Field-induced resistivity plateau and unsaturated negative magnetoresistance in topological semimetal TaSb2

0.29 MB·

by  Yuke Li

Field-induced resistivity plateau and unsaturated nega-
tive magnetoresistance in topological semimetal TaSb
2
YukeLi1∗, LinLi1, JialuWang1, TingtingWang1, XiaofengXu1, ChuanyingXi2, Chao Cao1, Jian-
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huiDai1†
1
0
2

n
a 1DepartmentofPhysicsandHangzhouKeyLaboratoryofQuantumMatter,HangzhouNormal
J

9
University,Hangzhou310036,China

]
i
c 2HighMagneticFieldLaboratory,ChineseAcademyofSciences,Hefei,Anhui230031,China
s
-
l
r
t
m
.
t
a
m Several prominent transport properties have been identified as key signatures of topological
-
d
n materials1,2. One is the resistivity plateau at low temperatures as observed in several topo-
o
c
[ logicalinsulators (TIs)3–6; another is the negative magnetoresistance (MR) when the applied

1
v magneticfield isparallelto thecurrent direction asobserved inseveraltopologicalsemimet-
2
6
0 als (TSMs) including Dirac semimetals (DSMs)7–12 and Weyl semimetals (WSMs)13–17. Usu-
2
0
. ally, these two exotic phenomena emerge in distinct materials with or without time reversal
1
0
6 symmetry (TRS), respectively. Here we report the discovery of a new member in TSMs,
1
:
v
TaSb , which clearly exhibits both of these phenomena in a single material. This compound
i 2
X
r
a crystallizes in a base-centered monoclinic, centrosymmetric structure, and is metallic with
a low carrier density in the zero field. While applying magnetic field it exhibits insulating
behavior before appearance of a resistivity plateau below T =13 K. In the plateau regime,
c
∗[email protected]
†[email protected]
1
the ultrahigh carrier mobility and extreme magnetoresistance (XMR) for the field perpen-
diculartothecurrentareobservedasinDSMs18–22 andWSMs23–29,inadditiontoaquantum
oscillationbehaviorwithnon-trivialBerry phases. Incontrasttothe mostknown DSMsand
WSMs, the negative MR in TaSb does not saturate up to 9 T, which, together with the al-
2
most linear Hall resistivity, manifests itself an electron-hole non-compensated TMS. These
findings indicate that the resistivity plateau could be a generic feature of topology-protected
metallic states even in the absence of TRS and compatible with the negative MR depending
on the field direction. Our experiment extends a materials basis represented by TaSb as
2
a new platform for future theoretical investigations and device applications of topological
materials.
Diverginglongitudinalresistivitywithdecreasingtemperatureisthemostapparenttransport
property of a simple band insulator in distinction to any metals. However, such a distinct feature
ceases tostandinvarioustopologicalinsulatorsduetotheexistingmetallicsurfacestates1,2. Nev-
ertheless there are other transport phenomena, such as resistivityplateau and negativeMR, which
may distinguish at least ideal TIs and ideal TSMs from topologicallytrivial materials. In an ideal
3D TI where the bulk states are completely gapped out near the Fermi level, a resistivity plateau
can beclearly establishedbecausetheonlyparticipatingsurfacestatesareTRSprotected andthus
robusttodisorders,leadingtoasaturationofresistivityinthelowtemperatureregime3–6. InTSMs
without coexisting bulk Fermi surfaces such as an ideal WSM, on the other hand, the bulk exci-
2
tations come from the two separated Weyl nodes in momentum space which are chiral in nature
owing to the lack of TRS or inversion symmetry30–32. When the applied magnetic field is parallel
to the electric field direction, thedensity of theright/left chiral excitationsincreases/decreases ac-
cordingly as a consequence of the chiral anomaly33–35, resulting in a non-dissipativecurrent from
theleftto rightnodesalongthefield direction,hencean unconventionalnegativeMRappears.
BecausetheresistivityplateauandnegativeMRareoppositeconsequencesforsystemswith
orwithoutTRSintheidealsituationsmentionedabove,coexistenceofthebothinasinglematerial
isunlikelyorverydifficult. Ofcourse,thesefeaturesshouldbemoreintriguingbutmuchinvolved
in realistic topological materials, and, TRS itself is not the only origin relevant to the resistiv-
ity plateau on a general ground. In two-dimensional electron gases or semiconducting films like
