Gate-defined electron-hole double dots in bilayer graphene

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Gate-defined electron-hole double dots in bilayer graphene Luca Banszerus, Benedikt Frohn, Alexander Epping, Daniel Neumaier, Kenji Watanabe, Takashi Taniguchi, and Christoph Stampfer Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01303 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 27, 2018

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Nano Letters

Gate-dened electron-hole double dots in bilayer graphene ∗,†,‡

L. Banszerus,

B. Frohn,

†

†,‡

A. Epping,

§

Taniguchi,

†JARA-FIT

¶

D. Neumaier,

and C. Stampfer

K. Watanabe,

§

T.

†,‡

and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU

‡Peter ¶

Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU

AMO GmbH, Gesellschaft für Angewandte Mikro- und Optoelektronik, 52074 Aachen, Germany, EU

§

National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan

E-mail: [email protected].

Abstract We present gatecontrolled single, double, and triple dot operation in electrostatically gapped bilayer graphene. Thanks to the recent advancements in sample fabrication, which include the encapsulation of bilayer graphene in hexagonal boron nitride and the use of graphite gates, it has become possible to electrostatically conne carriers in bilayer graphene and to completely pinch-o current through quantum dot devices. Here, we discuss the operation and characterization of electron-hole double dots. We show a remarkable degree of control of our device, which allows the implementation of two dierent gate-dened electronhole doubledot systems with very similar energy scales. In the single dot regime, we extract excited state energies and investigate their evolution in a parallel magnetic eld, which is in agreement with a Zeeman-spin-splitting expected for a g -factor of two. 1

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Keywords bilayer graphene, quantum dots, electrostatic connement, double dots Graphene and bilayer graphene (BLG) are attractive platforms for spin qubits, thanks to their weak spin-orbit and hyperne interaction, which promises long spin-coherence times.

1

This has motivated substantial experimental eorts in studying quantum dot (QD) devices based on graphene

210

and BLG.

1114

The major challenge in this context is the missing band-

gap in graphene, which does not allow conning electrons by means of electrostatic gates. A widely used approach to tackle this problem was to introduce a hard-wall connement by physically etching the graphene sheet.

2

In this way, a number of important milestones, such

as the implementation of charge detectors

5,6

and double quantum dots (DQDs)

as the observation of the electron-hole crossover, of charge relaxation times in graphene QDs of disorder, in particular the edge disorder,

7

15

of spin-states

have been reached.

17,18

16

911

as well

and the measurement However, the inuence

turned out to be a major road block for

obtaining clean QDs with a controlled number of electrons/holes and well tunable tunneling barriers. The problem of edge disorder can be completely circumvented in BLG, thanks to the fact that this material oers a tunable band-gap in the presence of a perpendicularly applied electric eld,

19,20

a feature that allows introducing electrostatic connement in BLG. This

route has been pursued by several groups to create QDs in BLG.

13,14,21

However, until very

recently, essentially all devices were limited by leakage currents due to shortcomings in opening a clean and homogeneous band gap. A very recent breakthrough in this eld has been the introduction of graphite back-gates.

2123

Together with the technology of encapsulating BLG

in hexagonal boron nitride (hBN), giving rise to high quality hBN-BLG-hBN heterostructures,

24

the use of a graphite back gate allows for a homogeneous and gate tunable band gap

in BLG. This technological improvement allowed for an unprecedented quality of quantized conductance measurements

23

and, most importantly, allowed realizing complete electrostatic

current pinch-o. The latter nally oers the possibility of electrostatically conning carriers

2


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in BLG and to implement quantum dots with a high level of control and low disorder, as very recently demonstrated by Eich and coworkers.

21

Here, we extend this approach and show the formation and operation of electrostatically dened single, double and triple dots in gapped BLG. The device consists of a high-mobility hBN-BLG-hBN heterostructure fabricated by mechanical exfoliation and a dry van-der-Waals pick-up technique.

