐ts ♠❛①✐♠✉♠ ❛t V◗❉✷ = −7.75 ❱ ❛♥❞ ❛ ✇✐❞t❤ ♦❢ 1 ❱ ✇✐t❤ st❡♣✲❧✐❦❡ ❢❡❛t✉r❡s ♦♥ t♦♣✳ ❚❤❡ r❡s♦♥❛♥❝❡ ✐s ❜r♦❛❞❡r ✐♥ V◗❉✷ t❤❛♥ ✐♥ V◗❉✶ ✱ ❞✉❡ t♦ t❤❡ ♠✉❝❤ s♠❛❧❧❡r ❧❡✈❡r ❛r♠ ♦❢ t❤❡ ❜❧✉❡ ✜♥❣❡r ❣❛t❡ ♦♥ t❤❡ s❡♥s✐♥❣ ❞♦t ❛s ❝♦♠♣❛r❡❞ t♦ t❤❡ r❡❞ ✜♥❣❡r ❣❛t❡✳ ❚❤❡ ❝♦♥❞✉❝t❛♥❝❡ st❡♣s ✭♠❛r❦❡❞ ✇✐t❤ ✈❡rt✐❝❛❧ ❞❛s❤❡❞ ❧✐♥❡s✮ ❛r❡ r❡❧❛t❡❞ t♦ ❛ s❤✐❢t ∆V◗❉✷ ✐♥ t❤❡ r❡s♦♥❛♥❝❡ ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦t ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ s✐❣♥❛❧ ❞♦t✬s ✈♦❧t❛❣❡ V◗❉✷ ✳ ❋r♦♠ ❛♥ ❛♥❛❧②s✐s ♦❢ t❤❡ ❝❤❛r❣✐♥❣ ❡✈❡♥ts ❛♥ ❛✈❡r❛❣❡ s❤✐❢t ✐♥ ∆V◗❉✷ = 61 ♠❱ ✭s❡❡ ❋✐❣✉r❡ ✷❜✮ ✐s ♦❜s❡r✈❡❞✳ ❚❤❡ ❝♦♥❞✉❝t❛♥❝❡ ✐♥ t❤❡ ❞❡t❡❝t♦r ❝❤❛♥♥❡❧ ∆G◗❉✶ = 0.2 e2 /h ✭s❡❡ ❋✐❣✉r❡ ✷❜✮ ❝❤❛♥❣❡s ❜② ✉♣ t♦ ✼✼✪ ❢♦r ❛ s✐♥❣❧❡ ❝❤❛r❣✐♥❣ ❡✈❡♥t✳ ❚❤✐s ❝❤❛♥❣❡ ✐♥ ❝♦♥❞✉❝t❛♥❝❡ ✐s ❝♦♠♣❛r❡❞ t♦ ♦t❤❡r ❞❡✈✐❝❡s ✐♥ ●r❛♣❤❡♥❡ ✐♥ ❚❛❜❧❡ ✶✳ ❋✉rt❤❡r♠♦r❡✱ ✇❡ ❡✈❛❧✉❛t❡ t❤❡ s✐❣♥❛❧ t♦ ♥♦✐s❡ r❛t✐♦ ✭❙◆❘✮ ♦❢ ∆IStep / < IN oise >≈ 3000 ❛t ❛ ♠❡❛s✉r❡♠❡♥t ❜❛♥❞✇✐❞t❤ ♦❢ ✺✵ ❍③✳ < IN oise > ✐s t❤❡ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ ❞❡t❡❝t♦r ❝✉rr❡♥t ❛♥❞ ∆IStep t❤❡ ❝✉rr❡♥t ❝❤❛♥❣❡ ✐♥ t❤❡ ❞❡t❡❝t♦r ❞✉❡ t♦ ♦♥❡ ❝❤❛r❣✐♥❣ ❡✈❡♥t✳ ■♥ ❋✐❣✉r❡ ✷❝ t❤❡ ❙◆❘ ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ✐s s❤♦✇♥ ❢♦r ❞✐✛❡r❡♥t ♠❡❛s✉r❡♠❡♥t ❜❛♥❞✇✐❞t❤✳ ❋r♦♠ t❤❡s❡ ♠❡❛s✉r❡♠❡♥ts ✇❡ ❡①♣❡❝t ❛ ♠❛①✐♠❛❧ ❜❛♥❞✇✐❞t❤ ♦❢ ✶✵ ❦❍③ ❢♦r ♦✉r ♠❡❛s✉r❡♠❡♥t✱ ✇❤✐❝❤ ✐s ❤✐❣❤❡r t❤❛♥ ✐♥ ❡t❝❤❡❞ ❣r❛♣❤❡♥❡ ❞❡✈✐❝❡s✳ ✸✸ ❚❤❡ t✉♥♥❡❧✐♥❣ ✽
ACS Paragon Plus Environment
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Page 9 of 21
r❛t❡s ✐♥ t❤❡ ♣r❡s❡♥t❡❞ ❞❡✈✐❝❡ ❛r❡ ❤✐❣❤❡r t❤❛♥ t❤❡ ♠❛①✐♠❛❧ ♠❡❛s✉r❡♠❡♥t ❜❛♥❞✇✐❞t❤✱ s♦ t❤❛t t✐♠❡✲r❡s♦❧✈❡❞ ♠❡❛s✉r❡♠❡♥ts ♦❢ ❡❧❡❝tr♦♥ t✉♥♥❡❧✐♥❣ ✐s ♥♦t ♣♦ss✐❜❧❡ ✐♥ t❤✐s ❞❡✈✐❝❡✳ a GQD1 (e2/h)
0.40
Signal dot
0.20 0.00
b
0.10 GQD2 (e2/h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
3
2
1
0.05 0.00 -9.5
Sensor dot -9.25
-9.0
-8.75 -8.5 VQD1 (V)
-8.25
-8.0
❋✐❣✉r❡ ✸✿ ✭❛✮ ❈♦♥❞✉❝t❛♥❝❡ G◗❉✶ ♦❢ t❤❡ s✐❣♥❛❧ ❞♦t ❛♥❞ ✭❜✮ ❝♦♥❞✉❝t❛♥❝❡ G◗❉✷ ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦t ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✶ ❢♦r ❛ ✜①❡❞ ❜❛❝❦ ❣❛t❡ ✭V❇● = 3 ❱✮ ❛♥❞ s♣❧✐t ❣❛t❡ ✈♦❧t❛❣❡ ✭V❙● = −3.5 ❱✮✳ ✭❛✮ ❚❤❡ ✜rst t❤r❡❡ ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡ ♦❢ t❤❡ s✐❣♥❛❧ ❞♦t ❛r❡ ♠❡❛s✉r❡❞ ❞✐r❡❝t❧② ✐♥ t❤❡ ❝✉rr❡♥t t❤r♦✉❣❤ t❤❡ ❞♦t ❛♥❞ ✭❜✮ ✐♥ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❆t V◗❉✶ = −8.9 ❱ t❤❡ ✜rst ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡ ❛♥❞ ❛❧s♦ t❤❡ ✜rst st❡♣ ✐♥ t❤❡ ❞❡t❡❝t♦r s✐❣♥❛❧ ✐s ♠❡❛s✉r❡❞✱ ♣r♦♦✜♥❣ t❤❡ ❝❤❛r❣✐♥❣ ♦❢ t❤❡ ◗❉ ✇✐t❤ t❤❡ ✜rst ❤♦❧❡✳ ■♥ t❤❡ ❢♦❧❧♦✇✐♥❣✱ ✇❡ ❡①❝❤❛♥❣❡ t❤❡ r♦❧❡ ♦❢ t❤❡ t✇♦ ❞♦ts✱ t♦ ❝♦♥✜r♠ t❤❛t ✇❡ ❛r❡ ❛❜❧❡ t♦ ❢✉❧❧② ❞❡♣❧❡t❡ t❤❡ q✉❛♥t✉♠ ❞♦t ❛♥❞ ✜❧❧ ✐t ✇✐t❤ ✐♥❞✐✈✐❞✉❛❧ ❤♦❧❡s✳ ❚❤❡ q✉❛♥t✉♠ ❞♦t ✐♥ ❝❤❛♥♥❡❧ ✷ ✭◗❉✷✮ ✇✐❧❧ ❜❡ ✉s❡❞ ❛s t❤❡ s❡♥s✐♥❣ ❞♦t✳ ❚❤❡ ❝♦♥❞✉❝t❛♥❝❡s t❤r♦✉❣❤ t❤❡ s✐❣♥❛❧ ❞♦t ✐♥ ❝❤❛♥♥❡❧ ✶ ✭◗❉✶✮ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸❛✳ ❋♦r ◗❉✶✱ ✇❡ ❝❛♥ ❝❧❡❛r❧② s❡❡ ❛ ✜rst ❈♦✉❧♦♠❜ r❡s♦♥❛♥❝❡
