# Charge detection using a WSe2 van der Waals heterostructure

Justin Boddison-Chouinard  Department of Physics, University of Ottawa,
Ottawa, Ontario, K1N 9A7  Alex Bogan  Emerging Technologies Division, National
Research Council of Canada, Ottawa, Ontario, K1A 0R6  Norman Fong  Emerging
Technologies Division, National Research Council of Canada, Ottawa, Ontario,
K1A 0R6  Pedro Barrios  Advanced Electronics and Photonics, National Research
Council of Canada, Ottawa, Ontario, K1A 0R6  Jean Lapointe  Advanced
Electronics and Photonics, National Research Council of Canada, Ottawa,
Ontario, K1A 0R6  Kenji Watanabe  Research Center for Functional Materials,
National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
Takashi Taniguchi  International Center for Materials Nanoarchitectonics,
National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
Adina Luican-Mayer  Department of Physics, University of Ottawa, Ottawa,
Ontario, K1N 9A7<EMAIL_ADDRESS>Louis Gaudreau  Louis.Gaudreau@nrc-
cnrc.gc.ca Emerging Technologies Division, National Research Council of
Canada, Ottawa, Ontario, K1A 0R6

###### Abstract

Detecting single charging events in quantum devices is an important step
towards realizing practical quantum circuits for quantum information
processing. In this work, we demonstrate that van der Waals heterostructure
devices with gated nano-constrictions in monolayer WSe2 can be used as charge
detectors for nearby quantum dots. These results open the possibility of
implementing charge detection schemes based on 2D materials in complex quantum
circuits.

The detection and manipulation of individual charges and spins is at the heart
of developing quantum technologies. In particular, the detection of individual
charges in a quantum dot (QD) can be realized by placing a quantum point
contact (QPC) in its vicinity and detecting changes in the conductance through
the QPC current as a result of the altered electrostatic environment around
the QD. While transport directly through a single quantum dot and charged
detection are equivalent this is not the case for circuits containing more
than a single quantum dot. In that situation direct transport only occurs
under specific resonance conditions between dots which becomes severely
restrictive as additional quantum dots are added. This is in contrast to
charge detection techniques which are able to identify the charge in each dot
separately without current flowing directly through the circuit. As a result
charge detection technology is a requirement for complex spin qubit quantum
circuits1, 2, 3. The implementation of this approach was initially
successfully demonstrated in GaAs two-dimensional electron gas (2DEG)
devices4. More recently, two-dimensional (2D) materials including graphene and
semiconducting transition metal dichalcogenides (TMDs) emerged as a novel
platform to realize electrostatically confined quantum circuits. Within the 2D
materials platform, QPC’s have been demonstrated in TMDs5, 6, 7, 8, 9, 10, and
more specifically, QPC charge detection has been demonstrated in monolayer and
bilayer graphene (BLG) devices 11, 12, 13, 14, 15, 16. However, charge
detection has not yet been implemented in semiconducting TMDs. The direct band
gap in TMDs, along with the interplay of the spin and valley degrees of
freedom, makes them an appealing platform for realizing hybrid quantum
circuits with optical and solid state qubits17, 18, 19. Additionally, the
strong spin-orbit coupling in TMDs could enable fast spin qubit manipulation
with AC electric fields20 and lead to the spin-valley locking, by which qubits
could be more robust against electro-magnetic noise. Although the first gated
quantum dots in TMDs have been recently realized5, 6, 21, 8, 22, 23, charge
detection using gated nano-constrictions is yet to be implemented. In this
work, we realize a nano-constriction in a monolayer WSe2 channel and,
demonstrate for the first time, charge detection of a gate controlled WSe2
quantum dot.