graphite36,37, for instance, the resistivity seemingly saturates after a field-induced metal-insulator
transition while a clear resistivity plateau at lower temperatures was not reported. More recently,
a field-induced plateau has been observed in LaSb, a potentially new candidate of TIs38. While
the interpretation of all these and related behaviors in topological materials remains a theoretical
challenge, materials realizations of these effects are highly desirable not only in confronting this
challengebutalsoin techniqueapplications.
HerewereportthediscoveryofanewTSMTaSb ,whichcrystallizesinamonoclinicstruc-
2
ture with centrosymmetricspace group C (SI-Fig. S1). The longitudinal resistivityand Hall
12/m1
effect were measured for various magneticfields applied along different directions. The semicon-
3
ductingbehaviorisassociatedwithalowcarrierdensityandafield-inducedmetal-to-insulator-like
transition. HighqualityofthemeasuredsamplesisindicatedbyultrahighmobilityandXMR.The
topologicalnatureofthecompoundisevidencedbytheShubnikovdeHaas(SdH)oscillationmea-
surement as well as band structure calculations (SI-Fig. S6). Surprisingly, both the field-induced
resistivityplateauandunsaturatednegativeMRcan beclearlyobservedinthiscompoundasillus-
trated in the following. Therefore, our experiment shows that the monoclinic TaSb represents a
2
potentiallynewclass oftopologicalmaterialsexhibitingallthesenovelphenomena.
Themagneto-transportpropertiesofthesample1forTaSb issummarizedinFigure1,where
2
theappliedmagneticfieldBisparalleltothec-axis,andnormaltothecurrent. Figure1adescribes
thetemperaturedependentlongitudinalresistivityρ(T)atvariousfields(µ Hupto9T).AtB = 0,
0
ρ(T)exhibitshighlymetallicbehaviordownto2K. Itsvalueat300K is7.4 10−2 mΩcm, about
×
one order smaller than that of WTe , an electron-hole compensated semimetal with XMR39. For
2
nonzero field B (= B ), ρ(T) firstly decreases, then increases rapidly upon cooling, showing
±| |
a crossover to insulating behavior. The insulating behavior becomes prominent when B > 1 T.
Remarkably, ρ(T) saturates at the low temperature regime, developing a resistivity plateau which
isclearly exhibitedinFigure1b withalogarithmscale.
This finding reminds us of the compound SmB , an important candidate of TIs exhibiting a
6
verysimilarresistivityplateauatzerofield5,6. Inthatcompound,thetopologicalnon-trivialsurface
stateshavebeenevidencedbybothexperiments40,41andbandstructurecalculations42,sotheorigin
4
oftheplateau isbestunderstoodas dueto thesurface states. Thesimilarplateauin ρ(T)butunder
appliedfieldshasbeenalsoobservedinLaSbandothersemimetalcompounds38,43,theformerwas
predicted as a new kind of TIs44. The plateau of TaSb onsets at T = 13 K, almost three times
2
largerthan T = 5 K inSmB , andcomparabletoT = 15K inLaSb.
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Figure 1c shows temperature dependence of the derivative ∂ρ(T)/∂T at different fields. A
clear drop is seen for B & 2 T and becomes prominent for larger B. The temperature location of
thedrop peak, T , where ∂2ρ(T)/∂T2 = 0, is the inflection pointwhere crossoverfrom insulating
i
behavior to plateau takes place. The metal-insulating-like transition takes place at an elevated
temperature, T , where ∂ρ(T)/∂T = 0. The inset of the Figure 1c shows the evolution of T
m m
and T vs. magnetic field B, indicating that T increases monotonously and T remains almost
i m i
unchanged. This silent feature impliesthat the insulatingbehavior is of magnetic origin whilethe
plateau may be of topologicalone. If this is true, the later could be there at zero field. Indeed, we
find that the lines of T and T seem to merge at B = 0 T, suggesting a possible plateau there. In
m i
order to estimate the insulating gap, E , Figure 1d plots the Log(ρ) as a function of T−1 in the
g
range of T < T < T using ρ(T) = ρ exp(E /K T) with constant ρ . The inset in Figure
i m 0 g B 0
1d shows the fitted activation energy gap E √B. This is consistent with the gap opening in
g
∝
relativisticDiracelectrons bythemagneticfield.
Figure 2 plots the field dependence of MR, where negativeB means the opposite direction.
As shown in the upper panel of Figure 2a, the XMR of TaSb at low temperatures is exhibited
2
5
when the field is perpendicular to the current, reaching 15000% at T = 2 K and B = 9 T. This
