Quantum oscillations in metallic Sb2Te2Se topological insulator

0.41 MB·

by  K. Shrestha

Quantum oscillations in metallic Sb Te Se topological insulator
2 2
K. Shrestha1∗ and V. Marinova2, D. Graf3, B. Lorenz4 and C. W. Chu4,5
1Idaho National Laboratory,2525 Fremont Ave, Idaho Falls, ID 83401, USA
2Institute of Optical Materials and Technology, Bulgarian Academy of Sciences,
Acad. G. Bontchev Street 109, Sofia 1113, Bulgaria
3National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306-4005, USA
4TCSUH and Department of Physics, University of Houston,
3201 Cullen Boulevard, Houston, Texas 77204, USA and
5Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
We have studied the magnetotransport properties of the metallic, p-type Sb Te Se which is a
2 2
7 topologicalinsulator. MagnetoresistanceshowsShubnikovdeHaasoscillationsinfieldsaboveB=15
1
T.Themaxima/minimapositionsofoscillationsmeasuredatdifferenttiltangleswithrespecttothe
0
B direction align with the normal component of field Bcosθ, implying the existence of a 2D Fermi
2
surface in Sb Te Se. The value of the Berry phase β determined from a Landau level fan diagram
2 2
n is very close to 0.5, further suggesting that the oscillations result from topological surface states.
a FromLifshitz-Kosevichanalyses,thepositionoftheFermilevelisfoundtobeE =250meV,above
F
J the Dirac point. This value of E is almost 3 times as large as that in our previous study on the
F
5 Bi2Se2.1Te0.9 topological insulator; however, it still touches the tip of the bulk valence band. This
explains the metallic behavior and hole-like bulk charge carriers in the Sb Te Se compound.
2 2
]
l
l
a Novel quantum phenomena arising from the topologi- due to defects, impurities, or intersite defects. These ef-
h
callyprotectedsurfacestateinsystemswithstrongspin- fects usually result in a shift of the bulk Fermi energy
-
s orbit coupling have been a focus of interest for several into the valence (down) or conduction (up) bands and
e years1,2,3,4,5. In topological insulators, the nontrivial thematerialshowsbulkconduction,asforexampleinthe
m
topology of the bulk band structure results in conduc- system Bi Se -Bi Te 8,9,10. The bulk states contribute
2 3 2 3
. tive electronic states at the surface since the transition totheconductioninparalleltothesurfacetransportand
t
a to the trivial topology of the vacuum demands passing the interference of both conduction paths makes it more
m
through gapless boundary states. The gapless surface difficult, if not impossible, to detect the typical signa-
- states are topologically protected and less sensitive to tureofthetopologicalsurfacestatesinmagnetotransport
d
perturbations or impurities, and their excitation spec- experiments11,12,13,14.
n
o trum within the bulk energy gap exhibits the character- In a recent study, however, we showed that SdH os-
c istic Dirac dispersion. cillations from bulk as well as surface carriers can be
[ Bulk and surface states can be observed through an- observed simultaneously in metallic Bi Se Te 15,16.
2 2.1 0.9
gle resolved photoelectron spectroscopy1,2,3. Electrical Conductance oscillations from bulk and topological sur-
1
v transportmeasurementsinmagneticfieldsarefrequently face states appeared to be well separated in the high-
7 usedtogatherinformationaboutthedetailsoftheFermi and low-field regions, respectively. This result revealed
7 surface of bulk and/or surface states. Quantum oscilla- thepossibilityofcharacterizingtopologicalsurfaceprop-
2 tionsoftheconductivity(Shubnikov-deHaas,SdH)have erties through magnetoconductance measurements even
1
their origin in the Landau level splitting of electron or- inmaterialswithbulkmetallicconduction. Itistherefore
0
bitsinmagneticfields. Forbulkcarriers,thecharacteris- ofinteresttoextendthestudyofmetallictopologicalsys-
.
1 ticSdHoscillationfrequenciesprovideinformationabout tems and search for other candidates where surface SdH
0
the Fermi surface and their dependence on the orienta- oscillations can be resolved despite metallic conduction
7
tion of the magnetic field probes the shape of the Fermi in the bulk.