24,25

encapsulated ake is conrmed using confocal Raman microscopy heterostructure, consisting of a

t1 ≈ 30

nm thick bottom and

The BLG nature of the

26

(data not shown). The

t2 ≈ 20

nm thick top hBN

crystal, is placed on a roughly 10 nm thick exfoliated graphite ake serving as a local backgate (BG). The use of the graphite BG improves the control over the device electrostatics by bringing the gate-structure substantially closer to the BLG layer than what is achievable with standard Si

++

back-gates (from typical values of

300 nm to

30 nm or less). At the

same time, it helps screening potential uctuations due to the Si/SiO2 substrate. The BLG is electrically contacted by one-dimensional Cr/Au side contacts, described in Ref.

27

25

following the strategy

On top of the upper hBN crystal we place metallic split gates using

electron beam lithography (EBL), evaporation of Cr/Au (5 nm/45 nm) and lift-o. The two split gates (SG) are 5

µm

wide and are separated by approximately 250 nm (see scanning

force microscope image in Fig. 1a). Next, we use atomic layer deposition (ALD) of alumina (Al2 O3 ) to fabricate a 25 nm thick top-gate dielectric layer on the structure. In a last step, we fabricate three nger gates (FG1-FG3) crossing the trench dened by the split-gates using EBL and Cr/Au evaporation followed by lift-o. The nger gates have a width of around 200 nm and are separated by around 60 nm. A scanning force microscope image of the gate structure is shown in Fig. 1a and schematic cross-sections of the device are shown in Fig. 1b. All measurements presented in this letter have been performed in a dilution refrigerator with a base temperature below 30 mK. We have measured the two-terminal conductance through the bilayer graphene by applying a symmetric DC bias voltage

Vb

while measuring

the current through the device. In Fig. 1c we show the source-drain two-terminal resistance

3


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as function of the voltages applied to the BG and SG, with all FGs set to ground.

The

opening of a band gap in the BLG areas covered by the SG is observed as an enhanced resistance along the diagonal line in Fig. 1c with a (negative) slope of 0.8, in good agreement with the ratio of the BLG-BG and BLG-SG capacitances given by data presented by Zhang the relation

Eg ≈ 80

t2 /t1 ≈ 0.7.

From the

et al. 19 we can estimate the size of the gateinduced band gap using

meV·D , where

D

is the perpendicularly applied displacement eld (in

units [V/nm]). This approximation is valid for small displacement elds, Assuming that the charge neutrality point is exactly at

VBG = VSG = 0

D < 0.4

V/nm.

V (which is in

agreement with our data; see dashed lines in Fig. 1c), the displacement eld can be estimated by

19

D ≈ hBN [VBG /(2t1 ) − VSG /(2t2 )],

the BG and SG voltages at to

where

hBN ≈ 4 is the dielectric constant of hBN. Fixing

VBG = 1.56 V and VSG = −1.22 V (see cross in Fig. 1c) corresponds

Eg ≈ 20 meV. In this conguration, we start tuning the nger gates FG1 and FG2.

Each of

these gates allows to individually pinch-o transport through the channel dened by the SG (see e.g. Fig. 1d). At suciently negative ngergate voltages, the current shows signatures of quantized conductance (see steps at currents below 20 nA in Fig. 1d), which becomes unambiguously quantized steps in a four-terminal conductance measurement (see inset of Fig. 1d). These results are very similar to the work recently reported by Overweg et al.

23

At large negative ngergate voltages, we reach maximum resistance values in the gigaohm regime. In Fig. 2a we show the conductance as function of both

VFG1

and

VFG2 .

In the upper

right corner (regime II) the nger gates are tuned such that there is no barrier along the channel (resulting in high conductance,

G > e2 /h).

In regimes I and III one of the gates is

tuned such that an island of holes is formed underneath gate FG1 (regime I) or FG2 (regime III), respectively. The formed p-island is tunnel-coupled to the n-doped channel leads giving rise to a single-dot conguration (see upper illustration in Fig. 2b). This behavior is well consistent with the very recent work by Eich et al.

4

21

Fig. 2c shows a close-up of regime I


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(dashed box with arrow in Fig. 2a, but with less negative

VFG2 )1 .