MR is quadratic for low field and almost linear for larger B without saturation, similar to many
known semimetallic materials including TaAs(P), NbAs(P) and WTe 13,23,27,29,39. Upon heating,
2
the MR decreases slowly below 10 K, but drops quickly at higher temperatures. The inset in the
upperpanelofFigure2ashowsawindowfor7T B 9TwheretheSdHoscillationsareclearly
≤ ≤
exhibitedat T = 2 K and 5K, respectively.
We also measured the MR by applying the magnetic field parallel to the current B I, as
||
shown in the low panel of Figure 2a. It is remarkable that (i) the MR in the whole temperature
regime is less than 100%, much smaller than that in the case of B I shown previously; (ii) in the
⊥
lowtemperatureregimesuchasT =2Kand10K,theMRispositiveandparabolicforB.6.5T;
(iii)whileforB&6.5T,itbecomesnegativeanddecreaseswithincreasingmagneticfieldwithout
saturation up to B = 9 T; (iv) when T & 50 K, the MR is very small and positive, increasing
monotonouslywithfield.
Figure2bdescribesthefielddependenceofMRatafixedtemperatureT =2Kwithdifferent
anglesθbetweenthemagneticfieldandcurrent. TheoverallprofileisnearlysymmetricunderB
→
B. By rotating θ = 90◦ 0◦, the MR drops quickly, in particular when approaching θ 10◦.
− → ≈
The tendency of negative MR for smaller θ is further illustrated in the low panel of Figure 2b.
At B = 9 T, the MR turns to negative for θ . 4◦. The window for the negative MR is limited
from this point to B & 6.5 T at θ = 0◦. The similar narrow θ window was observed in Na Bi
3
andTaPcompounds9,13. TheunsaturatednegativeMR,whichdecreasesmonotonicallywithfields
6
reaching about -74% at B = 9, is a remarkable feature compared to the prototype DSMs and
WSMs such as Na Bi9, Cd As 10–12, TaAs14, NbP16, where thenegativeMRis limitednot onlyin
3 3 2
anarrowwindowofθ,butalsoinawindowofB,namely,thenegativeMRwillsaturateandreturn
to positive for larger B even for θ = 0◦. In view of chiral anomaly, the MR should be always
negative as long as B I (or θ = 0◦). If imperfect alignment of the magnetic field and the current
||
in samples can be fully excluded, the limited window in B should be due to the disorder-induced
weaklocalization. SotheunsaturatednegativeMRobservedhereimpliestheconsistencywiththe
chiral anomalyinterpretationand thehighqualityofthemeasured samples.
Figure 3 maps the Hall effect and the SdH oscillations. The magnetic field dependence of
Hall resistivity at various temperatures is displayed in the main panel of Figure 3a. The negative
slope for all of curves implies that electron-type carriers dominate the transport from 300 K to 2
K. Theρ displaysan overalllinear dependence, and only slightlydeviatesfrom linear at around
xy
9 T as T 20 K. TheHallcoefficient R versustemperatureat 6 Tand 9 T is plottedin theinset
H
≤
of Figure 3a. R is always negative and drops soon below 50 K without a sign change. Notice
H
that the strong nonlinear behavior in ρ and the sign changed R in several semimetals 24,29,39
xy H
havebeenregardedasindicationsoftheelectron-holecompensation. Obviously,thisinterpretation
cannot applytothepresentTaSb sample.
2
Accordingly,thecalculatedcarrierconcentrationisn 3.2 1020cm−3usingn = 1/eR (T)
e e H
∼ ×
and the estimated mobility µ 1.96 104 cm2V−1S−1 at 2 K. Hence, TaSb has a low carrier
e 2
∼ ×
7
density of electron-type but with a high carrier mobility,similar to the results of LaSb39. A direct
consequenceofthesefortheSdHoscillationisshowninFigure3bforρ (B)at1.8K,4.2Kand8
xx
K,respectively. WeextracttheSdHoscillationsusingρ = ρ [1+A(B,T)cos2π(S /B γ+δ)],
H 0 F
−
~
with ρ being the non-oscillatory part, A(B, T) the amplitude, γ the Onsager phase, F = S
0 2eπ F
thefrequency,andS thecross-sectionareaoftheFermisurfaceassociatedwiththeLandaulevel
F
indexn. Thebackgroundissubtractedusingapolynomialfitting. Theobtained∆ρ asafunction
xx
of B−1 is then plotted in the inset of Figure 3b. Two oscillation sets can be extracted (SI-Fig.
S5), corresponding to two frequencies: a small oscillation frequency at F = 220 T, and a sec-
α
ond frequency at F = 465 T with its harmonic F 930 T and F 1377 T, as shown in
β 2β 3β
≈ ≈
Figure 3c. The Berry phase Φ can be identified via the relation γ = 1/2 Φ /2π, so Φ is
B B B
−
non-trivial when γ = 1/2. We thus plot the Landau fan diagram in Figure 3d, and count down
6