1
surface. Surfacecarriers, however, areboundtothetwo- Sb Te Se is a member of a larger class of ternary
: 2 2
v dimensional character of the surface and therefore the tetradymite-like compounds17 and predicted to be a
Xi SdH oscillation frequencies depend on the field compo- topological insulator18,19. Wang et al20 observed quan-
nentnormaltothesurface. Furthermore,theDiracchar- tum oscillations in magnetoresistance and magnetic
r
a acter of the surface carriers can be shown by evaluating torque measurements in Sb Te Se under high fields up
2 2
the temperature and field dependence of the SdH oscil- to 35 T. From the angle dependence of the quantum
lations and by extracting the Berry phase. oscillations frequency, they reported an existence of a
In a perfect topological insulator, the bulk Fermi en- quasi-two dimensional Fermi surface originated from the
ergy falls into a gap and the only contribution to the bulk states. However, the Berry phase, which is the crit-
conductivity at sufficiently low temperature is from the ical parameter to distinguish a topological material from
topological surface states. Therefore, attention has been non-topological materials, is lacking in their work. In
paid to the growth and synthesis of compounds with a this study, we have investigated the SdH oscillations in
minimum amount of defects or impurities6,7. However, magnetoresistance of Sb Te Se. From the angle depen-
2 2
manytopologicalinsulatorsarenotinsulatinginthebulk dence of quantum oscillations and the determination of
2

the Berry phase, we prove that the SdH oscillations are 1 2
from charge carriers of topological surface states. No 4 5
quantum oscillations from bulk carriers are detected up 0 T
1 0 3 0 7 T
the maximum field of 31 T and the possible reasons are /K)
discussed. (Vm1 5
8 S 0
High quality single crystals of Sb Te Se were grown
2 2 )
by the modified Bridgman method. First, binary com- m -1 5
c 1 0 1 0 0
pounds Sb2Se3 and Sb2Te3 were synthesized. The syn- W 6 T (K )
thesis was done by using stoichiometric quantities of the (mxx 0.02
starting materials Sb, Se, and Te, each with purity of r 4 ) 0.01 5 K
W(
99.9999%,mixedinquartzampouleswithdiametersof20 xy0.00
mmandvacuumpumpedto10−6torr. Thesynthesisand R-0.01
2
homogenization process lasts for 25 hours at a tempera- -0.02
tureintherangeof620-650oC.Thebinarycompositions -6 -4 -2 0 2 4 6
B (T )
0
prepared in this way were mixed to the desired ternary
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
compounds,placedinquartzampouleswithdiametersof
T (K )
10mm,vacuumpumpedto10−6 torr,andsealed. These
ampoules were further positioned in a Bridgman crys- FIG.1. TemperaturedependenceofresistivityofaSb Te Se
2 2
tal growth furnace. In the furnace the ampoules were single crystal. The lower right inset shows Hall data at 5
heated to 650 oC and homogenized for 36 hours. The K. The upper left inset displays the logarithmic temperature
crystal growth process was performed through tempera- dependenceof thethermoelectricpowerat0(black) and7T
ture decreasing with a speed of 0.5 oC per hour in the (red) fields.
range of 650-570 oC. The ampoules were further cooled
from 570 oC to room temperature at a speed of 10 oC
per hour. 5 0
Magnetotransport measurements were performed at 50
45
theNationalHighMagneticFieldLaboratory(NHMFL), 4 5 )W40
withfieldsupto31T.Sixgoldcontactsweresputteredon (mxx35
a freshly cleaved crystal face for standard resistivity and R30
Hall measurements. Platinum wires were attached using ) 4 0 25
W
sinilgveprlaptafionrtm. TofhtehseamstapnledwaradspthroebnemdoeusingtneeddoanttNheHrMotFaLt-. (mx 3 5 -30 -20 -10 B 0(T) 10 20 30
x
Longitudinal and Hall resistances were measured using R
a lock-in amplifier (SR 830). AC current of 1 mA was 3 0
passedthroughthesampleusingaKeithley(6221)source
T = 0 .4 K
meter. The longitudinal and Hall resistances were mea- 2 5
suredusingtwolock-inamplifiers,respectively. Thesam-
ple was mounted on a rotating platform that can be po-
-3 0 -2 0 -1 0 0 1 0 2 0 3 0
sitioned at different angles with respect to the applied
B (T )
magnetic field. The platform, mounted in a 3He Oxford
cryostat, was inserted into the bore of a resistive magnet
FIG. 2. The symmetrized magnetoresistance, obtained by
with a maximum field of 31 T. The position of the sam-
[R (B)+R (−B)]/2, of a Sb Te Se single crystal under
xx xx 2 2
ple with respect to the applied field was calibrated by
highfieldupto31TatT=0.4K.Therawmagnetoresistance
usingaHallsensor. Thermoelectricpowerwasmeasured data of the Sb Te Se single crystal is shown in the inset.