❖
✭♠❛r❦❡❞ ❜② ✶ ✮ ✐♥ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ t❤❡ ❝❤❛♥♥❡❧ ✶ ❛t −8.9 ❱✳ ❚❤❡ ❝♦♥❞✉❝t❛♥❝❡s G◗❉✶ ❛♥❞ G◗❉✷ ♦❢ ❜♦t❤ ❝❤❛♥♥❡❧s ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸❛ ❛♥❞ ❜✱ ✇❤✐❧❡ t❤❡ ❣❛t❡ ✈♦❧t❛❣❡ ♦❢ t❤❡ s✐❣♥❛❧
❞♦t ✭◗❉✶✮ ✐s ❝❤❛♥❣❡❞ ❛♥❞ ❛ s♦✉r❝❡✲❞r❛✐♥ ❜✐❛s ♦❢ V❙❉ = 100 µ❱ ✐s ❛♣♣❧✐❡❞ t♦ ❜♦t❤ ❝❤❛♥♥❡❧s✳ ■♥ t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ t❤❡ ❞❡t❡❝t♦r G◗❉✷ ❛ ✜rst st❡♣ ✐s ❛❧s♦ ♦❜s❡r✈❡❞ ❛t ❛❜♦✉t −8.9 ❱✳ ❋✉rt❤❡r♠♦r❡✱ ◗❉s ✇✐t❤ t✉♥❛❜❧❡ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs ❛♥❞ ♠✉❧t✐♣❧❡✲❞♦ts ❝❛♥ ❜❡ ❢♦r♠❡❞ ✐♥ ❝❤❛♥♥❡❧ ✷ ✉s✐♥❣ t❤❡ t✇♦ ❜r♦❛❞❡r ✜♥❣❡r ❣❛t❡s ✭❜❧✉❡ ✐♥ ❋✐❣✉r❡ ✹❜✮✳ ✶✷ ❋✐❣✉r❡ ✹❛ s❤♦✇s t❤❡ ❞✐❢✲ ❢❡r❡♥t✐❛❧ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r ∂I◗❉✶ /∂V◗❉✷ ✭t❤❡ ❝♦♥❞✉❝t❛♥❝❡ ❝❤❛♥❣❡ t❤r♦✉❣❤ t❤❡ s✐❣♥❛❧ ❞♦t ✐s ❧♦✇❡r t❤❛♥ ♦✉r ♠❡❛s✉r❡♠❡♥t r❡s♦❧✉t✐♦♥✮ ❛s ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ❣❛t❡ ✈♦❧t❛❣❡s V◗❉✷ ❛♥❞ V◗❉✸ t❤❛t ✇❡r❡ ❛♣♣❧✐❡❞ t♦ t❤❡ t✇♦ ♦✉t❡r ✜♥❣❡r ❣❛t❡s ✐♥ ❝❤❛♥♥❡❧ ✷✳ ❚❤r❡❡ ❞✐s✲
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ACS Paragon Plus Environment
Nano Letters
a
-5.8
2
1
b
0.3 0.2 0.1 0.0
-6.2
-0.1
1 ∂IQD1/∂VQD2 ( e2/h)
-6.0 VQD3 (V)
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Page 10 of 21
2
3
4
QD2 QD3
-0.2
-6.4 4 -6.0
3 -5.8
-5.6 VQD2(V)
-5.4
-0.3
❋✐❣✉r❡ ✹✿ ✭❛✮ ❉✐✛❡r❡♥t✐❛❧ ❝♦♥❞✉❝t❛♥❝❡ ∂I◗❉✶ /∂V◗❉✷ ✐♥ t❤❡ ❞❡t❡❝t✐♦♥ ❝❤❛♥♥❡❧✱ ✇❤❡♥ ♠✉❧t✐ ❞♦ts ❛r❡ ❢♦r♠❡❞ ✐♥ ❝❤❛♥♥❡❧ ✷✳ ❚❤❡ ✇❤✐t❡ ❞♦tt❡❞ ❧✐♥❡s ✐♥❞✐❝❛t❡ t❤❡ ❜♦✉♥❞❛r✐❡s ♦❢ ❢♦✉r ❞✐✛❡r❡♥t r❡❣✐♦♥s✳ ■♥ r❡❣✐♦♥ ✶ ✱ ❛ s✐♥❣❧❡ ❡❧❡❝tr♦♥ ❞♦t ✐s ❢♦r♠❡❞ ❜❡t✇❡❡♥ t✇♦ ❜❛rr✐❡rs✳ ■♥ r❡❣✐♦♥s ✷ ❛♥❞ ✸ ✱ ❛♥ ❡❧❡❝tr♦♥✲❤♦❧❡ ❞♦✉❜❧❡ ❞♦t ✐s ❢♦r♠❡❞ ❜❡t✇❡❡♥ t❤❡ ❣❛t❡s ❛♥❞ ❜❡❧♦✇ ♦♥❡ ♦❢ t❤❡ ❣❛t❡s✱ r❡s♣❡❝t✐✈❡❧②✳ ■♥ r❡❣✐♦♥ ✹ ✱ ❛ tr✐♣❧❡ ❞♦t ✐s ♠❡❛s✉r❡❞✳ ❚❤❡ t❤r❡❡ ❞♦ts ❛r❡ ❢♦r♠❡❞ ❜❡❧♦✇ ❡❛❝❤ ♦❢ t❤❡ ❣❛t❡s ❛♥❞ ❜❡t✇❡❡♥ t❤❡♠✳ ✭❜✮ ❙❝❤❡♠❛t✐❝ ♣✐❝t✉r❡ ♦❢ t❤❡ ❞❡✈✐❝❡ s❤♦✇✐♥❣ t❤❡ ❞✐✛❡r❡♥t ❞♦t ❝♦♥✜❣✉r❛t✐♦♥s ✐♥ ✭❛✮✳ ❘❡❞ ❞♦ts ❛♥❞ ❜❧✉❡ ❞♦ts s❤♦✇ t❤❡ ◗❉s ❢♦r♠❡❞ ❜❡❧♦✇ t❤❡ ❣❛t❡s ✭❤♦❧❡ ❞♦ts✮ ❛♥❞ ❜❡t✇❡❡♥ t❤❡♠ ✭❡❧❡❝tr♦♥ ❞♦ts✮✱ r❡s♣❡❝t✐✈❡❧②✳
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t✐♥❝t s❡ts ♦❢ r❡s♦♥❛♥❝❡s ❛r❡ ♦❜s❡r✈❡❞ ✈❡rt✐❝❛❧ ✭♠❛r❦❡❞ ✇✐t❤ r❡❞ ❛rr♦✇s✮✱ ❤♦r✐③♦♥t❛❧ ✭♠❛r❦❡❞ ✇✐t❤ ❜❧✉❡ ❛rr♦✇s✮ ❛♥❞ ❞✐❛❣♦♥❛❧ ✭♠❛r❦❡❞ ✇✐t❤ ✇❤✐t❡ ❛rr♦✇s✮ r❡s♦♥❛♥❝❡s ✐♥ ❋✐❣✉r❡ ✹❛✮✳ ❚❤❡
