Table Of ContentMagnetoresistance and Quantum Oscillations of an Electrostatically-Tuned
Semimetal-to-Metal Transition in Ultra-Thin WTe
2
VallaFatemi,1 QuinnD.Gibson,2 KenjiWatanabe,3 TakashiTaniguchi,3 RobertJ.Cava,2 andPabloJarillo-Herrero1
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
3Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
(Dated: February 1, 2017)
We report on electronic transport measurements of electrostatically gated nano-devices of the
semimetalWTe . Highmobilitymetallicbehaviorisachievedinthe2Dlimitbyencapsulatingthin
2
7 flakes in an inert atmosphere. At low temperatures, we find that a large magnetoresistance can
1 be turned on and off by electrostatically doping the system between a semimetallic state and an
0
electron-onlymetallicstate,respectively. Weconfirmthenatureofthetworegimesbyanalyzingthe
2
magnetoresistance and Hall effect with a two-carrier model, as well as by analysis of Shubnikov-de
n Haas oscillations, both of which indicate depletion of hole carriers via the electrostatic gate. This
a confirms that semiclassical transport of two oppositely charged carriers accurately describes the
J exceptional magnetoresistance observed in this material. Finally, we also find that the magnetore-
0 sistancepowerlawissub-quadraticanddensity-independent,suggestingnewphysicsspecificallyin
3 the semimetallic regime.
] PACSnumbers: 85.30.Tv,84.37.+q
l
l
a
h
Semimetals, electronic systems with partially popu- majordifficultyattheultrathinlimitisthatsamplequal-
-
s lated bands of both positive and negative curvature, itydegradessignificantlyasthethicknessisreduced: ox-
e have been sources of novel physics since at least 1930, idation induces insulating behavior below 6 layers thick,
m
with the discovery of Shubnikov-de Haas (SdH) oscilla- rendering phenomena related to the high quality bulk
t. tions in bismuth[1, 2]. The semimetal graphite, when crystals inaccessible in the 2D limit [21, 23, 24].
a
thinned down to the electronically two-dimensional (2D)
m In this Letter, we investigate exfoliated WTe devices
2
limit, displays remarkable physics that continues to be
thatarefabricatedinagloveboxunderinertatmosphere
-
explored[3, 4]. Even more recently, three-dimensional
d in order to minimize degradation[25]. Doing so enables
n (3D) bulk semimetals have had a resurgence of inter-
creation of high quality nanodevices that display the in-
o est due to recently discovered experimental and theoret-
trisic physics of the material [26]. At low temperatures,
c ical behaviors, including unusually large magnetoresis-
[ we use an electrostatic gate to dope the system from a
tances [5, 6] and new topological electronic states known
semimetallic regime to a single-carrier regime. During
1 as Dirac and Weyl semimetals [7, 8].
this crossover we observe an evolution of the magnetore-
v
9 The compound WTe bridges both of these phenom- sistance and Hall effect that is qualitatively well cap-
2
3 tured by a semiclassical two-carrier model. We addition-
ena: experimentally it showcases exceptionally large,
8 ally observe that the exponent of the magnetoresistance
quadratic magnetoresistance in magnetic fields up to
8
power law is subquadratic and gate-independent within
0 60T [9], and theoretically it is predicted to be a Weyl
thesemimetallicregime. Finally,thesemimetal-to-metal
. semimetal in 3D [10] and near a quantum spin Hall
1 transition is further confirmed by analysis of SdH oscil-
0 state in 2D [11]. The observed magnetoresistance in
lations, which give insight to the low-energy band struc-
7 bulk samples has been proposed to be the result of near-
ture.
