Lettershttps://doi.org/10.1038/s41565-020-0727-0

Room-temperature valleytronic transistorLingfei Li1,2,5, Lei Shao3,5, Xiaowei Liu4, Anyuan Gao4, Hao Wang   3, Binjie Zheng1, Guozhi Hou1, Khurram Shehzad   2, Linwei Yu   1, Feng Miao   4, Yi Shi   1, Yang Xu   2 ✉ and Xiaomu Wang   1 ✉

1School of Electronic Science and Engineering, Nanjing University, Nanjing, China. 2Colleges of ISEE and Microelectronics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, ZJU-UIUC Institute, State Key Labs of Silicon Materials and Modern Optical Instruments, Zhejiang University, Hangzhou, China. 3Beijing Computational Science Research Centre, Beijing, China. 4School of Physics, Nanjing University, Nanjing, China. 5These authors contributed equally: Lingfei Li, Lei Shao. ✉e-mail: yangxu-isee@zju.edu.cn; xiaomu.wang@nju.edu.cn

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In the format provided by the authors and unedited.

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1

Supplementary Materials for

Room-temperature Valleytronic Transistor

Lingfei Li, Lei Shao, Xiaowei Liu, Anyuan Gao, Hao Wang, Binjie Zheng, Guozhi Hou,

Khurram Shehzad, Linwei Yu, Feng Miao, Yi Shi, Yang Xu, Xiaomu Wang

1

Supplementary Text

1. Optical chirality for antenna/electrode coupling.

The coupling between nano-antenna/electrode system determines the final circular dichroism

(CD) spectra. We have plotted the distribution of local optical chirality at the plane of MoS2 under

the experimental condition: an 1550-nm laser polarized along the vertical direction (y axis) is

employed for illumination and the nanoantennae are placed close to the Au electrodes in different

manners, as suggested by the scanning electron microscope images in Figure 2c in the main text.

Figure S1 shows the local optical chirality map for different antenna orientations. Larger absolute

average values of optical chirality enhancement 𝐶̅ are observed in two configurations: “head (or

end) to electrode” and “tail (or tip) to electrode”, and they are of different signs. This is because

the chirality “hot spots” locate mainly at “head” and “tail” ends and the different coupling

configuration will change the local chirality largely. The “head (or end) to electrode” and “tail (or

tip) to electrode” configurations dominate the value of 𝐶̅ at different electrodes separately. Adding

the other two configurations into consideration will not change the main result. Noticing that, in

the calculation, we have considered the contribution from all parts of the nano-antenna. The sign

of 𝐶̅ is determined by which end is nearer (e.g. in the head to electrode configuration, “head” is

always nearer to the electrode than the “tail”). As Figure S1 shows, the “head (or end) to electrode”

configuration gives a negative 𝐶̅ = −0.4558 (gap = 10 nm) while all other coupling configurations

give positive 𝐶̅ values. Among them, the “tail (or tip) to electrode” configuration presents much

larger 𝐶̅ (= 0.6139, Figure S1).

2

Moreover, we also plot the CD spectra obtained as the difference between the RCP and LCP

absorption spectra for the nanoantennae coupled with the electrode (Figure S2). The calculated

circular dichroism spectra exhibit results in consistence with the local optical chirality analysis.

Accordingly, the “head (or end) to electrode” configuration gives major absorption by the antenna

at 1550-nm RCP illumination while the “tail (or tip) to electrode” configuration gives major

absorption by the antenna at LCP.

We also consider the effect of gap distance. The value of 𝐶̅ and the absorption difference

between RCP and LCP at 1550 nm depends on the gap distance, but its sign is unchanged when

the gap is not too large. This observation is consistent with the experimental results. In this scenario,

the alignment method presents equidirectional net optical chirality although the absolute value

may change from sample to sample.

2. Hot carrier injection and band filter effect.

We use an infrared laser with photon energy deeply below the band gap of MoS2. As a result,

photo-carriers in equilibrium states cannot be injected into MoS2 due to the large energy barrier

between its band edges and the photo-excitation carriers, as illustrated in the top panel of the Fig.