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♠❡❛s✉r❡♠❡♥t ❝❛♥ ❜❡ ❞✐✈✐❞❡❞ ✐♥t♦ ❢♦✉r q✉❛❞r❛♥ts ✭ ✶ t♦ ✹ ✮✱ s❡♣❛r❛t❡❞ ❜② t❤❡ ✇❤✐t❡ ❞❛s❤❡❞ ❧✐♥❡s✳ ❚❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ s❦❡t❝❤ ♦❢ t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡r ❞✐str✐❜✉t✐♦♥s ❛❧♦♥❣ ❝❤❛♥♥❡❧ ✷ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹❜✳ ■♥ t❤❡ ✜rst q✉❛❞r❛♥t ♦❢ ❋✐❣✉r❡ ✹❛ ✇❡ ♦❜s❡r✈❡ ❞✐❛❣♦♥❛❧ r❡s♦♥❛♥❝❡s ♦♥❧②✱ t❤❛t ❜❡❧♦♥❣ t♦ ❛ s✐♥❣❧❡ ❡❧❡❝tr♦♥ ❞♦t ❢♦r♠❡❞ ❜❡t✇❡❡♥ t❤❡ t✇♦ ♦✉t❡r ❣❛t❡s ✐♥ ❝❤❛♥♥❡❧ ✷ ✭❞❛r❦ ❜❧✉❡ ✐♥ ❋✐❣✉r❡ ✶❛ ❛♥❞ ❋✐❣✉r❡ ✹❜✮✳ ❚❤❡ t✇♦ ✜♥❣❡r ❣❛t❡s ❛r❡ t✉♥❡❞ ❝❧♦s❡ t♦ t❤❡ ❝❤❛r❣❡ ♥❡✉tr❛❧✐t② ♣♦✐♥t✱ t❤✉s ❝r❡❛t✐♥❣ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs ❜❡t✇❡❡♥ t❤❡ s♦✉r❝❡ ❛♥❞ ❞r❛✐♥ ❝♦♥t❛❝ts ✭s❡❡ ❋✐❣✉r❡ ✹❜
❖✶ ✮✳ ❇♦t❤ ❣❛t❡s ❤❛✈❡ t❤❡ s❛♠❡ ❧❡✈❡r ❛r♠ ♦♥ t❤❡ r❡s♦♥❛♥❝❡s ♦❢ t❤✐s ❞♦t✱ ❧❡❛❞✐♥❣ t♦ ❞✐❛❣♦♥❛❧ r❡s♦♥❛♥❝❡s ✇✐t❤ ❛ s❧♦♣❡ ♦❢ ❛❜♦✉t ✲✶ ✐♥ t❤✐s ♠❡❛s✉r❡♠❡♥t✳ ❚❤❡ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs ♦❢ t❤✐s ❞♦t ❛r❡ t✉♥❛❜❧❡✱ ✇❤✐❝❤ ❛❧❧♦✇s ❢♦r ❝❤❛♥❣✐♥❣ t❤❡ t✉♥♥❡❧✐♥❣ r❛t❡s t❤r♦✉❣❤ t❤❡ ❞♦t✳ ❇② ❞❡❝r❡❛s✐♥❣ t❤❡ ✈♦❧t❛❣❡s ♦❢ t❤❡ ✜♥❣❡r ❣❛t❡s V◗❉✷ ❛♥❞ V◗❉✸ ❢✉rt❤❡r✱ ✇❡ ❝❛♥ ❢♦r♠ ❞♦✉❜❧❡✲ ❛♥❞ tr✐♣❧❡✲❞♦ts ✐♥ ❝❤❛♥♥❡❧ ✷ ✭s❦❡t❝❤❡s ♦❢ t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡r ❞❡♥s✐t② ✐♥ t❤❡ ❝❤❛♥♥❡❧ ❛r❡ s❤♦✇♥ ✐♥
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❋✐❣✉r❡ ✹❜ ✷ t♦ ✹ ✮ s✐♠✐❧❛r ❛s ❞❡♠♦♥str❛t❡❞ ✐♥ ❘❡❢✳ ✶✷ ❈❤❛r❣❡ ♦❝❝✉♣❛t✐♦♥ ♦❢ t❤❡s❡ ♠✉❧t✐❞♦ts✱ ✶✵
ACS Paragon Plus Environment
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Nano Letters
✐s ❛❧s♦ ❞❡t❡❝t❡❞ ✉s✐♥❣ ◗❉✶ ❛s t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❖♥ t❤❡ ♦♥❡ ❤❛♥❞✱ t❤❡ ❣❛t❡ ✈♦❧t❛❣❡ V◗❉✷ ♦♥ t❤❡ ❧❡❢t ♦✉t❡r ✜♥❣❡r ❣❛t❡ ✐♥ ❝❤❛♥♥❡❧ ✷ ✐s ♠♦r❡ ♥❡❣❛t✐✈❡ ❛♥❞ ❛ ❤♦❧❡ ❞♦t ❢♦r♠s ❜❡❧♦✇ t❤❡ ❣❛t❡✳
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❍❡♥❝❡✱ ❛❞❞✐t✐♦♥❛❧ ✈❡rt✐❝❛❧ r❡s♦♥❛♥❝❡s ✭♠❛r❦❡❞ ✇✐t❤ r❡❞ ❛rr♦✇s✮ ❛r❡ ♦❜s❡r✈❡❞ ✐♥ r❡❣✐♦♥ ✷
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❛t V◗❉✷ = −5.61 ❱, −5.76 ❱, −5.87 ❱ ❛♥❞ −5.97 ❱ ✭s❡❡ s❝❤❡♠❛t✐❝ ♣✐❝t✉r❡ ✷ ✐♥ ❋✐❣✉r❡ ✹❜✮✳ ❋♦r t❤✐s s✐t✉❛t✐♦♥ ♦❢ ❛♥ ❡❧❡❝tr♦♥✲❤♦❧❡ ❞♦✉❜❧❡✲❞♦t✱ ✇❡ ♦❜s❡r✈❡ t❤❡ t②♣✐❝❛❧ ❤♦♥❡②❝♦♠❜ ♣❛tt❡r♥ ✉s✐♥❣ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ✇❡ ❞❡❝r❡❛s❡ t❤❡ ✈♦❧t❛❣❡ ♦♥ ✜♥❣❡r ❣❛t❡ ✸ ✭V◗❉✸ ✮ s✉❝❤ t❤❛t ❛ ❤♦❧❡
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◗❉ ✐s ❢♦r♠❡❞ ❜❡❧♦✇ t❤✐s ❣❛t❡✳ ❲❡ ♦❜s❡r✈❡ ❤♦r✐③♦♥t❛❧ r❡s♦♥❛♥❝❡s ✐♥ r❡❣✐♦♥ ✸ ✐♥ ❋✐❣✉r❡ ✹❛ ✭V◗❉✸ = −6.26 ❱, −6.38 ❱ ❛♥❞ −6.47 ❱✱ ♠❛r❦❡❞ ✇✐t❤ ❜❧✉❡ ❛rr♦✇s✮✱ ✇❤✐❝❤ ❛r❡ ♥♦t ✐♥✢✉❡♥❝❡❞
❖