1 compensated electron and hole carriers, described by a
:
v semiclassical two carrier model [5, 12, 13]. However, a Tofabricatethedevices,WTe2isexfoliatedinanargon
i numberofquestionshavebeenraisedregardingthemech- atmosphere(<1ppmoxygen)andthenencapsulatedbe-
X
anismsatplay. First,quantumoscillationsrevealedmul- tween layers of hexagonal Boron Nitride (h-BN) with a
r
tiple Fermi pockets as well as imperfect compensation polymer pick-up and transfer technique[27]. For the de-
a
[14–16], suggesting other effects may play a role. More- vicediscussedinthemaintext, wealsoincludefew-layer
over, the small Fermi energy and orbital helicity of the graphene(FLG)betweentheWTe andthebottomh-BN
2
Fermi surface suggest that the band structure and scat- layerasanelectroniccontact. ThisFLGlayerhasanatu-
tering mechanisms, respectively, are liable to change un- rallateralgapbetweentwoindependentsheets,whichthe
der application of a magnetic field [17–19]. To elucidate WTe spans. Finally, we contact the FLG with evapo-
2
the origins of the magnetoresistance, a natural experi- ratedCr-Auviatheedge-contacttechnique[28],andthen
mentwouldbetostudytheeffectofchangingthecarrier etch the device into a Hall bar geometry with a reac-
density of a thin sample in-situ, which recent transport tive ion etch. The FLG serves as an intermediary con-
studies have attempted with varying results [20–22]. A ductor between the evaporated electrodes and the WTe
2
2
FIG. 1. (Color online) (a) Optical image of a completed
device. The edges of the original FLG flakes are indicated
bydashedwhiteline,andtheoriginalboundaryoftheWTe
2
flake is outlined in purple. The dark regions are where the
stack was fully etched to the SiO substrate. Solid white
2
scale bar is 2 microns long. (b) Cross-sectional schematic of
the device structure, with all components labeled. (c) Tem-
perature dependence of device A at two representative gate
voltages. The average RRR for all gate voltages is 13. Inset:
Temperature dependence of a similar-thickness WTe device
2
fabricatedinairandwithoutencapsulation. (d)Gatedepen-
dence of R at B = 0T and T = 4K. The vertical dashed
xx
line at V =87 indicating the resistance maximum.
BG
while also maintaining a good van der Waals seal with FIG. 2. (Color online) (a) MR as a function of magnetic
the encapsulating h-BN[29]. The device sits on a doped field for a range of V at T = 30mK. Inset: a zoom-in
BG
silicon wafer with 285nm of thermal SiO2, which serve of the data at VBG = 120V. (b) Rxy as a function of mag-
as the back-gate electrode and dielectric, respectively. netic field for a range of VBG at T = 300mK, displaying a
transition from non-linear to linear Hall effect [31]. Inset:
All electronic transport measurements are conducted in
Extracted saturation parameter (equation (3)) as a function
a four-probe configuration. An optical micrograph and
of gate voltage (black) at B = 10T. The blue dotted line
a schematic cross-section of the device are shown in Fig.
is unity. (c) Individual carrier densities and the total carrier
1(a-b). Here we report on the behavior of a 3-layer thick density, including charge sign, from the semiclassical model
device (sample A, thickness confirmed by AFM and Ra- fit. Black dashed line is an extrapolation of the hole density
man spectroscopy [21]), and in the supplement we show fromtheslopeatlowergatevoltages. (d)Mobilitiesfromthe
data on additional devices [30]. modelfit. Errorbarsin(c-d)represent95%confidenceinter-
vals of the fit. (e) Same data as (a) in log-log format with
The first indication that inert atmosphere fabrication
eachcurveoffsetverticallyforclarity. Thebluedottedlineis
maintains crystal integrity is the temperature depen-
a quadratic power law, whereas the cyan line is a power law
dence of the resistance, shown in Fig. 1(c). We observe fit to the data at V =10V. (f) The fitted exponent of the
BG
metallic behavior with a residual resistivity ratio (RRR) MR power law for B ∈[0.4,1.5]T as a function of gate volt-
of 13. In contrast, non-encapsulated devices fabricated age. The limits were chosen to avoid the high relative noise
in air display insulating behavior (inset of Fig. 1(c)). In atlowfields(B <0.2T)andonsetofsaturationathighfield.