2 2
using an ac technique at low frequency (0.1 Hz). Two
heaters generate a sinusoidal temperature gradient with
amplitudeof0.25Katacertainfrequency, andthesinu-
Also, the bulk carrier concentration is estimated to be
soidal thermovoltage across the sample was measured at 3×1018cm−3 at5 K.Seebeckcoefficient, S, asafunction
the same frequency.
of logarithmic temperature is displayed in the upper left
Figure [1] shows the longitudinal resistivity as a func- inset in figure [1]. Zero-field S is positive above 150 K,
tion of temperature for a Sb Te Se single crystal. The becomesnegativebelow100K,andre-entersthepositive
2 2
sampleexhibitsametallicbehaviorfrom300to5K.The region below 10 K. This suggests that either electron- or
residual resistivity ratio RRR=ρ (300K)/ρ (5K)=3.5 hole-likechargecarriersdominateatvarioustemperature
xx xx
for the Sb Te Se single crystal indicates good crystalline regions for Seebeck coefficient of Sb Te Se. At 5 K, the
2 2 2 2
quality. Hallmeasurementswerecarriedouttodetermine positive value of S is consistent with the p-type nature
the nature of the bulk charge carriers and their concen- of bulk charge carriers determined by the Hall measure-
tration. ThepositiveslopeofHallresistance(lowerright ments. With an application of 7 T field, S is positive
insetinfigure[1])confirmshole-likebulkchargecarriers. throughout the entire temperature range.
3

3 0.21 50 50
01..47 KK 0.4 K 0 o 0 o
-3 R (10)DWxx-1012 511235.055500 KKKKKK Amplitude (arb. unit)00000.....0011169258 1511235..0555070 KKKKKKK R (m)Wxx344505 5112234 o050550 oooooo R (m)Wxx344505 5112234 o050550 oooooo
-2 0.03 30 30
-3 0.00
0.036 0.045 0.054 0.063 0.072 0 100 200 300 400 500 600
25 25
1/B (T -1) F (T) (a) (b)
5 10 15 20 25 30 5 10 15 20 25 30
FIG.3. (a)Temperaturedependenceofquantumoscillations B (T) B cosq (T)
of a Sb Te Se single crystal measured at θ=0o, obtained af-
2 2
ter subtracting a smooth polynomial background. (b) Fast FIG.4. (a)SdHoscillationsofaSb2Te2Sesinglecrystalatdif-
Fourier transform (FFT) of quantum oscillations in figure ferent tilt angles, θ. The oscillations cannot be distinguished
3(a). aboveθ=40o. (b)SdHoscillationsasafunctionofthenormal
component of the applied field, Bcosθ.
The magnetoresistance of Sb2Te2Se is measured un- states origin of the quantum oscillations, we have calcu-
der high magnetic field up to 31 T at the NHMFL. The lated the Berry phase, β, from the Landau level (LL)
magnetoresistanceisanisotropicinthemagneticfielddi- fan diagram, which should be β=0.5 for Dirac particles
rection as shown in the inset of figure [2]. However, and 0 for normal fermions. Figure [5(a)] shows mag-
the anisotropy can be removed by taking the average netoconductivity σ (B), obtained by using the formula
xx
of the magnetoresistance in the positive and negative σ (B)=ρ /(ρ2 +ρ2 ), where ρ and ρ are longi-
xx xx xx xy xx xy
field directions, i.e. [Rxx(B)+Rxx(−B)]/2. Figure [2] tudinal and Hall resistivity, respectively. We let 1/Bmax
shows the symmetrized magnetoresistance at T=0.4 K and 1/B represent the positions of maxima and min-
min
with field along the c-axis. Magnetoresistance is posi- ima of the quantum oscillations in σ (B), respectively.