to n =8 and 16 for F and F , respectively, up to magnetic field 30 T. Linear fitting of n versus
α β
B−1 yields the Onsager phase of γ = 0.29 and γ = 0.2, respectively, far away from one half,
α β
indicative of non-trivial π Berry phases in TaSb . The slopes of the linear fitting are F = 228
2 αfit
T and F = 461 T, respectively, consistent with the experimental values. The non-trivial Berry
βfit
phases identified here indicate the topological origin of the resistivity plateau. This conclusion is
also consistent with the first principle calculations for the electronic band structure of TaSb as
2
described in the Supplemental Information. The calculations indicate that TaSb has a small bulk
2
Fermi surface and a Dirac cone near the Fermi level, both of them are contributed by the partially
occupied,topologicallynon-trivialelectronicbands.
8
In summary, we report the discovery of a TMS TaSb with a monoclinic crystal structure.
2
It undergoes a metal-insulator-like transition induced by magnetic field upon cooling. Yet this
compoundshares a numberofexcellent transportproperties includingthepositiveXMR and high
mobility. Inthelowtemperatureregime,itexhibitsboththeresistivityplateauandunsaturatedMR
when the applied field is perpendicular and parallel to the current, respectively. The topological
property is manifested by the non-trivial Berry phases in the SdH oscillations as well as the band
structurecalculations.
Given the fact that the resistivity plateau and the negative MR are characteristic features
of ideal TIs and TSMs with and without TRS, respectively, the coexistence of these two distinct
phenomena in TaSb is a rather remarkable observation. It implies that the resistivity plateau
2
maybeagenericfeatureofawideclassoftopologicalmaterialspossessingmetallicsurfacestates
evenintheabsenceofTRS.ItalsoraisesachallengetounderstandthedifferentfatesofbulkFermi
surfaces,Diracconeexcitations,aswellasmetallicsurfacestatesinthepresenceofmagneticfield.
All these novel features, together with the field-induced metal-insulator transition, the XMR and
the high carrier mobilities, suggest TaSb as an interesting new platform of topological materials
2
forfuturetheoreticalinvestigationsand deviceapplications.
Methods
High quality single crystals of TaSb were grown via chemical vapor transport reaction using
2
iodine as transport agent. Ploycrystalline samples of TaSb have been first synthesized by solid
2
statereactionusinghighpurifiedTantalumpowdersandAntimonypowdersinasealedquartztube.
9
The final powders were ground thoroughly,and then were sealed in a quartz tube with a transport
agent iodine concentration of 10 mg/cm3 . The single crystals TaSb were grown by a chemical
2
vaportransportinatemperaturegradientof120◦Cbetween1120◦C-1000◦Cfor1-2weeks. X-
raydiffractionpatternswereobtainedusingaD/Max-rAdiffractometerwithCuK radiationanda
α
graphitemonochromatorat theroom temperature. Thesinglecrystal X-ray diffraction determines
thecrystal grown orientation. The compositionof the crystals were obtained by energy dispersive
X-ray (EDX)spectroscopy. Noiodineimpuritycan bedetectedin thesesinglecrystals.
The(magneto)resistivityandHallcoefficientmeasurementswereperformedwithastandard
four-terminal method covering temperature range from 2 to 300 K in a commercial Quantum De-
signPPMS-9 systemwithatorqueinsert. ThedeviationofMRandHallmeasurementsassociated
with misalignment of the voltage leads could be corrected by reversing the direction of the mag-
neticfield. Thehigh magneticfield resistivityand Shubnikov-deHaas oscillationswere measured
up to 31 T at Hefei High Magnetic Field Laboratory. To check those experimental data, we per-
formedresistivityandHalleffectmeasurementsinbothsample1andsample2withdifferentRRR
(See SI). Thesample2 withlowerRRR alsoshowsthesameexperimentalresults(See SI).
Theelectronicstructurecalculationswere performed in theframework ofdensityfunctional
theoryusingtheViennaAbinitioSimulationPackage(VASP)45,46 withprojectedaugmentedwave
(PAW) approximation and Perdew Burke Ernzerhoff (PBE) flavor of the generalized gradient ap-
proximation(GGA). A 400 eV plane-wave energy cut-off and a 8 8 5 Γ-centered K-grid was
× ×
chosentoensuretheconvergenceto1meV/atom. TheFermisurfacewasthenobtainedbyextrap-
olatingtheDFTbandstructuretoadenseK-gridof100 100 100. Thetopologicalindiceswere
× ×
10