Dot color corresponds to gate voltage in accordance with (a)
fact, in the literature a RRR of 13 is only achieved for
and (e). Dot size is larger than the 95% confidence interval
samples greater than 33nm thick[21]. Applying a bias
ofthefit. Theblackdashedlineindicatesthemeanexponent
V to the electrostatic gate, we capacitively modulate
BG for V <95V.
BG
the carrier density in the sample, finding that the low-
temperature resistivity increases linearly with V until
BG
∼ 87V, beyond which the resistivity drops sharply (see transverse (R ) resistances as a function of magnetic
xy
Fig. 1(d))[31]. The noted metallic temperature depen- field and gate voltage in order to investigate the mag-
dence with RRR of order 10 is observed for all gate volt- netoresistance behavior at different total carrier den-
ages,withtworepresentativegatevoltagesshowninFig. sities. Both measurements are shown in Fig. 2(a-
1(c). b) for a range of gate voltages, where in Fig 2(a)
We then measure both the longitudinal (R ) and we plot the magnetoresistance ratio (MR), defined as
xx
3
(R (B)−R (0))/R (0) [31]. The MR shows a clear thanthatestimatedfromSdHmeasurementsofthebulk
xx xx xx
transition from strong, superlinear behavior near zero Fermi surface[14, 18]. This suggests that other factors
gate voltage (∼ 400% increase at 11.5T) to suppressed may be involved in avoiding saturation at the highest
MR (< 3%) at the highest gate voltage (inset of Fig. fieldsfor3Dsamples[20]. Apossibleavenuewouldbeto
2(a)). Duringthecrossoveratintermediategatevoltages, investigatetheroleofmobilityanisotropies,knowntobe
we find that R saturates at large B, as expected for a important in bismuth[34]. Nonetheless, for the range of
xx
non-compensated semimetal [32, 33]. Importantly, we magnetic fields studied here, our analysis confirms that
observe that this crossover coincides with the Hall effect the large MR observed in WTe is rooted in the near-
2
transitioning from nonlinear to linear magnetic field de- compensation of electron and hole densities.
pendence, indicating a transition from two carrier types Upon closer examination of our data, we find that the
to a single carrier type. MRisactuallysub-quadratic[35]. Wecanseethisclearly
To investigate this behavior in more detail, we em- by looking at the data in log-log format, as shown in
ploy the semiclassical two-carrier model, which gives the Figure 2(e). An explicit fit of the power law gives an
following equations for the longitudinal and transverse exponent near 1.6, which is consistent for sample A in
resistivity of a semimetal: two different cooldowns as well as for additional devices
presented in the supplement[30]. The exponent is sta-
1nµ +pµ +(nµ +pµ )µ µ B2
ρ = n p p n n p (1) ble for nearly all gate voltages for all devices, except
xx e (nµ +pµ )2+(p−n)2µ2µ2B2
n p n p above VBG ∼ 100V for sample A, beyond which the ex-
1(cid:0)pµ2−nµ2(cid:1)B+(p−n)µ2µ2B3 ponent drops rapidly (Fig. 2(f)). This drop-off coincides
ρ = p n n p , (2)
xy e (nµ +pµ )2+(p−n)2µ2µ2B2 with the indications of depletion of the holes, reinforcing
n p n p that the MR can be understood as that of a standard
which include the electron charge e and four free param- semimetal with a correction to the exponent.