❜② V◗❉✷ ✳ ■♥ r❡❣✐♦♥ ✹ ✐♥ ❋✐❣✉r❡ ✹❛✱ t❤r❡❡ ❞♦ts ❛r❡ ❢♦r♠❡❞✲ ♦♥❡ ♣✲t②♣❡ ◗❉ ❜❡❧♦✇ ❡❛❝❤ ♦❢ t❤❡ ❣❛t❡s ❛♥❞ ❛♥ ♥✲t②♣❡ ❞♦t ❜❡t✇❡❡♥ t❤❡♠✳ ❚❤✐s ❧❡❛❞s t♦ ❞✐❛❣♦♥❛❧ r❡s♦♥❛♥❝❡s ❢♦r t❤❡ t✉♥♥❡❧✐♥❣ t❤r♦✉❣❤ t❤❡ ❡❧❡❝tr♦♥ ❞♦t ✐♥ t❤❡ ♠✐❞❞❧❡✱ ❤♦r✐③♦♥t❛❧ r❡s♦♥❛♥❝❡s ❢♦r t✉♥♥❡❧✐♥❣ t❤r♦✉❣❤ ◗❉✸ ❛♥❞ ✈❡rt✐❝❛❧ ❧✐♥❡ ❢♦r t✉♥♥❡❧✐♥❣ t❤r♦✉❣❤ ◗❉✷✳ ❚❤❡ t❤r❡❡ ❞♦ts ♠❡❛s✉r❡❞ ✐♥ ❋✐❣✉r❡ ✹❛ ❤❛✈❡ ❞✐✛❡r❡♥t ❞✐st❛♥❝❡s t♦ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t♦r✳ ❍❡♥❝❡✱ ❝❤❛r❣✐♥❣ t❤❡ ❞✐✛❡r❡♥t ❞♦ts ❧❡❛❞s t♦ ❞✐✛❡r❡♥t ❡♥❡r❣② s❤✐❢ts ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦ts r❡s♦✲ ♥❛♥❝❡✳ ❚❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ s✐❣♥❛❧ ❞♦t ❛♥❞ t❤❡ s❡♥s✐♥❣ ❞♦t ❝❤❛♥❣❡s ❢r♦♠ 260 ♥♠ ✭❞♦t ❜❡t✇❡❡♥ t❤❡ ❣❛t❡s✱ ❜❧✉❡ ✐♥ ❋✐❣✉r❡ ✹❜✮ t♦ 315 ♥♠ ✭❞♦t ❜❡❧♦✇ ❧❡❢t ❣❛t❡ ✐♥ ❋✐❣✉r❡ ✹❜✮✳ ❚❤❡ ❡♥❡r❣② s❤✐❢t ♦❢ t❤❡ ❞❡t❡❝t♦r r❡s♦♥❛♥❝❡ ✐s ❡✈❛❧✉❛t❡❞ ❢r♦♠ t❤❡ ❞❡t❡❝t✐♦♥ s✐❣♥❛❧ ✉s✐♥❣ t❤❡ s❤✐❢t ✐♥ ❣❛t❡ ✈♦❧t❛❣❡ ❛♥❞ t❤❡ r❡❧❛t✐✈❡ ❧❡✈❡r ❛r♠s α✱ α❋●✷✲◗❉✶/α
❋●✶✲◗❉✶
❛♥❞ α❋●✸✲◗❉✶/α
❋●✶✲◗❉✶
= 0.01✳
■t ❞❡❝r❡❛s❡s ✇✐t❤ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ s❡♥s✐♥❣ ❛♥❞ s✐❣♥❛❧ ❞♦t ❢r♦♠ 50 µ❡❱ t♦ 5 µ❡❱ ✐♥ ❛❣r❡❡✲ ♠❡♥t ✇✐t❤ ❛ ❈♦✉❧♦♠❜ s❝r❡❡♥✐♥❣ ♠♦❞❡❧✳ ❖✉r s❛♠♣❧❡ ❞❡s✐❣♥ ❛❧❧♦✇s ❢♦r ❛ ♠✐♥✐♠❛❧ ❞✐st❛♥❝❡ ♦❢ 150 ♥♠ ❜❡t✇❡❡♥ t❤❡ s❡♥s✐♥❣ ❞♦t ❛♥❞ t❤❡ s✐❣♥❛❧ ❞♦t✱ ✇❤✐❝❤ ❧❡❛❞s t♦ ❛♥ ❡♥❡r❣② s❤✐❢t ♦❢ 6 ♠❡❱
✇❤✐❝❤ ✐s ♦❢ t❤❡ s❛♠❡ ♦r❞❡r ❛s t❤❡ ❝❤❛r❣✐♥❣ ❡♥❡r❣② ♦❢ t❤❡ s❡♥s✐♥❣ ❞♦t✳ ■♥ ❝♦♥❝❧✉s✐♦♥✱ ✇❡ ♣r❡s❡♥t❡❞ ❛♥ ❡❧❡❝tr♦st❛t✐❝❛❧❧②✲❞❡✜♥❡❞ ❞❡✈✐❝❡ t❤❛t ❛❧❧♦✇s ✉s t♦ ❞❡t❡❝t s✐♥❣❧❡ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ❯s✐♥❣ ❝♦♥❞✉❝t❛♥❝❡ r❡s♦♥❛♥❝❡s ✐♥ t❤❡ ❈♦✉❧♦♠❜✲❜❧♦❝❦❛❞❡ r❡❣✐♠❡ ♦❢ ❛ s❡❝♦♥❞ q✉❛♥t✉♠ ❞♦t ❛s ❛ s❡♥s✐t✐✈❡ ❞❡t❡❝t♦r✱ ✇❡ r❡❛❝❤❡❞ ❛ ♠❛①✐♠✉♠ r❡❧❛t✐✈❡ ❝♦♥❞✉❝t❛♥❝❡ ❝❤❛♥❣❡ ♦❢ ✼✼✪ ❢♦r ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥✳ ❖✉r ♠❡❛s✉r❡♠❡♥ts ✶✶
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
s❤♦✇ t❤❛t ❛ ✇✐❞t❤ ♦❢ 150 ♥♠ ❢♦r t❤❡ ▼● ✐s s✉✣❝✐❡♥t t♦ ❛✈♦✐❞ ❧❡❛❦❛❣❡ ❜❡t✇❡❡♥ t❤❡ s❡♥s✐♥❣ ❛♥❞ s✐❣♥❛❧ ❞♦t ❛♥❞ t♦ r❡❛❝❤ ❛ ❤✐❣❤ s✐❣♥❛❧✲t♦✲♥♦✐s❡ r❛t✐♦ ✐♥ t❤❡ ❞❡t❡❝t♦r✳ ❯s✐♥❣ t❤✐s ❞❡✈✐❝❡✱ ✇❡ ✇❡r❡ ❛❜❧❡ t♦ s❤♦✇ ❝♦♠♣❧❡t❡ ❞❡♣❧❡t✐♦♥ ♦❢ ♦♥❡ ♦❢ t❤❡ q✉❛♥t✉♠ ❞♦ts✳ ❋✉rt❤❡r♠♦r❡✱ ✇❡ ✇❡r❡ ❛❜❧❡ t♦ ♦❜s❡r✈❡ t❤❡ ❝❤❛♥❣❡s ✐♥ t❤❡ ❝❤❛r❣❡ st❛t❡ ♦❢ ❛ q✉❛♥t✉♠ ❞♦t ✇✐t❤ t✉♥❛❜❧❡ t✉♥♥❡❧✐♥❣ ❜❛rr✐❡rs✱ ❛♥❞ ♦❢ ❛ ♠✉❧t✐✲❞♦t s②st❡♠✳ ■♥ t❤❡ ♠✉❧t✐✲❞♦t r❡❣✐♠❡✱ t❤❡ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ❡♥❛❜❧❡s ✉s t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♥✉♠❜❡r ♦❢ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ❡❛❝❤ ♦❢ t❤❡ ❞♦ts✳ ❖✉r ❡①♣❡r✐♠❡♥ts ❞❡♠♦♥str❛t❡ ❛ ❞❡✈✐❝❡ t❤❛t ✐s ♥❡❡❞❡❞ ❛s t❤❡ st❛rt✐♥❣ ♣♦✐♥t ❢♦r t✐♠❡✲r❡s♦❧✈❡❞ ♠❡❛s✉r❡♠❡♥ts ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✱ ✇❤✐❝❤ ♠❛② ❛❧❧♦✇ ✉s t♦ ✐♥✈❡st✐❣❛t❡ t❤❡ s♣✐♥✲❧✐❢❡t✐♠❡ ✐♥ ❣r❛♣❤❡♥❡✳ ✺