2a. On the other hand, the hot carriers obey a modified Fermi-Dirac distribution f(E)=1/(exp(-(E-

EF)/kTc)+1), in which a higher carrier equivalent temperature Tc replaces the lattice temperature

(in equilibrium condition, the electron temperature equals to lattice temperature). As shown in the

bottom panel of Fig. 2a, in this scenario a portion of energetic carriers in prolonged thermal tail of

3

f(E) has enough energy to eject into MoS2. The carrier equivalent temperature of hot carriers is

approximately proportional to the absorption coefficient. Surface plasmonic resonance tightly

confines electromagnetic field of incident light, resulting in an enhanced absorption coefficient

and therefore an elevated carrier equivalent temperature.

In addition, because the incident photon energy is lower than the bandgap of MoS2, only

energetic carriers in prolonged thermal tail of f(E) with excess energy higher than the band edges

can be ejected into the MoS2. The injected carrier density (equals the integration of the high energy

tail of f(E) product the density of states) exponentially increases with the temperature. Or in other

words, the band edge of MoS2 efficiently filters out the carrier injection from the valley with lower

absorption rate. Accordingly, the valley contrasting carriers in MoS2 are largely magnified

compared with the helical contrasting absorption of plasmonic antennae.

3. Generation of valley polarization.

We briefly summarize the hot injection process as follows. We adapt a model which describes

electrical doping of 2D materials by plasmon-induced hot carrier from Ref1,2.This process can be

understood by four main steps: i) The first step is light absorption (of metal, due to the sub-gap

photon energy). In our device, absorption of light is enhanced by exciting localized surface

plasmon resonances in nano-antenna. ii) Plasmon in metal nano-structure damped through the

creation of hot electron-hot hole pairs via Landau damping on a time scale from 1 to 100 fs2. iii)

Hot electron-hole pairs quickly redistribute energy to form a Fermi-Dirac distribution with

equivalent temperature obviously higher than the lattice temperature. iv) A charge transfer of high

energy parts (higher than the conduction band of MoS2) of hot electrons generated in the antenna

4

structure upon plasmon decay.

The chiral absorption in our system moves forward to the general process: A linearly-

polarized excitation can be divided into two opposite circularly-polarized components. They result

in different optical orientation of electron spins in heavy metal. In our device, the asymmetric

absorption (Figure S2) between different optical helicity generates unbalanced population of hot

electron-hot hole pairs between different spins. This net spin information carried by hot carrier can

be maintained after charge transfer process if the spin relaxation rate is lower than charge injection

rate3. This is possible because the spin relaxation time in metal is on the orders of several ps, slower

than the hot carrier relaxation time of ~100 fs as aforementioned. Fig. S4 schematically illustrates

this framework.

Besides the chiral absorption, the chiral near-field distribution could also help to promote the

valley polarization of free electrons. As shown in Fig. S1, the average near field presents strong

optical chirality. The near-field interaction between localized electromagnetic field and

semiconductor may selectively excite hot electrons of MoS2 in specific valleys, especially when

the Fermi-level is near the bottom of conduction band (such as those parts of MoS2 in the depletion

region). Again the injected electrons retain spin information because in MoS2, electron-electron

scattering time (~10-13s) is much shorter than spin relaxation time (tens of ps).

5

4. Photocurrent mechanism.

Generally speaking, the photo-response in 2D materials mainly involves photo-gating, photo-

voltaic, bolometric and photo-thermoelectic effects. We use photo-current mapping to identify the

dominant mechanism.

Fig. 2c shows a photo-current mapping of our device. Before loading nano-antennae, the

device does not respond to 1550 nm excitation (Fig. S3). After loading nano-antennae, obvious

photo-current is generated in one contact (either source or drain, depending on the bias condition).

This result clearly indicates that the photocurrent is due to photo-voltaic like carrier injection:

1. For photo-gating or bolometric effects, the photo-conductivity should mostly change at the

center of the channel rather at the contacts, as we measured.

2. For photo-thermoelectric related process, the thermoelectric voltage generates at both contacts4.

We should observe photo-currents with opposite polarity at different contacts.

3. For our device, the photocurrent generation is schematically presented in Fig. S5. Photo-

generated virtual electron-pairs are separated by the Schottky built-in field at the contact.

Therefore, drift photocurrent generates if and only if an external electric field is applied.

6

5. Valley-selective doping induced PL polarization.

The mechanism of room temperature photoluminescence (PL) polarization, illustrated in

Fig.2b, is not due to unbalanced exciton concentration in different valleys. Because 514 nm laser

generates equal populations of K and K’ valley excitons. Especially, the exciton-depolarization is

very strong at room temperature because intervalley scattering begins to occur when the exciton

energy exceeds a threshold corresponding to twice the LA phonon energy. This is indeed a major

reason for the short room-temperature excitonic lifetime.