These data indicate (i)

Coulomb peaks in the single-dot regime and (ii) the absence of any cross-talk due to FG2 on this dot (only vertical lines are observed in Fig. 2c). A line-cut at xed FG2 of this plot is shown as inset in Fig. 2c. From Coulomb diamond measurements we extract an addition energy of

Ea ≈ 1.75

meV (see white arrows in Fig. 1d and supplementary materials for

α = Ea /(eVFG2 )=0.05 (see Fig. 2d).

details) and a gate lever arm of

Although this single-dot

system is not perfectly clean (most likely because of some parallel dot close to the band edge caused by disorder in the 250 nm wide channel) we observe excited states with a characteristic energy of

∆ ≈ 0.17

meV (see right panel in Fig. 2d).

The electronic nature of the excited states can be shown by applying an in-plane magnetic eld while measuring

dI/dVb

at nite bias. In Fig. 2e we show the evolution of a ground and

excited state as function of an in-plane

B -eld,

recorded at

Vb = 0.2

mV (see e.g. dashed

line in the right panel of Fig. 2d). These data show a zig-zag pattern due to a series of level crossings, which become apparent in the considered range of energy scale of the excited states.

B -eld

thanks to the small

Notably, only two slopes can be detected in this data

pattern, which only dier in sign and agree well with a Zeeman splitting

g = 2 (see black dashed lines).

Here

µB

is the Bohr magneton. Taking

∆EZ = gµB B

with

g = 2, we can extract

the energy of the the excited states from the relative position of the crossings. By repeating this type of measurements for dierent dot llings, we extract a total of 14 excited state energies with a reasonably constant value of the diameter of the dot electron mass in BLG obtain

d ≈ 170

28

11

by

and

∆ = 159±23 µeV. This value allows to estimate

d = (2¯h2 /∆ m∗ )1/2 ,

me

where

is the electron mass.

m∗ = 0.033 me

is the eective

For the diameter of the island, we

nm, which is compatible with our device geometry.

Tuning both nger gates to more negative voltage, we enter a regime that can be understood as a triple-dot conguration consisting of a p-island, tunnel coupled to an n-island, tunnel coupled to a second p-island, where the electric eld-induced band gap serves as tun-

1 Please

note that the plot in Fig. 1d consists of only 200 data points making it hard to observe Coulomb

peaks at very negative FG2 voltages.

5


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neling barriers (see lower illustration in Fig. 2b). In Fig. 2f we show a close-up of Fig. 2a in this gate-voltage regime (see box (1) therein). the charge stability diagram of a triple-dot,

29

These data show the typical pattern of

with three characteristic slopes: (i) vertical

features, related to the hole-dot discussed above, (ii) almost horizontal ones related to a hole

0 dot (HD ) right underneath FG2, and (iii) features with slope

−1,

which we attribute to an

electron dot (ED) sitting right between FG1 and FG2. Moving to even more negative values of

VFG1

and

VFG2 ,

we nally reach the electron

hole doubledot regime (with a similar band alignment as in a nanotube electron-hole double dot (VFG3

30

= −6

).

In this regime, the negative voltage applied to the third nger gate FG3

V) breaks the symmetry of the triple-dot lifting the right tunneling barrier of

0 HD . This is most likely due to an up shift of the band edge, which allows for a crossing of the charge neutrality point and the Fermi level in a region with a reduced band gap, resulting in an eectively non-gaped pn-junction (see illustration in Fig. 3a). The characteristic honeycomb pattern of the charge stability diagram in Fig. 3b (measured at

Vb = 0.1

31

of this double dot is shown

mV). A line-cut for xed VFG1 (dashed line in Fig. 3b)

evidences the strong current suppression in the Coulomb blockaded regime, see Fig 3c. The current suppression become even more marked at lower bias voltages, see Fig. 3d (recorded at

Vb = −0.03

mV). In this case, elastic transport through the double dot is only possible

when the electrochemical potential of both dots is aligned with the Fermi level in the leads, which is the case of the so-called triple-points at the corners of the honeycombs of constant charge. At larger bias voltage, the triple points become triangular-shaped regions of nite conductance, see Fig. 3e (recorded at

Vb = 0.17

mV). The size of these regions allows to

determine the conversion factors between gatevoltage and energy (see discussion below), while the broadening of the cotunneling lines provides insights on the bias voltage drop. From the substantially stronger broadening of the lines associated with the electron dot, we conclude that a large fraction of the bias voltage drops over ED.