xx
tiveandshowsSdHoscillationsabove15T.Figure[3(a)] Wesubtractedalineardriftterminthequantumoscilla-
shows the quantum oscillations obtained after subtract- tions and the positions of minima and maxima were as-
ingasmoothpolynomialbackgroundatdifferenttemper- signedintegerandhalfintegervaluesrespectivelytocon-
atures. The oscillations are clear, and periodic in 1/B, structtheLLfandiagramshowninfigure[5(b)]. Wehave
showing the existence of a well-defined Fermi surface in extrapolated 1/B to zero for both maxima and minima
Sb2Te2Se. Figure [3(b)] displays frequencies of quantum separately in the LL fan diagram. In the limit 1/B→0,
oscillations, obtained by taking a fast Fourier transform we have obtained β=0.45±0.02 and 0.42±0.02 for min-
(FFT)ofthequantumoscillationsshowninfigure[3(a)]. ima and maxima extrapolations, respectively. These β
There exists a single frequency at f=215 T. The am- values are in agreement with each other and are very
plitude of the frequency decreases with an increase in close to the theoretical value 0.5 for the Dirac particles.
temperature but the frequency remains the same for all Thisfurtherconfirmsthatquantumoscillationsoriginate
temperatures. from topological surface states.
The angle dependence of quantum oscillations at dif- The frequency of quantum oscillations at θ=0o
ferent tilt angles θ provides the information about the is f=215 T. Using Onsagar’s relation f = (cid:126)/(2e)k2,
F
shape,size,anddimensionalityoftheFermisurface. Fig- the Fermi momentum corresponds to k =8×106 cm−1.
F
ure [4(a)] shows magnetoresistance at different θ values. Other physical parameters characterizing the surface
The positions of maxima/minima change systematically states were calculated using Lifshitz Kosevich (LK)
with tilt angle θ. The maxima/minima positions align theory22. From LK analyses, as shown in figure [6]
with one another with the normal component of mag- and lower left inset, the cyclotron mass is estimated
netic field, Bcosθ, as shown in figure [4(b)]. The oscilla- to be m =0.1m , where m is the rest mass of an
cyc 0 0
tions depend only on the normal component of B, indi- electron. Using the linear dispersion relation for the
cating the 2D nature of the Fermi surface. This provides surface state v = (cid:126)k /m , we have estimated the
F F cyc
astrongevidencethattheobservedquantumoscillations Fermi velocity v =6.7×105 ms−1. Following the stan-
F
result from topological surface states21. The amplitude dard Dingle temperature analyses (upper inset in figure
ofthequantumoscillationsdecreasesathigherangle,and [6]), we have calculated the Dingle temperature, T =35
D
theoscillationscouldnotberesolvedinmagnetorestance K. With the value of T =35 K, the surface carrier life
D
and its derivative for angles above 40o. This further time τ =(cid:126)/2πK T is estimated to be τ=3.5×10−14 s.
B D
supports oscillations originating from surface states, i.e. Similarly, other physical parameters like the mean free
Dirac fermions3,11. path l = v τ , mobility µ = eτ/m , and Fermi en-
F cyc
In order to provide further evidence for the surface ergy E are estimated to be 23 nm, 600 cm2/Vs, and
F
4

280 existence of topological surface states in the Sb Te Se
16 M axim a 2 2
260 15 16 17 1124 MMM iainnxiimmimaaa LLinineeaarr EExxttrraappoolalattioionn sfaincgelestcartyesstailn. ItthiesimnteetraelslitcinSgbt2oToeb2Sseervweitthopsoulocghicaalhsiugrh-
-1 (Scm)sxx 222400 11 12 13 14 n180 oqsasucmeinlplcalyetsio1a5ns,1fs6re.eeqnTuehinnecyoh.uigrWhpeerredvvaiidoluunesootsftoutbdhsyeeroFvneermBaiis2ewSceao2vn.1edTvefer0ec.9--
10 6 tor k in Sb Te Se indicates the higher position of the
F 2 2
200 9 4 Fermi energy from the Dirac point. Following a simi-
8 2
(a) (b) lar argument as in our previous work on Bi2Se2.1Te0.9,
1800.03 0.04 0.05 0.06 0.07 0.08 00.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 althoughtheFermienergyishigherintheSb2Te2Secrys-
B -1 (T -1) B -1 (T -1) tal,itstillcutsthetwovalencebandmaximaintheband
structure. This is why it still shows a metallic behavior
FIG.5. (a)MagnetoconductivityofaSb Te Sesinglecrystal
2 2 and has p-type bulk carriers. Due to the higher value of
plottedasafunctionoftheinverseofmagneticfieldB−1. The
the bulk states Fermi wave vector, an even higher mag-
minimapositionsareassignedasintegerLandaulevelindices.