Instead of unbalanced population, the PL polarization is due to unbalanced quantum yields in

different valleys resulted from the valley-selective doping induced by 1550 nm illumination. The

doping modulated (either gate-induced doping or chemical doping) PL intensity have already been

discussed in previous literatures5-8,9 . The PL intensity of the A exciton in MoS2 can continuously

decrease with increasing doping because of Pauli blockade and many-body interactions10. Pauli

blockade results in an overall reduction of excitonic absorption and therefore lower PL with

increasing doping. Under 1550 nm illumination, one specific valley (the excited one) is n-doped,

for that hot carriers are selectively injected from the resonated plasmonic antennae. Similar to the

gate/chemical doped PL, it shows a reduced PL intensity compared with the other valley, as shown

in Fig. 2b and Fig. S6.

7

6. The speed of the valleytronic transistor device.

The speed of the device depends on two processes: the valley-polarized hot carrier injection

process and the following transport process.

For the valley-polarized free carrier injection process, many previous literatures have studied

it in detail by pump-probe experiment6,11. The reported results show that the time for valley-

polarized carrier injection is ~100 fs (including the charge transfer time). Taken the surface

plasmonic resonance (SPR) decay and SPR-excited hot carrier time into account (1~100fs)2, the

total injection time is no more than 1ps. Hence, the theoretical limit of the device speed could be

ultrafast (~1THZ).

For the transport process, it is quite true that the speed depends on the mobility of channel

material. In this case, the diffusive mobility of free carrier is linked to drift mobility by the Einstein

relation. Recent works have reported many possible techniques to improve the free carrier mobility

in MoS2 channel12-14. The carrier mobility in transition metal dichalcogenide (TMDCs) is

comparable to the strained silicon widely used in industry. In addition, the rich 2D material family

may help to find other better candidates, such as Dirac semimetal etc.

8

7. Drift and diffusive valley current in the valleytronic transistor.

The transport mechanism depends on in what ways the valley current is driven, i.e. drift valley

current is driven (together with charge current) by external electric field, and diffusive valley

current is driven (without charge current) by the gradient of valley-polarized carriers. Therefore,

the transport mode of valley current can be simply determined by whether a photo-current exists.

The “drift” current means the motion of quasi-particles under the external field. The drift

valley current results from the flow of valley-polarized free electrons driven by bias-voltage, or

the photocurrent. It is thus reasonable that drift valley current appears at the contact where

photocurrent generates.

The diffusive valley current is totally different. Firstly, considering the zero-bias case, the

injected carriers could acquire velocity from the built-in field due to the existence of a Schottky

barrier. Fig. S14 schematically illustrated the carrier distribution at the boundary of space charge

region (SCR). Although there is a non-zero initial average velocity for the injected valley-polarized

carriers, the high scattering rate (the mean free path of electrons is about several nanometers)

suggests that the momentum of carriers is randomly distributed in K space, as shown in Fig. S15.

In addition, it should be noted that the scattering mainly happens intravalley due to the spin-valley

locking effect. In addition, the electric field outside the SCR is zero (A trivial calculation indicates

that the SCR in our devices is typically smaller than 100 nm. The photocurrent mapping also

implies that the SCR is much shorter than the channel length). Thus the injected valley-polarized

free electrons cannot be collected by the opposite electrode and no photocurrent generates.

9

Furthermore, the carrier distribution between the two non-degenerate valleys is different at

the boundary of SCR (which is also the valley-polarized carrier injection region), but balanced

inside the channel. Therefore, the density gradient of valley carrier contrast yields a diffusion

process: random walk (exchange) of valley-polarized carriers leads a valley flow propagating

along the channel. Because the electric filed outside the SCR is zero , the process is very similar

to that in Ref 6, once the initial momentum is fully scattered.

Lastly, the above picture does not significantly change under an external bias. For the contact

where built-in field is opposite to the bias field, the electric field force does not drive the motion

of electrons (instead it decelerates the motion and lowers the Schottky barrier). As a result, the

valley current is also driven by diffusion and no photocurrent can be measured.

8. Zero-bias operation of the valleytronic transistor.

We operate the device at zero-bias condition. Firstly, as aforementioned, pure diffusive

valley current is generated even with a Schottky barrier, because the built-in field is only non-

vanishing around the metal contact, no field exists in most of the channel under zero-bias.