6


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Nano Letters

This double dot regime shows a surprisingly high stability in ngergates voltage space. Fig. 4a represents a largerange charge stability diagram of the double dot regime as function of

VFG1

and

VFG2

at a xed bias of

Vb = 70 µV.

The features associated with the co-tunneling

lines show a remarkable periodicity over the entire presented voltage range of Fig. 4a that spans the addition of more than 100 holes and more than 100 electrons in each dot, indicating that the charging energy of the dots remains constant over this whole range. We verify these numbers by explicit counting of the charging events of the ED and the HD (see supplementary gure 4). This periodicity is further conrmed by taking the two-dimensional Fourier transform of the data, see in Fig. 4b. Here, the diagonally spaced maxima are associated with the cotunneling lines related to the ED, which is located between FG1 and FG2, while the vertical features are associated with the cotunneling lines related to the HD, which resides below FG1 and does not tune with FG2. The

x

and

y component

of the maximum high-

lighted by the circle (I) describe the cotunneling line spacing frequency with respect to FG2,

ED ED fFG2 ≈ 34 V−1 , and FG1, fFG1 ≈ 38 V−1 , which nicely coincide with the cotunneling line spacing extracted from Fig. 3b, of around 33 mV and 25 mV (see inset of Fig. 4a), respectively. Similarly, the frequency of the vertical line marked by II,

HD ≈ 76 fFG1

V

−1

, nicely matches the

spacing extracted from Fig. 3b of around 12 mV. These results are a good indication that this gatedened doubledot system presents a parabolic connement potential. These results exhibit a remarkable degree of reproducibility. In Fig. 5 we present data from a second doubledot system obtained by interchanging the role of FG1 and FG3, i.e.

0 0 in this double dot the HD is located below FG3, while the ED sits between FG2 and FG3 (see illustration in Fig. 5b). Fig. 5b and Fig. 5c show high bias

Vb = −0.03

Vb = 0.17

mV and low bias

mV charge stability diagrams of this double dot, which compare very well with

those of the other conguration presented in Fig. 3, as one would expect from the geometry of the system.

For a more quantitative comparison between the two double-dot systems,

we use the charge stability diagrams at high bias (e.g. Vb

= 0.17

mV as shown in Fig. 5e)

to extract the relevant energy scales (see schematic in Fig. 5d and gure caption).

7


From

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Page 8 of 21

this kind of analysis we extract the total capacitance of the dots, which are and

CED = 369

aF for the system of Fig. 3, and

CHD0 = 400

aF and

system of Fig. 5. This corresponds to single-dot charging energies

ECED = 0.43

meV for the rst system, and

0

ECHD = 0.39

meV and

second one. In both systems the electron dot has a roughly

CHD = 297

CED0 = 582

aF for the

ECHD = 0.53 0

ECED = 0.3

aF

meV and

meV for the

0.1 meV smaller charging energy

compared to the hole dot located below a nger gate. The overall level of reproducibility of our double dot systems should be compared with the very high variability of etched dot systems, where edge roughness and fabrication contaminations played a large role in determining the behavior of each device. In conclusion, we have showed single, double and tripledot operation of a gatecontrolled BLG quantum dot device based on the electrostatic connement of carriers. Our device is based on three nger gates, which allows to locally tune the band-gap and the chemical potential in a one-dimensional channel formed by two split gates. In this device geometry, the presence of the third nger gate seems to be essential to reach the doubledot regime, which is then formed by an electron dot tunnel coupled to a hole dot. This electron hole double dot regime shows clear features of parabolic connement over a remarkably wide range of gate voltages. Exchanging the role of the nger gates, we can study two dierent electron-hole double dot systems, which show extremely similar behavior, in agreement with the geometry of the system and our understanding of its behavior. This work represents a rst step towards the experimental investigation of spin relaxation times in BLG quantum dots. Next necessary steps are the further down-scaling of the devicesize, the implementation of charge detectors and of high frequency read out schemes, which are all realistic goals with the current technology. Furthermore, thanks to the recent advancements in the synthesis of high quality BLG grown by chemical vapor deposition, the synthesis of isotopically puried

12

32

which will allow for

C BLG, this technology promises realizing spin-qubit

systems with very long life times.

8


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We thank M. Müller for help with the setup and F. Hassler, F. Haupt and K. Ensslin for helpful discussions. cility,

33

Support by the ERC (GA-Nr.