eters: the density (n, p) and mobility (µ ) of each car- The origin of the correction to the exponent is as yet
n,p
rier type, where n and p refer to electron-like and hole- unclear. ManystudiesonbulkWTe havenotedalarge,
2
like carriers, respectively. We fit R (B) and R (B) quadratic MR [5, 14, 16, 18, 21, 22, 36], but some that
xx xy
simultaneously to extract all four quantities at each gate explicitly fit the power law also find sub-quadratic ex-
voltage. (Here we constrain the electron density based ponents [20, 37]. While we observe a similar deviation,
on the SdH analysis presented below, but the important our sample is in the 2D limit, whereas the Fermi sur-
qualitative behavior doesn’t require this. See SI for the face of bulk WTe is 3D in character[14, 18], suggesting
2
details[30].) The fit parameters are plotted as a func- that dimensionality is not a driving factor. Additionally,
tion of V in Fig. 2(c-d). Most notably, we find that we find that the power law is density-independent in the
BG
the hole density decreases monotonically to nearly zero semimetallic regime, and almost no MR is observed in
at V ∼ 100V, consistent with our earlier, qualitative the electron-only regime. This suggests that the coexis-
BG
interpretation of the data. tenceofelectronsandholesiscrucial. Onemightlookto
We highlight now a particular aspect of the semiclas- semimetallic Boltzmann transport models which predict
sicalmodelregardingtheonsetofsaturation(orabsence that boundary effects can generate linear MR when the
thereof). The condition for onset of significant satura- valley recombination length is comparable to the trans-
tion in the MR is given by the ratio of the two terms in port channel width [12, 13], but this requires classically
the denominator of equation (1): strong magnetic fields not present here (µn,pB <∼ 3 for
thiswork). Inter-speciesdrageffectsmayalsoplayarole
(p−n)2µ2µ2B2
n p ∼1, (3) in magnetoresistance [38], but finite inter-valley scatter-
(nµ +pµ )2 ingshouldsuppresssuchphysics. Thequestionoftheun-
n p
usual magnetoresistance poses an experimental and the-
which is plotted in the inset to Fig. 2(b) for B = 10T.
oretical challenge for future investigation.
This condition is satisfied for V >22V, around which
BG We now turn to analysis of the quantum oscillations.
gate voltage we see the onset of saturation in the MR.
In Fig. 3(a) we show representative measurements of
The ratio is greater than 10 for V > 70V for which
BG ∆R (1/B), the resistivity after subtracting a smooth
xx
gatevoltagesweobservenearcompletesaturationathigh
quadratic background above 2 T, in the electron-only
magnetic field. When seemingly unsaturating MR is ob-
regime (V = 120V). At this gate voltage, two os-
BG
served in a semimetal, equation (3) can set a bound for
cillations are clearly visible, confirmed by the two peaks
the degree of non-compensation. For example, Ali, et
visible in the Fourier transform of the data in Fig. 3(b),
al, [5] measure effectively no saturation in bulk WTe
2 which we label α and β. In Fig. 3(c) we show a map of
in fields up to 60T. From this and the mobility (which
∆R with respect to both B and V . A third, hole-
xx BG
sets the magnitude of the MR), one may estimate an
like dispersing oscillation is additionally visible for lower
upper bound for the relative carrier density difference
(cid:12) (cid:12) gate voltages (highlighted by dotted white lines), which
(cid:12)(cid:12)nn−+pp(cid:12)(cid:12) <∼ 0.3%, which is an order of magnitude smaller we label δ. This is made clearer by fast Fourier trans-
4
tax 20 fects, which can be explored in future devices employing
a dual-gate geometry[11, 39]. The third oscillation fre-
Ω]
quency, δ, decreases monotonically with increasing gate
[
X
X voltage, which we can extrapolate to zero frequency (full
R
∆ depletion) at roughly V = 90V. This depletion volt-
BG
-40 age agrees with what is found for the positive charge
0.09 0.13 1/Bf[1/T] 0.17 0.21 carriers in the semiclassical analysis, so we ascribe the δ
tbx 1
α pocket to a valence band. Curiously, this depletion also
b] 30mK
ar 400mK coincides with a peak in the amplitude of the SdH oscil-
mp.f[ β 24..52KK lationsoftheαandβ pockets(seeFig. 3(c)), suggesting
a 7.1K that scattering between the electron and hole valleys is
Tf
F important.