Secondly, the zero-bias operation is without any charge current which could potentially

advance the current CMOS technology. To directly prove the charge current free diffusive valley

transport, we experimentally measured the vanishing charge current under zero bias as summarized

in Fig. 4c. As shown in Fig. 4c, both conductive charge current Idc and photocurrent Ipc is non-

detectable (below the instrumental noise floor) when Vds = 0 V. Naturally, there is no external

10

conductive current in the channel due to the zero bias. And the injected carriers cannot be collected

by the opposite contact to generate a net photocurrent although the built-in field can accelerate the

hot carriers in the space charge region of the injection contact. owing to the high electron scattering

rate.

Thirdly, even without charge current, a significant valley signal that originates from diffusive

valley current was still detected (as shown in Fig. 3c & Fig. 4c). This is because the aforementioned

built-in electric field of Schottky contact deflects the valley-polarized carriers inside the SCR,

owing to the valley Hall effect. As a result, the valley-polarized carriers have a non-uniform spatial

distribution at the boundary of space charge region. Through consequential valley diffusion

process, we could observe a transverse voltage even in the zero-bias case. Interestingly, this

process indicates that the polarity of zero-bias Hall output must be the same for different contacts.

Because both electrical fields (here played by the built-in filed as discussed above) and valley-

polarization (and thus the Berry curvature) are reverse in source and drain contact, as shown in

Fig. S11. This is in stark contrast to the non-zero bias cases, where the Hall voltage is of opposite

sign for different contacts because a universal external field deflect the injected valley-polarized

carriers (Noticing that the transverse velocity . Where is the electric field,

is the Berry curvature. For both opposite and E, the VH are of the same sign).

Finally, we would like to emphasize that the device is not unconditionally free of charge

current. Above discussions imply that the charge current free operation only refers to zero-bias

case. Finite bias voltage definitely generates conductive current in the channel.

T

ev (k)= - E Ω(k) E

Ω(k) Ω(k)

11

9. The discussion on energy dissipation.

The energy loss of a transistor can be categorized into static and dynamic power

consumptions. Under zero bias, the only scattering experienced by valley current is the relaxation

of momentum obtained from built-in field in Schottky contact. The energy loss of valley current

can be much lower than that of charge transport in traditional transistor. Because the transport of

valley current only involves in lower field intensity (charge current drift in larger field in a normal

transistor), occurs in smaller dimension (charge current flows through the whole channel in a

normal transistor) and influenced by less contact effect (charges are injected from external

electrical source in a normal transistor). As a result, the static power consumption is significantly

compressed in our device compared with traditional transistor. Given the fact that more than 50%

of the total power consumption comes from the static power consumption, our device already

presents a major technical advantage.

In addition, switching the output signal brings dynamic power consumption. The valley Hall

voltage acts as the output in our device. Under zero bias, it is generated by the following process:

the built-in electric field of Schottky contact deflects the valley-polarized carriers inside the space

charge region owing to the valley Hall effect. Consequently, the valley-polarized carriers observe

a non-uniform spatial distribution at the boundary of space charge region. Through succeeding

valley diffusion process, we could observe a transverse voltage even in the zero-bias case. In this

scenario, dynamic equilibrium is established between diffusion of valley-polarized carriers and

electric field force of valley Hall voltage in transverse direction. The dynamic power consumption

thus originates from changing of the valley diffusion by modulating the injection and distribution

of valley polarized carriers. This energy loss is also potentially lower than that used for switching

12

an electronic transistor, because the redistribution of valley current also does not require high drift

field, does not go through the whole channel and does not heat the contact.

Thirdly, as discussed in Ref6, for the charge current free cases, the scaling law between power

consumption and spin-valley current amplitude is fundamentally different from non-zero charge

current. As they calculated, for charge current free cases VP I .While for non-zero charge current

cases, 2

VP I R . Where Iv is the valley current, R is then resistivity of the materials, P is the

power consumption. The lack of charge current enables high power efficiency, especially at large

current amplitude.