280140), the Helmholtz Nano Fa-

the DFG are gratefully acknowledged. This project has received funding from the

European Union's Horizon 2020 research and innovation programme under grant agreement No 785219.

Growth of hexagonal boron nitride crystals was supported by the Elemental

Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI Grant Numbers JP26248061, JP15K21722 and JP25106006.

Supporting Information Available: Extraction of the addition energy from the Coulomb diamonds in the single dot regime. Additional single-, double- and triple dot data recorded in the hole regime and stability on the double dot regime over a wide gate range.

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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

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(29) Gaudreau, L.; Studenikin, S. A.; Sachrajda, A. S.; Zawadzki, P.; Kam, A.; Lapointe, J.; Korkusinski, M.; Hawrylak, P.

Phys. Rev. Lett.

(30) Laird, E. A.; Pei, F.; Kouwenhoven, L. P.

2006, 97, 036807.

Nat. Nanotechnol.

2013, 8, 565568.

(31) van der Wiel, W. G.; De Franceschi, S.; Elzerman, J. M.; Fujisawa, T.; Tarucha, S.; Kouwenhoven, L. P.

Rev. Mod. Phys.

2002, 75, 122.

(32) Schmitz, M.; Engels, S.; Banszerus, L.; Watanabe, K.; Taniguchi, T.; Stampfer, C.; Beschoten, B.

(33)

Appl. Phys. Lett.

2017, 110, 263110.

Research Center Juelich GmbH HNF - Helmholtz Nano Facility. Journal of large scale research facilities

2017, 3, A112.

12


Page 13 of 21

(a)

(c) 2

Source Split Gate

R (kΩ) 2.4 3 3.6 4.2

(V)

1 0

V

Finger Gates

x

-1

2µm

y

Drain

-2 -3

(b)

-2

-1

t2 t1

2

3

30 12

Graphite Back Gate

Graphite BG

Drain

20

2

G4T (e /h)

I (nA)

x

10

8 4 0 -10

y

Figure 1:

0 1 (V)

V

(d)

Al2O 3 SG

Source

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

0 -10

-8

V

V

(V) -8.5

-6

-4

(V)

(a) Scanning force microscopy image and schematic cross sections (b) of the

device. For more information on labeling see text. (c) Two terminal resistance of the device as function of VBG and VSG with all FG voltages set to ground. device as function of VFG2 at a bias of cross in panel c).

Vb =

100

µV

and xed

Inset:

VBG

(d) Current through the and

VSG

indicated by the

Four-terminal measurement highlight the presence of quantized 2 conductance (see dashed lines at 4, 8 and 12 e /h). Here, a serial resistance of 600 Ω has been subtracted to account for the 5

µm

long channel.

Graphical TOC Entry Source Split Gate FG1 Finger Gates

FG2 FG3 2µm Drain

13


Nano Letters

G (e 2 /h) 2 3 4

5

(b)

(e)

0 0.2 0.4 0.6 0.8 1 0 0.3 0.6

(V)

0.4 -7.8

-10

-9.95

(d) 2 ED

2

HD -11

Figure 2:

Vb (mV)

-11

-10 V FG1 (V)

-9

HD

-8

0

0.04 0.08 0.12

-9.3 -9.32

2

2

0.8

G (e /h)

-7.7

n

-9.9

0 0.8

-9.85

1

0.4

0

0

-1

-0.4

-2

-0.8 -9.88 -9.786 -9.778

-9.96

-9.92

V

(V)

V

BII (T)

Drain

HD

Vb (mV)

n

1

G (e 2 /h)

(f)

(V)

Source

-9

dI/dVb (e 2/h) 0.15 0.3

4

-7.6

I

-12 -12

dI/dVb (e 2/h)

G (e 2 /h)

(c)

0

-2

-4

(V)

VFG3 = −6

-9.34 -9.36 -9.38

-9.824 -9.820 V FG1 (V)

(a) Conductance as function of the nger gate voltages

BG and SG voltages (see cross in Fig. 1c) and

(V)

1

V

-8

0

V

(a)

V

-9.4 -10

VFG1

-9.98 -9.96 -9.94 -9.92 -9.9 V FG1 (V)

and

VFG2

at xed

V. For more information on

the dierent transport regimes marked by IIV see text. (b) Schematic representations of the band alignment for the single and triple dot regime. (c) Charge stability diagram and Coulomb peaks for the single dot regime (I). The corresponding color bar is on the top left. (d) Coulomb diamonds of the single dot regime.