F
0 We also conduct temperature dependence of the SdH
0 100 Freqf[T] 200 300
oscillations. Fitting the Lifshitz-Kosevich formula to the
tcx 11 tdx α β δ δ-fit temperaturedependenceofresistanceoscillationmaxima
allowsforextractionoftheeffectivemass. Inmulti-band
systemscaremustbetakentoextracttheoscillationam-
9 100 β plitude of an individual frequency, which can be done by
T] anappropriateFFTanalysis(seeSIformoredetails[30]).
sf[ An example fit for the α pocket oscillation is shown in
k
Bf[T] 7 TfPea50 α bFaigr.e 3el(eec)t,rgoinvimngasms.αS/immeil=ar0a.n2a5ly±si0s.0fo2r, wthheeroethmerebisanthdes
F
F give m /m =0.30±0.02 and m /m =0.36±0.04 (see
β e δ e
5
δ Fig. 3(f))[30][40]. These values are somewhat smaller
-30 25 than those reported for bulk crystals, which range from
ΔRxxf[Ω] 0.3 to 1 m [14, 36]. The electron effective masses are in
3 0 e
0 V [V] 100 0 V [V] 100 goodagreementwiththeoryforthemonolayer,whilethe
BG BG
tex tfx 0.4 hole mass is again smaller than that prediction by about
a factor of two[41]. We note that explicit predictions for
40
few-layer WTe have not yet been made.
2
[Ω] 30 m]e In summary, we investigated electronic transport in
X [ 0.3 encapsulated, ultra-thin WTe . We find that a strong,
RX20 eff 2
m intrinsic MR can be turned off by electrostatically dop-
∆
ing the sample from a semimetallic state to an electron-
10
only regime. We confirm the basis of the two regimes
0 0.2 by simultaneously analyzing the MR and the Hall ef-
0 2 4 6 α β δ
Tf[K] fect with a two-carrier model as well as by analysis
of Shubnikov-de Haas oscillations, both of which indi-
FIG.3. (Coloronline)(a)SdHoscillationsin∆R (1/B)at cate depletion of hole-like carriers in the suppressed-MR
xx
different temperatures and (b) their fast Fourier transforms regime. These observations confirm that the MR in
(FFTs) at VBG = 120V.(c) Gate- and field-dependence of WTe2 is qualitatively explained by semiclassical trans-
∆Rxx at T = 30mK. White dotted lines guide the eye to port of a semimetal, with potentially new physics in a
the δ pocket oscillation. (d) FFT peak frequencies (dots) at
modified exponent to the MR power law.
eachgatevoltage,andextrapolationoftheδfrequencytozero
This work was partly supported by the DOE, Basic
(dotted line). (e) Temperature dependence of ∆R maxima
xx
associated with the α pocket at V = 120V. (f) Effective Energy Sciences Office, Division of Materials Sciences
BG
mass of each pocket, from fits such as in (e) (see SI for more andEngineering,underawardde-sc0006418(samplefab-
details[30]). rication and measurements) and partly through AFOSR
Grant No. FA9550-16-1-0382 (data analysis), as well as
the Gordon and Betty Moore Foundation’s EPiQS Ini-
form (FFT) analysis, as shown in Figure 3(d) where the tiative through Grant No. GBMF4541 to P.J.H.. De-
threeobservedpeakfrequenciesaretrackedasafunction vice nanofabrication was partly supported by the Cen-
of gate voltage[30]. The α and β frequencies disperse ter for Excitonics, an Energy Frontier Research Center
weakly with gate voltage in a very similar manner as fundedby the DOE,BasicEnergy SciencesOffice, under
the electron carrier density from the semiclassical anal- Award No. de-sc0001088. Crystal growth at Princeton
ysis. The non-monotonic gate dependence of the elec- University was supported by the NSF MRSEC program
tron bands is likely the result of strong electric field ef- grant DMR-1005438. This work made use of the Ma-
5
terials Research Science and Engineering Center Shared N. Kikugawa, E. Manousakis, and L. Balicas, Physical
Experimental Facilities supported by NSF under award Review B 92, 125152 (2015).
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