❆❝❦♥♦✇❧❡❞❣♠❡♥ts ❲❡ t❤❛♥❦ P❡t❡r ▼är❦✐✱ ❊r✇✐♥ ❙t✉❞❡r✱ ❛s ✇❡❧❧ ❛s t❤❡ ❋■❘❙❚ st❛✛ ❢♦r t❤❡✐r t❡❝❤♥✐❝❛❧ s✉♣♣♦rt✳ ❲❡ ❛❧s♦ ❛❝❦♥♦✇❧❡❞❣❡ ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ❢r♦♠ t❤❡ ❊✉r♦♣❡❛♥ ●r❛♣❤❡♥❡ ❋❧❛❣s❤✐♣✱ t❤❡ ❙✇✐ss ◆❛t✐♦♥❛❧ ❙❝✐❡♥❝❡ ❋♦✉♥❞❛t✐♦♥ ✈✐❛ ◆❈❈❘ ◗✉❛♥t✉♠ ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤♥♦❧♦❣②✱ t❤❡ ❊❯ ❙♣✐♥✲ ◆❛♥♦ ❘❚◆ ♥❡t✇♦r❦ ❛♥❞ ❊❚❍ ❩✉r✐❝❤ ✈✐❛ t❤❡ ❊❚❍ ❢❡❧❧♦✇s❤✐♣ ♣r♦❣r❛♠✳ ●r♦✇t❤ ♦❢ ❤❡①❛❣♦♥❛❧ ❜♦r♦♥ ♥✐tr✐❞❡ ❝r②st❛❧s ✇❛s s✉♣♣♦rt❡❞ ❜② t❤❡ ❊❧❡♠❡♥t❛❧ ❙tr❛t❡❣② ■♥✐t✐❛t✐✈❡ ❝♦♥❞✉❝t❡❞ ❜② t❤❡ ▼❊❳❚✱ ❏❛♣❛♥ ❛♥❞ t❤❡ ❈❘❊❙❚ ✭❏P▼❏❈❘✶✺❋✸✮✱ ❏❙❚✳
❘❡❢❡r❡♥❝❡s ✭✶✮ ❚r❛✉③❡tt❡❧✱ ❇✳❀ ❇✉❧❛❡✈✱ ❉✳ ❱✳❀ ▲♦ss✱ ❉✳❀ ❇✉r❦❛r❞✱ ●✳ ❙♣✐♥ q✉❜✐ts ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ◆❛t✉r❡ P❤②s✐❝s ✷✵✵✼✱ ✸✱ ✶✾✷✳ ✭✷✮ ◆♦✈♦s❡❧♦✈✱ ❑✳ ❙✳❀ ●❡✐♠✱ ❆✳ ❑✳❀ ▼♦r♦③♦✈✱ ❙✳❀ ❏✐❛♥❣✱ ❉✳❀ ❑❛ts♥❡❧s♦♥✱ ▼✳❀ ●r✐❣♦r✐❡✈❛✱ ■✳❀ ❉✉❜♦♥♦s✱ ❙✳❀ ❋✐rs♦✈✱ ❆✳ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❣❛s ♦❢ ♠❛ss❧❡ss ❉✐r❛❝ ❢❡r♠✐♦♥s ✐♥ ❣r❛♣❤❡♥❡✳ ◆❛t✉r❡ ✷✵✵✺✱ ✹✸✽✱ ✶✾✼✳
✭✸✮ ❩❤❛♥❣✱ ❨✳❀ ❚❛♥✱ ❨✳✲❲✳❀ ❙t♦r♠❡r✱ ❍✳ ▲✳❀ ❑✐♠✱ P✳ ❊①♣❡r✐♠❡♥t❛❧ ♦❜s❡r✈❛t✐♦♥ ♦❢ t❤❡ q✉❛♥✲ t✉♠ ❍❛❧❧ ❡✛❡❝t ❛♥❞ ❇❡rr②✬s ♣❤❛s❡ ✐♥ ❣r❛♣❤❡♥❡✳ ◆❛t✉r❡ ✷✵✵✺✱ ✹✸✽✱ ✷✵✶✳ ✶✷
ACS Paragon Plus Environment
Page 12 of 21
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Nano Letters
✭✹✮ ❇❛♥s③❡r✉s✱ ▲✳❀ ❙❝❤♠✐t③✱ ▼✳❀ ❊♥❣❡❧s✱ ❙✳❀ ❉❛✉❜❡r✱ ❏✳❀ ❖❡❧❧❡rs✱ ▼✳❀ ❍❛✉♣t✱ ❋✳❀ ❲❛t❛♥✲ ❛❜❡✱ ❑✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❇❡s❝❤♦t❡♥✱ ❇✳❀ ❙t❛♠♣❢❡r✱ ❈✳ ❯❧tr❛❤✐❣❤✲♠♦❜✐❧✐t② ❣r❛♣❤❡♥❡ ❞❡✲ ✈✐❝❡s ❢r♦♠ ❝❤❡♠✐❝❛❧ ✈❛♣♦r ❞❡♣♦s✐t✐♦♥ ♦♥ r❡✉s❛❜❧❡ ❝♦♣♣❡r✳
❙❝✐❡♥❝❡ ❛❞✈❛♥❝❡s
✷✵✶✺✱ ✶✱
❡✶✺✵✵✷✷✷✳ ✭✺✮ ❊❧③❡r♠❛♥✱ ❏✳❀ ❍❛♥s♦♥✱ ❘✳❀ ❱❛♥ ❇❡✈❡r❡♥✱ ▲✳ ❲✳❀ ❲✐t❦❛♠♣✱ ❇✳❀ ❱❛♥❞❡rs②♣❡♥✱ ▲✳❀ ❑♦✉✇❡♥✲ ❤♦✈❡♥✱ ▲✳ P✳ ❙✐♥❣❧❡✲s❤♦t r❡❛❞✲♦✉t ♦❢ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ❡❧❡❝tr♦♥ s♣✐♥ ✐♥ ❛ q✉❛♥t✉♠ ❞♦t✳ ◆❛t✉r❡
✷✵✵✹✱ ✹✸✵✱ ✹✸✶✳ ✭✻✮ P❡tt❛✱ ❏✳ ❘✳❀ ❏♦❤♥s♦♥✱ ❆✳ ❈✳❀ ❚❛②❧♦r✱ ❏✳ ▼✳❀ ▲❛✐r❞✱ ❊✳ ❆✳❀ ❨❛❝♦❜②✱ ❆✳❀ ▲✉❦✐♥✱ ▼✳ ❉✳❀ ▼❛r❝✉s✱ ❈✳ ▼✳❀ ❍❛♥s♦♥✱ ▼✳ P✳❀ ●♦ss❛r❞✱ ❆✳ ❈✳ ❈♦❤❡r❡♥t ♠❛♥✐♣✉❧❛t✐♦♥ ♦❢ ❝♦✉♣❧❡❞ ❡❧❡❝tr♦♥ s♣✐♥s ✐♥ s❡♠✐❝♦♥❞✉❝t♦r q✉❛♥t✉♠ ❞♦ts✳
❙❝✐❡♥❝❡
✷✵✵✺✱ ✸✵✾✱ ✷✶✽✵✕✷✶✽✹✳
✭✼✮ ❉✐❈❛r❧♦✱ ▲✳❀ ▲②♥❝❤✱ ❍✳❀ ❏♦❤♥s♦♥✱ ❆✳❀ ❈❤✐❧❞r❡ss✱ ▲✳❀ ❈r♦❝❦❡tt✱ ❑✳❀ ▼❛r❝✉s✱ ❈✳❀ ❍❛♥✲ s♦♥✱ ▼✳❀ ●♦ss❛r❞✱ ❆✳ ❉✐✛❡r❡♥t✐❛❧ ❝❤❛r❣❡ s❡♥s✐♥❣ ❛♥❞ ❝❤❛r❣❡ ❞❡❧♦❝❛❧✐③❛t✐♦♥ ✐♥ ❛ t✉♥❛❜❧❡ ❞♦✉❜❧❡ q✉❛♥t✉♠ ❞♦t✳
P❤②s✐❝❛❧ r❡✈✐❡✇ ❧❡tt❡rs
✷✵✵✹✱ ✾✷✱ ✷✷✻✽✵✶✳
✭✽✮ ●✉st❛✈ss♦♥✱ ❙✳❀ ▲❡t✉r❝q✱ ❘✳❀ ❙✐♠♦✈✐↔✱ ❇✳❀ ❙❝❤❧❡s❡r✱ ❘✳❀ ■❤♥✱ ❚✳❀ ❙t✉❞❡r✉s✱ P✳❀ ❊♥ss❧✐♥✱ ❑✳❀ ❉r✐s❝♦❧❧✱ ❉✳❀ ●♦ss❛r❞✱ ❆✳ ❈♦✉♥t✐♥❣ st❛t✐st✐❝s ♦❢ s✐♥❣❧❡ ❡❧❡❝tr♦♥ tr❛♥s♣♦rt ✐♥ ❛ q✉❛♥t✉♠ ❞♦t✳