10. Calculation of the valley polarization lifetime.

According to two-probe measurement shown in Fig. 4b, the mobility of our MoS2 FET is

estimated to be around 20 cm2V-1s-1 according to the equation

(S1)

Where the Cg is the gate channel capacitance per unit area, L and W are the length and width

of the channel of the MoS2 FET. For the drift dominated propagation, the polarization length λdrift

is around 18 μm, thus we can estimate the corresponding lifetime from

(S2)

It reads ~100 ns in our experiment.

ds

g ds g

ILμ=

WC V V

drif

drift

t driftτ = =

ν

λ λ

μE

13

For the diffusion dominated propagation, the actual diffusion length should exclude the

depletion region and a small scattering length in and near space charge region ( ), as shown

in Fig. S14, that is diff SCR .Thus the corresponding lifetime is estimated from

(S3)

where D is the diffusion coefficient which can be estimated from the Einstein relation

(S4)

Where for hole and for electron. The μ, kB and T are

mobility, Boltzmann constant and electron temperature, respectively. Taking the above

discussions into account, the valley lifetime in diffusive process is 2( )SCR

diffD

. A rough

estimation gives around 100 ~ 300 ns.

11. Employing the valleytronic transistor to achieve valleytronic logic circuits.

The valley switching behavior of our device possesses two important merits which render the

device potentially works as a valley transistor for integrated valleytronics. Firstly, for a functional

valleytronic building block, it is necessary to realize a valley-controlled valley polarization. This

process fundamentally requires a unified way to read and modulate valley polarized carriers, which

is unfortunately elusive in previously reported valleytronic devices. Our device fulfills this

requirement because its valley current is read and controlled all by electrical signals (valley Hall

output and electrostatic gating input). Second equally important merit is that for a valley transistor

λSCR

2

diff

λ λτ =

D

（ ）- SCR

(1 ) (1 )Bk TD Ln

q

exp( )V F

B

E E

k T

exp( )F C

B

E E

k T

diff

14

that possibly outperform its electronic counterpart, the manipulation of valley degree of freedom

should be uncorrelated with the charge degree of freedom; otherwise it will be limited by all the

major challenges involved in state-of-art semiconductor technology. In this regard, we have

demonstrated a promising candidate: the working mechanism of our valleytronic transistor is

distinctively different from that of a normal one. For normal transistor such as CMOS, the binary

output is embodied by either pulling the output node up to Vds or down to GND. This generally

requires applying an external bias voltage between the Source and Drain electrodes, and employing

a conductive charge current flow through the entire channel. In stark contrast, the valleytronic

transistor employ Hall voltage as output which does not demand a bias voltage and net charge

current through the channel. All the electrical outputs will be only exposed to gate of subsequent

stages, which controls further valleytronic information and does not drive the motion of charge.

Accordingly, this valley transistor could operate with much smaller power consumption (acquired

from the infrared light pumping) than the CMOS transistor.

We also anticipate that integrating with silicon photonic waveguide and utilizing more

advanced plasmonic structures may permit scaling down of the device. We propose a methodology

to achieve fully functional valleytronic circuit by employing our valleytronic transistor as building

blocks in two basic logical circuits (a NAND gate and a ring oscillator) to verify the concept of

combinational logic and sequential logic.

Firstly, we placed a silicon waveguide underneath metal/TMDC contacts for valley-

polarization. As a result, a point light source (either external or on-chip) coupled into the

waveguide is able to efficiently illuminate all the transistors, and therefore launches valleytronic

current.

15

Figure S18 illustrates the valleytronic NAND gate. The logic gate is akin to its CMOS

counterpart; it consists of two pairs of p-type and n-type transistors (whose valleytronic transfer

characteristics are schematically shown in the insets). Two p-type transistors are in series and two

n-type transistors are in parallel. In this case, if and only if both input valley states are “positive”,

the output valley state is “negative” (OUT = out+ - out-). The truth table of the valleytronic gate is

also shown in inset. Obviously, the circuit behaves as a NAND gate. Figure S19 schematically

shows the valleytronic ring oscillator. We use a 3-stage ring oscillator as an example. Briefly, it

consists of 3 reversely connected inverter stage. Again similar as CMOS inverter, each valleytronic

inverter is made of two complementary transistors. It can be simply deduced the device flips an

input valleytronic signal and acts as a valleytronic inverter.

It is not difficult to find out that the kernel design rule is very similar to CMOS circuit, all

other combinational logic circuit and sequential logic circuit can be seamlessly implemented based

on the same elementary building blocks and design rules.

16

Supplementary Figures

Supplementary Fig. 1 | Distributions of local optical chirality at the plane of MoS2 for Au

nanoantennae coupled to electrodes at different manners under the illumination of a linearly

polarized 1550-nm laser. The polarization is along y direction. The average values of the local

optical chirality enhancement, 𝐶̅, are therefore calculated.