The right panel highlights the presence

of excited states. The corresponding color bar (for the main panel) is on the top right of panel c. (e) Magneto-spectroscopy of excited states in the single dot regime. The black lines correspond to a g-factor of

g = 2,

the arrows indicate the position of the level crossings.

(f ) Charge stability diagram of the triple dot regime. The black lines highlight the slopes 0 corresponding to HD (solid line) and ED (dashed line).

(a)

(b)

G (e 2 /h) 0

0.08

0.16

-10.80 ED HD pn-junction

G (e 2 /h) 0.12

-10.84

-10.90

V

(V)

-10.82

(V)

(d)

-10.86 V

0.06 -11.00

-10.88 -10.90 -11.56

(e)

-11.55 -11.54 -11.53 VFG1 (V)

0

-11.59

-10.82

G (e 2 /h)

(c)

(V)

-10.84 0.2 I (pA)

-10.86 0.1

-10.88 -10.90 -11.56

Figure 3:

-11.56 VFG1 (V)

-11.53

150

V

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 14 of 21

-11.55 VFG1 (V)

-11.54

100 50 0

0

-11.00 V

-10.90 (V)

-10.80

(a) Schematic representation of the band alignment in the double dot regime.

While one HD is formed underneath FG1 the ED resides between two p-regions formed by 0 FG1 and FG3. By detuning the right tunneling barrier of FG2 HD is destroyed (compare to Fig. 2b). (b) Charge stability diagram of the double dot as function of

VFG1

and

VFG2 .

(c)

Current as function of VFG2 at xed VFG1 (marked by the line in panel b). (d) Close-up of the charge stability diagram (marked by the rectangle in panel b) recorded at (e) Charge stability diagram recorded at

Vb = 0.17

panel d.

14

Vb = −0.03

mV.

mV approximately in the same region as


Page 15 of 21

(a)

G (e 2 /h) 0

0.1

0.2

(b)

Amplitude 0 (a.u.)

10

20

30

100 1/VFG2 (1/V)

VFG2 (V)

-10.6

-11.0 HD ED

-11.4

50 0

I II

-50

-100 -11.8 -11.8

-11.4

-11.0 VFG1 (V)

-10.6

-100 -50 0 50 1/VFG1 (1/V)

100

Figure 4: (a) Largerange charge stability diagram of the doubledot regime as function of

VFG1 and VFG2 (these data represent a close-up of the are enclosed by the large dashed rectangle Fig. 3b). The inset shows data from Fig. 3b and the spacing between the cotunneling lines. (b) Two-dimensional Fourier transform of the data presented in panel a.

The diagonally

oriented periodic features stems from the cotunneling lines associated with the ED, while the periodic vertical features stems from cotunneling lines associated with the HD. The circle and the dashed line mark the features that exactly correspond to the line spacing extracted from the inset in panel a.

(b)

(a) ED

0.12

V

(c)

0.06

(V)

pn-junction

G (e 2 /h) 0

-10.84 (V)

G (e 2 /h) 0

-10.86

-10.88

-10.92

-10.96 -11.55

-10.88

(e) -11.54

(d)

-11.53 VFG3 (V)

V

dV dVFG3 V

-11.53 VFG3 (V)

G (e 2 /h) 0

0.08

-11.51

0.16

-10.88

-11.52

(V)

-10.90 -11.55

0.15

0.075

-10.84

HD

V

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

FG3

-10.90 -10.92 -10.94 -11.54

VFG3

-11.53 VFG3 (V)

-11.52

Figure 5: (a) Double dot conguration in which FG2 and FG3 are used to form an electronhole double dot. (b, c) Biasspectroscopy map recorded at respectively.