P❤②s✐❝❛❧ r❡✈✐❡✇ ❧❡tt❡rs
✷✵✵✻✱ ✾✻✱ ✵✼✻✻✵✺✳
✭✾✮ ❱❛♥❞❡rs②♣❡♥✱ ▲✳❀ ❊❧③❡r♠❛♥✱ ❏✳❀ ❙❝❤♦✉t❡♥✱ ❘✳❀ ❲✐❧❧❡♠s ✈❛♥ ❇❡✈❡r❡♥✱ ▲✳❀ ❍❛♥s♦♥✱ ❘✳❀ ❑♦✉✇❡♥❤♦✈❡♥✱ ▲✳ ❘❡❛❧✲t✐♠❡ ❞❡t❡❝t✐♦♥ ♦❢ s✐♥❣❧❡✲❡❧❡❝tr♦♥ t✉♥♥❡❧✐♥❣ ✉s✐♥❣ ❛ q✉❛♥t✉♠ ♣♦✐♥t ❝♦♥t❛❝t✳
❆♣♣❧✐❡❞ P❤②s✐❝s ▲❡tt❡rs
✷✵✵✹✱ ✽✺✱ ✹✸✾✹✕✹✸✾✻✳
✭✶✵✮ ❊✐❝❤✱ ▼✳❀ P✐s♦♥✐✱ ❘✳❀ ❖✈❡r✇❡❣✱ ❍✳❀ ❑✉r③♠❛♥♥✱ ❆✳❀ ▲❡❡✱ ❨✳❀ ❘✐❝❦❤❛✉s✱ P✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳❀ ❍❡r♠❛♥✱ ❋✳❀ ❙✐❣r✐st✱ ▼✳ ❙♣✐♥ ❛♥❞ ❱❛❧❧❡② ❙t❛t❡s ✐♥ ●❛t❡✲❉❡✜♥❡❞ ❇✐❧❛②❡r ●r❛♣❤❡♥❡ ◗✉❛♥t✉♠ ❉♦ts✳
P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❳
✷✵✶✽✱ ✽✱ ✵✸✶✵✷✸✳
✭✶✶✮ ❇❛♥s③❡r✉s✱ ▲✳❀ ❋r♦❤♥✱ ❇✳❀ ❊♣♣✐♥❣✱ ❆✳❀ ◆❡✉♠❛✐❡r✱ ❉✳❀ ❲❛t❛♥❛❜❡✱ ❑✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❙t❛♠♣❢❡r✱ ❈✳ ●❛t❡✲❉❡✜♥❡❞ ❊❧❡❝tr♦♥✕❍♦❧❡ ❉♦✉❜❧❡ ❉♦ts ✐♥ ❇✐❧❛②❡r ●r❛♣❤❡♥❡✳ ◆❛♥♦ t❡rs
✷✵✶✽✱ ✶✽✱ ✹✼✽✺✕✹✼✾✵✳ ✶✸
ACS Paragon Plus Environment
▲❡t✲
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✭✶✷✮ ❊✐❝❤✱ ▼✳❀ P✐s♦♥✐✱ ❘✳❀ P❛❧❧②✱ ❆✳❀ ❖✈❡r✇❡❣✱ ❍✳❀ ❑✉r③♠❛♥♥✱ ❆✳❀ ▲❡❡✱ ❨✳❀ ❘✐❝❦❤❛✉s✱ P✳❀ ❲❛t❛♥❛❜❡✱ ❑✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳❀ ●r❛♣❤❡♥❡✳
◆❛♥♦ ▲❡tt❡rs
❡t ❛❧
❈♦✉♣❧❡❞ ◗✉❛♥t✉♠ ❉♦ts ✐♥ ❇✐❧❛②❡r
✷✵✶✽✱ ✶✽✱ ✺✵✹✷✕✺✵✹✽✳
✭✶✸✮ ❖✈❡r✇❡❣✱ ❍✳❀ ❊❣❣✐♠❛♥♥✱ ❍✳❀ ❈❤❡♥✱ ❳✳❀ ❙❧✐③♦✈s❦✐②✱ ❙✳❀ ❊✐❝❤✱ ▼✳❀ P✐s♦♥✐✱ ❘✳❀ ▲❡❡✱ ❨✳❀ ❘✐❝❦❤❛✉s✱ P✳❀ ❲❛t❛♥❛❜❡✱ ❑✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ♣♦✐♥t ❝♦♥t❛❝ts ✐♥ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✳
❡t ❛❧
◆❛♥♦ ❧❡tt❡rs
❊❧❡❝tr♦st❛t✐❝❛❧❧② ✐♥❞✉❝❡❞ q✉❛♥t✉♠
✷✵✶✼✱ ✶✽✱ ✺✺✸✕✺✺✾✳
✭✶✹✮ ❑r❛❢t✱ ❘✳❀ ❑r❛✐♥♦✈✱ ■✳❀ ●❛❧❧✱ ❱✳❀ ❉♠✐tr✐❡✈✱ ❆✳❀ ❑r✉♣❦❡✱ ❘✳❀ ●♦r♥②✐✱ ■✳❀ ❉❛♥♥❡❛✉✱ ❘✳ ❱❛❧❧❡② ❙✉❜❜❛♥❞ ❙♣❧✐tt✐♥❣ ✐♥ ❇✐❧❛②❡r ●r❛♣❤❡♥❡ ◗✉❛♥t✉♠ P♦✐♥t ❈♦♥t❛❝ts✳ ▲❡tt✳
P❤②s✳ ❘❡✈✳
✷✵✶✽✱ ✶✷✶✱ ✷✺✼✼✵✸✳
✭✶✺✮ ▼❝❈❛♥♥✱ ❊✳ ❆s②♠♠❡tr② ❣❛♣ ✐♥ t❤❡ ❡❧❡❝tr♦♥✐❝ ❜❛♥❞ str✉❝t✉r❡ ♦❢ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✳ P❤②s✲ ✐❝❛❧ ❘❡✈✐❡✇ ❇
✷✵✵✻✱ ✼✹✱ ✶✻✶✹✵✸✳
✭✶✻✮ ❖❤t❛✱ ❚✳❀ ❇♦st✇✐❝❦✱ ❆✳❀ ❙❡②❧❧❡r✱ ❚✳❀ ❍♦r♥✱ ❑✳❀ ❘♦t❡♥❜❡r❣✱ ❊✳ ❈♦♥tr♦❧❧✐♥❣ t❤❡ ❡❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ♦❢ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✳
❙❝✐❡♥❝❡
✷✵✵✻✱ ✸✶✸✱ ✾✺✶✕✾✺✹✳
✭✶✼✮ ❖♦st✐♥❣❛✱ ❏✳ ❇✳❀ ❍❡❡rs❝❤❡✱ ❍✳ ❇✳❀ ▲✐✉✱ ❳✳❀ ▼♦r♣✉r❣♦✱ ❆✳ ❋✳❀ ❱❛♥❞❡rs②♣❡♥✱ ▲✳ ▼✳ ●❛t❡✲ ✐♥❞✉❝❡❞ ✐♥s✉❧❛t✐♥❣ st❛t❡ ✐♥ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ❞❡✈✐❝❡s✳
◆❛t✉r❡ ♠❛t❡r✐❛❧s
✷✵✵✽✱ ✼✱ ✶✺✶✳
✭✶✽✮ ❉❡❛♥✱ ❈✳ ❘✳❀ ❨♦✉♥❣✱ ❆✳ ❋✳❀ ▼❡r✐❝✱ ■✳❀ ▲❡❡✱ ❈✳❀ ❲❛♥❣✱ ▲✳❀ ❙♦r❣❡♥❢r❡✐✱ ❙✳❀ ❲❛t❛♥❛❜❡✱ ❑✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❑✐♠✱ P✳❀ ❙❤❡♣❛r❞✱ ❑✳ ▲✳❀
❡t ❛❧
❣r❛♣❤❡♥❡ ❡❧❡❝tr♦♥✐❝s✳
✷✵✶✵✱ ✺✱ ✼✷✷✳
◆❛t✳ ◆❛♥♦t❡❝❤♥♦❧✳
❇♦r♦♥ ♥✐tr✐❞❡ s✉❜str❛t❡s ❢♦r ❤✐❣❤✲q✉❛❧✐t②