17

Supplementary Fig. 2 | Circular dichroism spectra obtained as the difference between the

RCP and LCP absorption spectra for nanoantennae coupled with the electrode at different

manners. a, Tail-to-Electrode configuration. b, Head-to-Electrode configuration.

18

Supplementary Fig. 3 | Photocurrent mapping and Hall voltage mapping of one MoS2 FET

device without plasmonic antennae under the illumination of 1550-nm laser. a-b, The

photocurrent mapping at Vds = -1.6 V(a) and 1.6 V (b) respectively. c, The Hall voltage (VH)

mapping of the device under the same condition (P = 2.82 mW. Scale bar: 4 μm). Compared with

Fig. 2 (c) and Fig. 3 in the main text, no visible photocurrent and Hall voltage were detected, which

prove that the demonstrated phenomenon result from surface plasmonic-induced plasmonic effect

instead of intrinsic photo-response of MoS2.

c

700

0

a b

1.6 V-1.6 V0

-800

IPC (pA)IPC (pA)

D

S

D

S

30

-50

VH (μV)

-1.6 VD

S

1.6 V D

S

19

Supplementary Fig. 4 | Unbalanced population of hot electron-hot hole pairs between

different spins and resulted valley contrast

Supplementary Fig. 5 | The schematic injection of photo-excited carriers and generation

process of photocurrent under different bias condition. a, Photo-excited carriers are generated

and separated at contacts while no net photocurrent produced due to zero electric field in channel

a b c

20

at Vds = 0. b-c, External field provided by Vds tilts the electric potential in MoS2 channel

and reverse bias the Schottky junction at one contact, causing net photocurrent flow. The photo

response appears in the reverse biased Schottky contact where the built-in field is aligned with

external field.

21

Supplementary Fig. 6 | Circular polarized photoluminescent measurement of one MoS2

device. a, The optical image of the device. The green and red dots represent the position of 514

nm and 1550 nm laser spots (Scale bar, 2 μm). b, Schematic of the circular polarized PL

measurement of our device under three different conditions (corresponds to PL spectra in (c)-(e)).

600 620 640 660 680 700 720

PL inte

nsity (

a.u

.)

(nm)

s -

s +

600 620 640 660 680 700 720

s -

PL inte

nsity (

a.u

.)

(nm)

s +

2 μm

b c

d

e

a

600 620 640 660 680 700 720

PL

in

ten

sity (

a.u

.)

(nm)

s -

s +

1550 nm ON

“D” electrode

1550 nm ON

“S” electrode

1550 nm OFF

Right-hand

excitation

Left-hand

excitation

22

Without 1550 nm excitation, the PL signal is circular un-polarized. With 1550 nm excitation,

valley polarized free carriers are injected into MoS2, resulting in obvious PL helicity. c, The spectra

of circular polarized PL when turning off the infrared excitation (top panel in (b)). d-e, The spectra

of circular polarized PL spectrum with 1550 nm laser excitation at ‘D’ (d) and ‘S’contact (e),

respectively. The experimental details are summarized in method.

Supplementary Fig. 7 | The linear photogalvanic effect photocurrent components. The

linear photogalvanic effect (LPGE) photocurrent components extracted from Fig. 2d-e, ILPGE =

Lsin (4α+φl). No significant phase difference is seen between two LPGE components extracted

from 2 V and -2 V cases.

23

Supplementary Fig. 8 | Detection and transport of valley current of another short channel

device. a-b, Valley Hall voltage mappings of a short channel device under different bias polarities

(data taken with Vds = 0.4 V and -0.4 V for (a) and (b) respectively). The white lines represent the

edges of the metallic electrodes. Scale bar: 4 μm. c, Valley Hall voltage (VH) as functions of Vds

under illumination of linearly polarized laser (1550 nm and 532 nm). The label “Region S (D)”

represents the response region around S (D) electrode in (a) and (b). The measurements were

performed by focusing linearly polarized lasers at VHE “hot spots”. The powers for 1550-nm and

532-nm test were set at 2.82 mW and 0.13 mW, respectively. The error bars indicate the 2σ

uncertainty on each individual data point.