The charge detector device used in this work is based on monolayer
$\mathrm{WSe_{2}}$, schematically described in Figure 1a. Its optical
micrograph is shown in Figure 1b. The device was assembled on a
$\mathrm{p-Si/SiO_{2}}$ (285 nm) substrate using standard dry transfer
methods. Local nano-constriction gates [Ti (2.5 nm) / Au (2.5 nm)] were first
deposited on the substrate using electron beam lithography (Fig 1b inset).
They are 100nm in width, with a lateral spacing of 50 nm, and varying gap
spacing (50 nm, 100 nm, and 75 nm). The local nano-constriction gates are
responsible for locally depleting the carriers in the monolayer
$\mathrm{WSe_{2}}$ flake. A flake of hexagonal boron nitride (hBN) with 44nm
thickness was transferred on top of the pre-patterned gates and electrical
contacts [Cr (2 nm) / Pt (8 nm)] were subsequently lithographically patterned
on top of the hBN. To increase sample cleanliness and, consequently, reduce
contact resistance, the device was cleaned in a vacuum furnace ($10^{-7}$
Torr) at 300∘C for 30 minutes. Additionally, remaining polymer residues were
removed using an atomic force microscope (AFM) tip in contact mode24, 25, 23.
A $\mathrm{WSe_{2}}$ monolayer and a 37 nm thick hBN flake were exfoliated and
identified on independent substrates. Using dry transfer techniques, the hBN
flake was first picked-up an then used to pick-up the $\mathrm{WSe_{2}}$
flake; subsequently, the $\mathrm{WSe_{2}}$/hBN stack was precisely placed on
top of the cleaned electrical contacts. We note that prior to the deposition
of the hBN/$\mathrm{WSe_{2}}$ stack, the $\mathrm{WSe_{2}}$ surface was also
mechanically cleaned using an AFM tip. A last lithographic step was performed
to deposit a top gate [Ti (5 nm) / Pd (20 nm) / Au (100 nm)] used to globally
modify the charge carrier density of the $\mathrm{WSe_{2}}$ flake and to
achieve ohmic contacts.

Figure 1: (a) Schematic architecture of the charge detection device based on
monolayer $\mathrm{WSe_{2}}$. (b) Optical micrograph of the completed device
used in this work. The $\mathrm{WSe_{2}}$ flake is outlined in red for
clarity. Scale bar: $20\leavevmode\nobreak\ \mu m$. Inset: false-color
scanning electron micrograph of the control gates. (c) Source-drain current as
a function of the top gate voltage ($\mathrm{V_{TG}}$) showing the activation
curve of the device. Inset: linear I-V characteristic observed when
$\mathrm{V_{TG}<-6\leavevmode\nobreak\ V}$. The temperature of these
measurements was $\mathrm{T=4\leavevmode\nobreak\ K}$. (d) Contact resistance
of the source and drain contacts as a function of the top gate voltage
$\mathrm{V_{TG}}$, as indicated. The grey (red) curve represents the
resistance associated to the source (drain) contact. The temperature of these
measurements was $\mathrm{T=1.5\leavevmode\nobreak\ K}$.

In a first measurement step, the source-drain current was monitored as a
function of the top gate voltage ($\mathrm{V_{TG}}$) at a temperature of
$\mathrm{T=4\leavevmode\nobreak\ K}$ as shown in Figure 1c. The current
increases at higher negative values of $\mathrm{V_{TG}}$, indicating hole
conduction across the $\mathrm{WSe_{2}}$ channel. At top gate voltage values
below – 6 V, the current voltage characteristics across the source-drain
contacts show a linear behaviour, as presented for select values of
($\mathrm{V_{TG}}$) in the inset of Figure 1c. One of the principal challenges
in developing quantum devices in 2D semiconductors is realizing good
electrical contacts. Thus, when the temperature was further reduced
($\mathrm{T=1.2\leavevmode\nobreak\ K}$), by using a three-terminal
measurement scheme, the contact resistance of the source and drain were
individually measured as a function of ($\mathrm{V_{TG}}$) as seen in Figure
1d. The importance of the top-gate for achieving high quality contacts is
evidenced by the low contact resistance measured when
$\mathrm{V_{TG}=-10\leavevmode\nobreak\ V}$. At this top-gate voltage, a
contact resistance of 404 ${\Omega}$ was measured for the source contact and
1240 ${\Omega}$ for the drain contact.

We then investigated the influence of the local control gates on the transport
properties of the device in a dilution refrigerator with a base temperature
below 10 mK. Specifically, the pair of gates $\mathrm{G_{3L}}$ and
$\mathrm{G_{3U}}$ (right-most control gates in the inset of Figure 1b) were
studied while all other control gates were grounded (Figure 2). A bias voltage
of $\mathrm{500\mu V}$ was applied to the source contact, while the drain
contact was grounded. A gradually increasing voltage was applied to both
$\mathrm{G_{3L}}$ and $\mathrm{G_{3U}}$ to create a channel by locally
depleting the $\mathrm{WSe_{2}}$ flake of holes in the areas directly above
the two control gates. Keeping $\mathrm{G_{3L}}$ at
$\mathrm{15.12\leavevmode\nobreak\ V}$, $\mathrm{G_{3U}}$ was varied, while
the source-drain current $I$ was monitored, as shown in Figure 2a (blue dotted
curve). The source-drain current decreased as a function of $\mathrm{G_{3U}}$
until $\mathrm{G_{3U}=15.6\leavevmode\nobreak\ V}$, when it suddenly
increased, and, as $\mathrm{G_{3U}}$ is further increased, the current
eventually pinches off. We demonstrate below that it is related to the nano-
constriction acting as a non-invasive probe of the charge of a nearby
incidental quantum dot.