✭✶✾✮ ❲❛♥❣✱ ▲✳❀ ▼❡r✐❝✱ ■✳❀ ❍✉❛♥❣✱ P✳❀ ●❛♦✱ ◗✳❀ ●❛♦✱ ❨✳❀ ❚r❛♥✱ ❍✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❲❛t❛♥✲ ❛❜❡✱ ❑✳❀ ❈❛♠♣♦s✱ ▲✳❀ ▼✉❧❧❡r✱ ❉✳❀ ❞✐♠❡♥s✐♦♥❛❧ ♠❛t❡r✐❛❧✳
❙❝✐❡♥❝❡
❡t ❛❧
❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr✐❝❛❧ ❝♦♥t❛❝t t♦ ❛ t✇♦✲
✷✵✶✸✱ ✸✹✷✱ ✻✶✹✕✻✶✼✳
✭✷✵✮ ❩✐❜r♦✈✱ ❆✳❀ ❑♦♠❡tt❡r✱ ❈✳❀ ❩❤♦✉✱ ❍✳❀ ❙♣❛♥t♦♥✱ ❊✳❀ ❚❛♥✐❣✉❝❤✐✱ ❚✳❀ ❲❛t❛♥❛❜❡✱ ❑✳❀ ❩❛❧❡✲ t❡❧✱ ▼✳❀ ❨♦✉♥❣✱ ❆✳ ❚✉♥❛❜❧❡ ✐♥t❡r❛❝t✐♥❣ ❝♦♠♣♦s✐t❡ ❢❡r♠✐♦♥ ♣❤❛s❡s ✐♥ ❛ ❤❛❧❢✲✜❧❧❡❞ ❜✐❧❛②❡r✲ ❣r❛♣❤❡♥❡ ▲❛♥❞❛✉ ❧❡✈❡❧✳
◆❛t✉r❡
✷✵✶✼✱ ✺✹✾✱ ✸✻✵✳ ✶✹
ACS Paragon Plus Environment
Page 15 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
✭✷✶✮ ❙t❛♠♣❢❡r✱ ❈✳❀ ●ütt✐♥❣❡r✱ ❏✳❀ ❍❡❧❧♠ü❧❧❡r✱ ❙✳❀ ▼♦❧✐t♦r✱ ❋✳❀ ❊♥ss❧✐♥✱ ❑✳❀ ■❤♥✱ ❚✳ ❊♥❡r❣② ❣❛♣s ✐♥ ❡t❝❤❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✳ P❤②s✐❝❛❧ r❡✈✐❡✇ ❧❡tt❡rs ✷✵✵✾✱ ✶✵✷✱ ✵✺✻✹✵✸✳ ✭✷✷✮ ▲✐✉✱ ❳✳❀ ❖♦st✐♥❣❛✱ ❏✳ ❇✳❀ ▼♦r♣✉r❣♦✱ ❆✳ ❋✳❀ ❱❛♥❞❡rs②♣❡♥✱ ▲✳ ▼✳ ❊❧❡❝tr♦st❛t✐❝ ❝♦♥✜♥❡♠❡♥t ♦❢ ❡❧❡❝tr♦♥s ✐♥ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✳ P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❇ ✷✵✵✾✱ ✽✵✱ ✶✷✶✹✵✼✳ ✭✷✸✮ ❍❛♥✱ ▼✳ ❨✳❀ ❇r❛♥t✱ ❏✳ ❈✳❀ ❑✐♠✱ P✳ ❊❧❡❝tr♦♥ tr❛♥s♣♦rt ✐♥ ❞✐s♦r❞❡r❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜✲ ❜♦♥s✳ P❤②s✐❝❛❧ r❡✈✐❡✇ ❧❡tt❡rs ✷✵✶✵✱ ✶✵✹✱ ✵✺✻✽✵✶✳ ✭✷✹✮ ❙t❛♠♣❢❡r✱ ❈✳❀ ❙❝❤✉rt❡♥❜❡r❣❡r✱ ❊✳❀ ▼♦❧✐t♦r✱ ❋✳❀ ●✉tt✐♥❣❡r✱ ❏✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳ ❚✉♥✲ ❛❜❧❡ ❣r❛♣❤❡♥❡ s✐♥❣❧❡ ❡❧❡❝tr♦♥ tr❛♥s✐st♦r✳ ◆❛♥♦ ❧❡tt❡rs ✷✵✵✽✱ ✽✱ ✷✸✼✽✕✷✸✽✸✳ ✭✷✺✮ P♦♥♦♠❛r❡♥❦♦✱ ▲✳❀ ❙❝❤❡❞✐♥✱ ❋✳❀ ❑❛ts♥❡❧s♦♥✱ ▼✳❀ ❨❛♥❣✱ ❘✳❀ ❍✐❧❧✱ ❊✳❀ ◆♦✈♦s❡❧♦✈✱ ❑✳❀ ●❡✐♠✱ ❆✳ ❈❤❛♦t✐❝ ❉✐r❛❝ ❜✐❧❧✐❛r❞ ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ❙❝✐❡♥❝❡ ✷✵✵✽✱ ✸✷✵✱ ✸✺✻✕✸✺✽✳ ✭✷✻✮ ❙❝❤♥❡③✱ ❙✳❀ ▼♦❧✐t♦r✱ ❋✳❀ ❙t❛♠♣❢❡r✱ ❈✳❀ ●ütt✐♥❣❡r✱ ❏✳❀ ❙❤♦r✉❜❛❧❦♦✱ ■✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳ ❖❜s❡r✈❛t✐♦♥ ♦❢ ❡①❝✐t❡❞ st❛t❡s ✐♥ ❛ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦t✳ ❆♣♣❧✐❡❞ P❤②s✐❝s ▲❡tt❡rs ✷✵✵✾✱ ✾✹✱
✵✶✷✶✵✼✳
✭✷✼✮ ●ütt✐♥❣❡r✱ ❏✳❀ ▼♦❧✐t♦r✱ ❋✳❀ ❙t❛♠♣❢❡r✱ ❈✳❀ ❙❝❤♥❡③✱ ❙✳❀ ❏❛❝♦❜s❡♥✱ ❆✳❀ ❉rös❝❤❡r✱ ❙✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳ ❚r❛♥s♣♦rt t❤r♦✉❣❤ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ❘❡♣♦rts ♦♥ Pr♦❣r❡ss ✐♥ P❤②s✐❝s
✷✵✶✷✱ ✼✺✱ ✶✷✻✺✵✷✳ ✭✷✽✮ ●ütt✐♥❣❡r✱ ❏✳❀ ❙t❛♠♣❢❡r✱ ❈✳❀ ❍❡❧❧♠ü❧❧❡r✱ ❙✳❀ ▼♦❧✐t♦r✱ ❋✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳ ❈❤❛r❣❡ ❞❡t❡❝t✐♦♥ ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ❆♣♣❧✐❡❞ P❤②s✐❝s ▲❡tt❡rs ✷✵✵✽✱ ✾✸✱ ✷✶✷✶✵✷✳ ✭✷✾✮ ❲❛♥❣✱ ▲✳✲❏✳❀ ❈❛♦✱ ●✳❀ ❚✉✱ ❚✳❀ ▲✐✱ ❍✳✲❖✳❀ ❩❤♦✉✱ ❈✳❀ ❍❛♦✱ ❳✳✲❏✳❀ ❙✉✱ ❩✳❀ ●✉♦✱ ●✳✲❈✳❀ ❏✐❛♥❣✱ ❍✳✲❲✳❀ ●✉♦✱ ●✳✲P✳ ❆ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦t ✇✐t❤ ❛ s✐♥❣❧❡ ❡❧❡❝tr♦♥ tr❛♥s✐st♦r ❛s ❛♥ ✐♥t❡❣r❛t❡❞ ❝❤❛r❣❡ s❡♥s♦r✳ ❆♣♣❧✐❡❞ P❤②s✐❝s ▲❡tt❡rs ✷✵✶✵✱ ✾✼✱ ✷✻✷✶✶✸✳ ✭✸✵✮ ❋r✐♥❣❡s✱ ❙✳❀ ❱♦❧❦✱ ❈✳❀ ◆♦r❞❛✱ ❈✳❀ ❚❡rrés✱ ❇✳❀ ❉❛✉❜❡r✱ ❏✳❀ ❊♥❣❡❧s✱ ❙✳❀ ❚r❡❧❧❡♥❦❛♠♣✱ ❙✳❀ ❙t❛♠♣❢❡r✱ ❈✳ ❈❤❛r❣❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦t✳ ♣❤②s✐❝❛ st❛t✉s s♦❧✐❞✐ ✭❜✮