20

VH (μV)

0.4 V -0.4 V20

-20

D

S

D

S

a b c

VH (μV)

00

-25-0.6 -0.3 0.0 0.3 0.6

-40

-30

-20

-10

0

10

20

Region S (1550 nm)

Region D (1550 nm)

532 nm

VH

(

V)

Vds (V)

24

Supplementary Fig. 9 | Light helicity-dependent Hall voltage measurement. a-b, The VH as a

function of angles of a quarter waveplate with laser spot focusing at drain electrodes for Vds = -1.5

V(a) and 1.5 V(b). c-d, The VH as a function of angles of a quarter waveplate with laser spot

focusing at source electrodes for Vds = -1.5 V (c) and 1.5 V (d). The empty circles are the

experimental data. The thin solid curves are the fitting results based on the formula VH = C/sin

(2α+φc/) + L/sin (4α+φl

/) + D/. Here, α is the rotation angle of the quarter waveplate. Similar to Ipc

in Fig. 2 (d& e), φc/ and C/ are the parameters related to CPGE, characterizing the valley contrasting

carriers. φl/, L /and polarization-independent D/ arise from LPGE and it’s coupling with CPGE.

0 90 180 270 360

80

120

160

200

240 Region D

VH (

V

)

q (°)

Vds = -1.5 V

0 90 180 270 360

40

60

80

100 Region S

VH (

V

)

j (°)

Vds = 1.5 V

0 90 180 270 360

50

100

150

Region D

ab

s(V

H)

(V

)

j (°)

Vds = 1.5 V

a

c

b

d

0 90 180 270 360

90

120

150Region S

ab

s(V

H)

(V

)

q (°)

Vds = -1.5 V

25

The bold solid curves are the circular polarized components C/sin (2α+φc/) +D/ (measured at 1550-

nm laser, P = 2.82 mW. Scale bar: 4 μm).The error bars indicate the 2σ uncertainty on each

individual data point. θ and φ are rotational angles of quarter-wave plate in two sequential rounds

of measurements.

26

Supplementary Fig. 10 | Light helicity-dependent photocurrent under 532-nm illumination.

Photocurrent as a function of angles of a quarter waveplate of a pristine MoS2 FET without chiral

plasmonic nanoantennae measured under 532-nm illumination (P = 0.13 mW, Vds = -2 V). For 532

-nm laser, no hot carrier effect is presented. And no valley-polarization features can be obtained

due to its linear polarization and large energy mismatch with A exciton. It is used to exclude trivial

photo-related artifacts in our device.

27

Supplementary Fig. 11 | Photocurrent and Hall voltage mapping images of a pristine MoS2

FET without chiral plasmonic antennae under 532-nm illumination. a-b, Photocurrent

mapping results at Vds = -1.4 V(a) and 1.4 V(b) under the illumination of 532-nm laser. c-d,

Corresponding VH mapping images at the same condition as in (a-b) (Scale bar: 8 μm. P = 0.13

mW).

6

0

IPC (nA)

D

S

1.4 V0

-25

IPC (nA)

D

S

-1.4 V

100

-150

-1.4 V

VH (μV)

D

S

100

-200

VH (μV)

1.4 V D

S

a b

c d

28

Supplementary Fig. 12 | Photocurrent/valley Hall test of a bilayer MoS2 device. a, Optical

image of a bilayer MoS2 device. Scale bar, 8 μm. b , Photocurrent (IPC) as a function of angles of

a quarter waveplate. The solid and dashed curves are the fitting results and circular polarized

components, respectively. The error bars indicate the 2σ uncertainty on each individual data point.

c, Valley Hall voltage (VH) as a function of source-drain voltage Vds under illumination of 1550

nm laser for monolayer and bilayer, respectively. d-e, Photocurrent mapping of the bilayer MoS2

device at Vds = -1.7 V and 1.7 V, respectively (optical power P = 3.5 mW). f, Transverse voltage

mappings of a monolayer MoS2 device. Clear Hall signal is seen at source and drain electrode. The

2000VH (μV)

8 μm

-0.6 -0.3 0.0 0.3 0.6

-80

-40

0

40

80

120 monolayer (S)

monolayer (D)

bilayer (S)

bilayer (D)

VH (

V

)

Vds

(V)0 90 180 270 360

140

160

180

200

220

240

ab

s(I

pc)

(pA

)

a (°)

Vds = -1.4 V

a b

Ix

0-400

PC (pA)

4 μm

- 1.7 V

D

S

Vx

d

2500PC (pA)

4 μm

1.7 V

D

SIx

Vx

e

VH (μV)

c

B

- 100 0VH (μV)

40

4 μm

1.7 V

DS

VxIx

Ag

- 30 0VH (μV)

60

4 μm

1.7 V

DSVx

Ix

B

A

hbilayer

A

- 60 0 80

4 μm

1.7 V

DSVxIx

B

bilayer

4 μm

monolayer -0.7 V

Ix

S

B

A

Vx

f

D

i

-100

bilayer

29

yellow dashed boxes outline the response region where we count the Hall signals. g-i, Scanning

valley-Hall voltage mappings of three pairs of Hall probes of the bilayer MoS2 device. Only

photovoltage signals are seen around Hall probes, while negligible Hall signal is observed around

source and drain electrodes.