Figure 2b illustrates the model for the blue current trace characteristics
observed in Figure 2a. A nearby quantum dot has an initial population of
$\mathrm{N}$ holes. As a larger positive voltage is applied to the local
control gate $\mathrm{G_{3U}}$, the width of the channel formed between
$\mathrm{G_{3U}}$ and $\mathrm{G_{3L}}$ decreases, resulting in a decrease of
current. At the same time, $\mathrm{G_{3U}}$ controls the chemical potential
of the nearby quantum dot and can therefore remove holes from it by applying a
larger positive voltage. At a specific gate voltage, the population of the
quantum dot transitions from $\mathrm{N}$ holes to $\mathrm{N-1}$ holes,
resulting in a widening of the channel and, as a result, a sudden increase in
current through the charge detector.

Assuming no change in the number of holes (N) in the quantum dot as a function
of gate voltage, the current is expected to follow the leftmost grey dashed
curve in Figure 2a. If a hole is removed from the quantum dot, which would be
therefore populated by N-1 holes, a larger voltage applied to
$\mathrm{G_{3U}}$ would be needed to achieve the same result (rightmost grey
dashed curve). Thus, the jump between the two gray curves indicates a switch
between a nearby quantum dot population of N and N-1 holes.

Figure 2: (a) The blue dotted curve is the source-drain current as a function
of the local control gate $\mathrm{G_{3U}}$, while the local control gate
$\mathrm{G_{3L}=15.12\leavevmode\nobreak\ V}$. The grey dashed curves are
guides for two distinct quantum dot populations N and N-1, as indicated. (b)
Schematic explanation of the result observed in (a), where a change in the
hole population of a nearby quantum dot affects the channel width and the
source-drain current. $\mathrm{T<7\leavevmode\nobreak\ mK}$.

To demonstrate that the observed step in the source-drain current of Figure 2
is caused by a change in the charge population of a nearby quantum dot, we
studied the evolution of the charge detection step as a function of
$\mathrm{G_{3U}}$ for different values of $\mathrm{G_{3L}}$ between 15 V (dark
red curve) and 15.4 V (dark blue curve) as shown in Figure 3a. We observe that
as $\mathrm{G_{3L}}$ increases, the constriction pinch-off voltage decreases
as a function of $\mathrm{G_{3U}}$, while the voltage at which the charge
transfer step occurs remains mostly constant. This indicates that the origin
of the step is distinct from the nano-constriction. In addition, we note that
a current peak is still visible, but with considerably less amplitude, after
the detector is pinched-off for higher $\mathrm{G_{3L}}$ values. We attribute
this behaviour to parallel transport through the quantum dot in the Coulomb
Blockade regime.

To investigate this further, we extract the position of three distinct events
in each current trace of Figure 3a: the first pinch-off, the second pinch-off
and the charge transfer step. The first pinch-off point is extracted by taking
a linear regression of the initial downward slope of the current and obtaining
its x-intercept. Similarly, the second pinch-off point is the x-intercept of
the linear regression which fits the current’s second downward slope. The
charge transfer step is taken to be the middle point between the current’s
local minimum and local maximum around the step. An example of this is
illustrated in Figure 3b. This analysis is performed for all values of
$\mathrm{G_{3L}}$ and plotted in Figure 3c. The slope associated to the first
pinch-off point and the charge transfer step are each constant as a function
of $\mathrm{G_{3L}}$ and have values of $\mathrm{-1.7\pm
0.1\leavevmode\nobreak\ V_{G_{3U}}/V_{G_{3L}}}$ and $\mathrm{-0.34\pm
0.03\leavevmode\nobreak\ V_{G_{3U}}/V_{G_{3L}}}$ respectively. The difference
in slopes between the linear dependencies of these events (first pinch-off,
and charge transfer) further indicate that the origin of the charge transfer
step and the nano-constriction are independent.