✷✵✶✶✱ ✷✹✽✱ ✷✻✽✹✕✷✻✽✼✳ ✶✺
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 16 of 21
✭✸✶✮ ❱♦❧❦✱ ❈✳❀ ◆❡✉♠❛♥♥✱ ❈✳❀ ❑❛③❛rs❦✐✱ ❙✳❀ ❋r✐♥❣❡s✱ ❙✳❀ ❊♥❣❡❧s✱ ❙✳❀ ❍❛✉♣t✱ ❋✳❀ ▼ü❧❧❡r✱ ❆✳❀ ❙t❛♠♣❢❡r✱ ❈✳ Pr♦❜✐♥❣ r❡❧❛①❛t✐♦♥ t✐♠❡s ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ ◆❛t✉r❡ t✐♦♥s
❝♦♠♠✉♥✐❝❛✲
✷✵✶✸✱ ✹✱ ✶✼✺✸✳
✭✸✷✮ ❇✐s❝❤♦✛✱ ❉✳❀ ❱❛r❧❡t✱ ❆✳❀ ❙✐♠♦♥❡t✱ P✳❀ ❊✐❝❤✱ ▼✳❀ ❖✈❡r✇❡❣✱ ❍✳❀ ■❤♥✱ ❚✳❀ ❊♥ss❧✐♥✱ ❑✳ ▲♦❝❛❧✐③❡❞ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ❣r❛♣❤❡♥❡ ♥❛♥♦❞❡✈✐❝❡s✳
❆♣♣❧✐❡❞ P❤②s✐❝s ❘❡✈✐❡✇s
✷✵✶✺✱ ✷✱
✵✸✶✸✵✶✳ ✭✸✸✮ ●ütt✐♥❣❡r✱ ❏✳❀ ❙❡✐❢✱ ❏✳❀ ❙t❛♠♣❢❡r✱ ❈✳❀ ❈❛♣❡❧❧✐✱ ❆✳❀ ❊♥ss❧✐♥✱ ❑✳❀ ■❤♥✱ ❚✳ ❚✐♠❡✲r❡s♦❧✈❡❞ ❝❤❛r❣❡ ❞❡t❡❝t✐♦♥ ✐♥ ❣r❛♣❤❡♥❡ q✉❛♥t✉♠ ❞♦ts✳ P❤②s✐❝❛❧
✶✻
ACS Paragon Plus Environment
❘❡✈✐❡✇ ❇
✷✵✶✶✱ ✽✸✱ ✶✻✺✹✹✺✳
Page 17 of 21
Quantum dot Quantum dot Detector
Conductance
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Detector
Bilayer graphene Finger gate voltage
✶✼
ACS Paragon Plus Environment
Nano Letters n
Al3O2
finger gate
Page of 21 split18 gate
p
middle gate
EF drain
0.4 0.2
VSD1 (mV)
1 2 E 3 4 5 hBN 6 Bilayer graphene hBN 7 source dot 8 Graphit back gate 9 10 d b11 QD2 12 13 el2 5 nn 14 a Ch 15 QD2 16 3 2 1 0 17 MG QD1 18 l1 19 hanne C 20 -5 21 SG -9.0 ACS Paragon Plus-9.2 Environment -8.8 -9.4 22 VQD1 (V) 23 24
n
0.0 -0.2
-8.6
-0.4
∂IQD1/∂VSD1(e2/h)
c
a
0.04
Signal dot
0.02
-7.6 -7.4 VQD2 (V) c
-7.2
-7.0
0.0
GQD1 (e2/h)
0.1
GQD1 (e2/h)
VQD1 (V)
0.2
Signal dot
0.02 0.01 0.00 0.3
0.00
Sensor dot
ΔGQD1
0.2
0.0 -8.0
103 100 10
ACS Paragon Plus Environment 10
Sensor dot ΔVQD2
0.1
104
SNR
-7.8
0.03
GQD2 (e2/h)
-9.10
1 2 -9.11 3 4 -9.09 5 6 -9.10 7 -9.11 8 -8.0 9 10 11 12 13 14 15 16 17 18 19 20 21 22
b
Nano Letters
GQD2 (e2/h)
Page 19 of 21 -9.09
VQD1 (V)
a
100 103 Bandwidth (Hz)
104
-7.8
-7.6 -7.4 VQD2 (V)
-7.2
-7.0
GQD1 (e2/h)
a
0.40
Nano Letters
Signal Page 20dot of 21
0.20
GQD2 (e2/h)
1 2 0.00 b 3 0.10 3 2 1 4 5 6 0.05 7 ACS Paragon Plus Environment Sensor dot 8 0.00 -9.5 -9.25 -9.0 -8.75 -8.5 -8.25 -8.0 9 VQD1 (V) 10
Page -5.8 21 of 221
1
b 0.3 Nano Letters 0.2
-6.0
0.1 0.0
-6.2
-0.1 -6.4
1 ∂IQD1/∂VQD2 ( e2/h)
1 2 3 4 5 6 7 8 9 10
VQD3 (V)
a
-0.2 4
-6.0
-5.8
-5.6 VQD2(V)
-5.4
3 ACS Paragon Plus Environment -0.3
QD2 QD3
2
3
4