Vb = 0.17 mV and Vb = −0.03 mV,

(d) Schematic representation of the charge stability measurements at high

bias, indicating the relevant quantities for extracting the total capacitance and the charging 0 energy of the dots. For example, the total capacitance of the HD dot can be extracted and αFG3 = Vb /δ VFG3 are the capacitance and 0 the lever arm between FG3 and the HD , respectively. The single-dot charging energy is 0 ECHD = αFG3 ∆VFG3 . Analogous relations hold for the ED0 , with ED0 ↔ HD0 and FG2 ↔ FG3. as

CHD0 = CFG3 /αFG3 ,

where

CFG3 = e/∆VFG3

αFG3 = 0.045, αFG2 = 0.013, CFG3 = 13.4 aF and CFG2 = 4.8 aF. (e) High-resolution zoom-in on four triple points measured at Vb = 0.17 mV used to extract the values above. In all the data present in this gure VFG1 is set to VFG1 = −7.15 V. Quantitatively we obtain

15


(a)

(c) 2

Source

Nano Letters

Split Gate (V)

1

2µm

0

V

Finger Gates

x

-1 y

Drain

-2 -3

-2

-1

0 1 (V)

V

2

3

(d) t2 t1

30 12

Graphite Back Gate

y

Graphite BG

Drain

20

2

G4T (e /h)

I (nA)

x

Source

1 2 3 4 5 6 7 (b) 8 9 2O 3 Al 10 SG 11 12 13 14 15 16 17 18 19 20 21 22

R (kΩ) Page 16 of 21 2.4 3 3.6 4.2

10

4 0 -10

ACS Paragon Plus Environment 0 -10

8

-8

V

V -6

(V)

(V) -8.5 -4

dI/dVb (e 2/h)

(e)

0 0.2 0.4 0.6 0.8 1 0 0.3 0.6

ED

2

HD -11

-10 V FG1 (V)

-9

-8

HD

0.04 0.08 0.12

-9.32

2

-9.95

-9.9

0 0.8

-9.85

1

0.4

0

0

-1

-0.4

ACS -2 Paragon Plus Environment -9.96

-9.92

V

(V)

-0.8 -9.88 -9.786 -9.778

V

(V)

BII (T)

V -11

0

-9.3

(V)

0.4

-7.8 (d) 2

-10

G (e 2 /h)

(f)

2

n

0.8

G (e /h)

HD

-7.7

Vb (mV)

n

1

Drain

V

Source

-9

dI/dVb (e 2/h) 0.15 0.3

4

-7.6

I

-12 -12

Nano G (e 2Letters /h)

(c)

Vb (mV)

-8

5

(b)

(V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

G (e 2 /h) 1 2 3 4

0

-2

-4

(V)

(a)

-9.34

V

Page 17 of 21

-9.36 -9.38

-9.824 -9.820 V FG1 (V)

-9.4 -10

-9.98 -9.96 -9.94 -9.92 -9.9 V FG1 (V)

(a)

(b)

Nano Letters

-10.80

G (e 2 /h) 0

0.08 Page 18 of0.16 21

ED

V

V

(V)

(V)

HD 1 2 pn-junction 3 4 (d) -10.90 G (e 2 /h) 5-10.82 0.12 6 7-10.84 8 -10.86 0.06 9 10 -11.00 -10.88 11 0 -10.90 12 -11.56 -11.55 -11.54 -11.53 13 VFG1 (V) 14 (e) -11.59 -11.56 15 -10.82 2 V (V) FG1 G (e /h) (c) 16 150 17 -10.84 18 0.2 19 100 -10.86 20 21 0.1 50 -10.88 22 ACS Paragon Plus Environment 23 -10.90 0 0 24 -11.00 -10.90 -11.56 -11.55 -11.54 25 V (V) V (V) V

I (pA)

(V)

-11.53

FG1

-10.80

2

Page 19Gof(e21/h)

0

0.1

0.2

-10.6

Amplitude 0 (a.u.)

10

20

30

100

VFG2 (V)

1 2 3 4 -11.0 5 6 7 -11.4 8 9 10-11.8 11 -11.8 12

(b)

Nano Letters

HD ED

1/VFG2 (1/V)

(a)

50 0

I II

-50

-100

ACS Paragon Plus Environment -11.4

-11.0 VFG1 (V)

-10.6

-100 -50 0 50 1/VFG1 (1/V)

100

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 20 of 21

Page 21 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


Gate-defined electron-hole double dots in bilayer graphene

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