(b) Landau level fan diagram of a Sb Te Se single crystal. neticfieldstrengthisneededtoobservequantumoscilla-
2 2
Thepositionsofminimaandmaximainmagnetoconductivity tions from the bulk states as constrained by the relation
areshownbyredandblackdots,respectively. Thesolidblue f/B − β = (n − 1), where n represents the Landau
n
line is the linear extrapolation of the linear fit to the data. level. This explains qualitatively the dominance of topo-
logical surface states in the Sb2Te2Se single crystal. The
bulk states interference might be seen at higher mag-
1 .0
E)]/D--22..50 15. 7 KK ntheitsicstfiuedldy,. bTehyoensdmtahlleer31vaTlume aoxfitmhuemelemctargonnetmiceafineldfreoef
d) 0 .8 2sinh(2KTpB---433...050 10 K p3en9actehnm(olf=fom2r3ontrhmee)sBcianit2tStehere2i.n1SgTbe2c0Te.9net2seSaremsspianlmetpihnleediaScsabtceTosmetphSaeerepsdaremtso--
malize 0 .6 [lnBRDxx--54..005.034 0.036 0.038 0.040 0.042 pBlie2.SeT2.h1eTeh0i.g9hsearmRpRleRa=scρoxmx(p3a0r0eKd)t/oρ3xx.5(2fo0rKt2)h=e1S22b2foTre2tShee
or B -1 (T -1) sample further supports the presence of larger scattering
(N centers in the Sb2Te2Se sample. The higher the number
xx0 .4 19 of scattering centers, the smaller the electron mobility.
RD eV)18 This is consistent with the lower value of electron mobil-
E (mD17 ity(µ=600cm2/Vs)inSb2Te2Sethanthe2200cm2/Vs
0 .2 16 in the Bi Se Te sample.
2 2.1 0.9
15
24 25 26 27 28 29
B (T )
0 1 0 2 0 3 0 4 0 5 0
T (K )
ACKNOWLEDGEMENTS
FIG. 6. Temperature-dependence of the amplitude of SdH
oscillations(∆Rxx)atB=28.8T.Theredlinerepresentsthe This work is supported in part by the U.S. Air Force
fit using LK equation22. Upper right inset: Dingle plot to
Office of Scientific Research, the T. L. L. Temple Foun-
determinetheDingletemperatureT andthecarrierlifetime
D dation, the J. J. and R. Moores Endowment, and the
τ. The dotted lines are linear fitting to the data. Lower left
State of Texas through the TCSUH. V. Marinova ac-
inset: Landaulevelenergyspacing(∆E)vsBplottoestimate
knowledges support from the Bulgarian Science Fund,
effectivecyclotronmassm . Thesolidredlineisthelinear
cyc
project FNI-T-02/26. A portion of this work was per-
fit.
formed at the National High Magnetic Field Laboratory,
which is supported by National Science Foundation Co-
250 meV, respectively. These physical parameters are operativeAgreementNo. DMR-1157490andtheStateof
comparable with those of the previous reports on other Florida. The work at Idaho National Laboratory is sup-
topological systems21,23. ported by Department of Energy, Office of Basic Energy
From the angle dependence of quantum oscillations Sciences, Materials Sciences, and Engineering Division
and the Berry phase calculations, we have proven the and through grant DOE FG02-01ER45872.
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