30

Supplementary Fig. 13 | Voltage drop between different Hall probes and grounded electrode

(S) as a function of Vds. The Vba is the potential differences between “a” and “b” electrodes in the

transverse direction, that is, the measured Hall voltage VH. the Va-gnd (Vb-gnd) is the potential

difference between “a” (“b”) electrode and the grounded electrode (source) (P = 2.82 mW). The

Vb-gnd almost equal to Vba (VH) and Va-gnd is nearly zero, suggesting that only one type of free carriers

(electrons) dominate the valley current.

31

Supplementary Fig. 14 | Schematic illustration of the potential profile and valley polarized

diffusion current under zero-bias condition. Different from the non-zero bias case, where the

Hall voltage is of opposite sign for different contacts because of a universal external field E and

opposite berry curvature, the Hall voltage is of same sign for zero bias conditions due to the

direction of built-in electric field E at different electrodes is opposite. Combined with opposite

valley polarities, the Hall voltage is thus of the same sign at source and drain electrodes under zero

bias condition. Noticing that the build-in field only exist in SCR, no electric field exists outside

the SCR. Thus valley-polarized carriers are pure valley flow with no charge current in the channel

away from the SCR at zero-bias condition.

K’

SCR SCR

φ

E E

D S

x

K

32

Supplementary Fig. 15 | Scattering process of the valley-polarized electrons. The initial valley-

polarized flow is of non-zero momentum caused by built-in field in SCR. Outside the SCR, the

valley-polarized free electrons are scattered and within a same valley. After intravalley scattering,

the momentum is nearly randomly distributed in K space.

33

Supplementary Fig. 16 | Valley Hall voltage measurement of one long channel device. a-b, VH

mappings at Vds = -1.5 V(a) and 1.5 V(b). Hall signals from drift valley current are observed, while

signals from diffusion are not detectable. (Scale bar, 4 μm). c, The Vds dependence of the Hall

voltage (VH) measured (corresponding to mapping in (a-b)) (1550-nm laser, P = 2.82 mW). The

error bars indicate the 2σ uncertainty on each individual data point. All data is shown as mean ±

s.d.

200

-100

VH (μV)

300

-500

VH (μV)

1.5 V-1.5 V

-1 0 1

0

-30

-60

VH (

V

)

Region D

Region S

Vds (V)

VH (

V

)

0

-100

-200

-300D

S

D

S

a b c

34

Supplementary Fig. 17 | Manipulation of valley signal using electrostatic gating. a, Hall

voltage VH and Hall conductivityσH as a function of gate voltage Vg (1550-nm laser, P = 2.82

mW). The calculated ON/OFF ratio (corresponding to VH-max/VH-min) is larger than 103. b, Source-

drain current as a function of back gate voltage Vg at Vds = -1.7 V. Inset shows the Vds dependence

of the source-drain current at different back gate voltages Vg (test in dark condition). The error bars

indicate the 2σ uncertainty on each individual data point. All data is shown as mean ± s.d.

-40 -20 0 20 40

10-13

10-11

10-9

10-7

-2 0 2

-0.4

0.0

0.4

-40

-20

0

20

40

I ds (

A

)

Vds

(V)

Vg (V) =a

bs

(Id

s)

(A)

Vg (V)

Vds= -1.7 V

a b

-40 -20 0 20 40

0.0

-0.6

-1.2

Vg (V)

VH (

mV

)

Vds = -1.7 V

1550 nm

2.82 mW

ON/OFF ratio >103

6

4

2

0

sH (

nS

)

35

Supplementary Fig. 18 | The valleytronic NAND gate. The p-type and n-type transistors are

demonstrated in green and purple, respectively. The valleytronic transfer characteristics are

schematically shown in the insets. The truth table of the valleytronic gate is also shown in inset.

36

Supplementary Fig. 19 | Schematic illustration of a 3-stage valleytronic ring oscillator. The

p-type and n-type transistors are demonstrated in green and purple respectively.

37

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