Looking at the extrapolations associated to the second pinch-off point, we
observe a change in slope at $\mathrm{V_{G_{3L}}=15.22\leavevmode\nobreak\
V}$, the voltage where the charge transfer step transitions into a Coulomb
blockade peak, associated to parallel transport through the quantum dot. The
slope corresponding to the second pinch-off point in the charge detection
regime ($\mathrm{-1.6\pm 0.2}$ $\mathrm{\leavevmode\nobreak\
V_{G_{3U}}/V_{G_{3L}}}$) is similar to the slope associated to the first
pinch-off point, suggesting its origin being the nano-constriction. However,
in the Coulomb blockade regime, the slope corresponding to second pinch-off
($\mathrm{-0.35\pm 0.05\leavevmode\nobreak\ V_{G_{3U}}/V_{G_{3L}}}$) no longer
follows the first pinch-off, but instead it follows the charge transfer step.
This is due to the fact that at $\mathrm{V_{G_{3L}}>15.22\leavevmode\nobreak\
V}$ the constriction is completely pinched off and we are measuring only
parallel transport through the quantum dot. We note that the quantum dot
transport is still present in the charge detection regime, however the signal
is dominated by the transport through the nano-constriction.

Figure 3: (a) Source-drain current as a function of the local control gate
$\mathrm{G_{3U}}$. Curves are taken for different values of $\mathrm{G_{3L}}$
ranging from 15 V (dark red) to 15.4 V (dark blue). Experimentally, curves
were taken at an interval of $\mathrm{{\Delta}G_{3L}=0.01\leavevmode\nobreak\
V}$ but for clarity, an interval of
$\mathrm{{\Delta}G_{3L}=0.05\leavevmode\nobreak\ V}$ is shown here. (b) An
example of how the “position” of the first pinch-off (green), the second
pinch-off (red) and the charge transfer step (orange) are obtained. The trace
is taken when the voltage on $\mathrm{G_{3L}}=15.12$. (c) The position of the
first pinch-off (green), the second pinch-off (red) and the charge transfer
step (orange) plotted as a function of $\mathrm{G_{3L}}$ along with fitted
linear regression. $\mathrm{T<7\leavevmode\nobreak\ mK}$.

figureThe charge detection sensitivity ($\mathrm{{\Delta}G}$) of the measured
device as a function of the voltage applied to $\mathrm{G_{3U}}$.

Reference | $\mathrm{{\Delta}G}\leavevmode\nobreak\ (e^{2}/h)$ | Material
---|---|---
Appl. Phys. Lett. (2008)11 | $10^{-4}$ | Graphene
Appl. Phys. Lett. (2010)12 | $<0.1$ | Graphene
Phys. Status Solidi B (2011)15 | $0.005$ | BLG
Phys. Rev. B (2011)13 | $0.02$ | Graphene
Nat. Commun. (2013)14 | $0.002$ | Graphene
Nano Lett. (2019)16 | $0.2$ | BLG
This work (2022) | $0.09$ | ML WSe2

tableComparison of the charge detector sensitivity ($\mathrm{{\Delta}G}$) in
various 2D material devices.

The sensitivity of the charge detector, taken as the change in conductance
($\mathrm{{\Delta}G}$) per hole in units of $\mathrm{e^{2}/h}$, was tuned as a
function of the voltage applied to $\mathrm{G_{3L}}$ as can be seen in figure
4a. An optimal value of $\mathrm{0.09e^{2}/h}$ is reached when
$\mathrm{G_{3L}=15.17\leavevmode\nobreak\ V}$. Table 1 compares this
sensitivity with previously reported charge detectors using graphene and
bilayer graphene devices, suggesting that TMDs show promising prospects of
being used in charge detection scheme based on nano-constrictions.

In summary, we fabricated van der Waals hetetostructure devices where we
electrostatically define nano-constrictions in monolayer WSe2. Our fabrication
technique results in very low contact resistance, which allows the study of
transport properties through the constrictions. By monitoring the current in a
nano-contriction, we demonstrate for the first time using TMDs, the
possibility of using such a device as a charge sensor for nearby quantum dots.
The sensitivity of the WSe2 is comparable to similar devices implemented in
graphene and bilayer graphene. These results pave the way for future the
development of complex quantum circuits, where charge detectors can be
integrated into gated quantum dot architectures.

This work was supported by the High Throughput and Secure Networks Challenge
Program at the National Research Council of Canada. AL-M and JBC acknowledge
funding from the National Sciences and Engineering Research Council (NSERC)
Discovery Grant RGPIN-2016-06717. We also acknowledge the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC) through
Strategic Project STPGP 521420.

K.W. and T.T. acknowledge support from JSPS KAKENHI (Grant Numbers 19H05790,
20H00354 and 21H05233).

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