Fermi Surface and Anisotropic Spin-Orbit Coupling of Sb(111) studied by Angle-Resolved Photoemission Spectroscopy

0.22 MB·English

by  K. Sugawara

Fermi Surface and Anisotropic Spin-Orbit Coupling of Sb(111) studied by
Angle-Resolved Photoemission Spectroscopy
K. Sugawara,1 T. Sato,1,2 S. Souma,1 T. Takahashi,1,2 M. Arai,3 and T. Sasaki3
1 Department of Physics, Tohoku University, Sendai 980-8578, Japan
2CREST, Japan Science and Technology Agency (JST), Kawaguchi 332-0012, Japan and
3 Computational Materials Science Center, NIMS, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
(Dated: February 6, 2008)
6
0
High-resolutionangle-resolvedphotoemissionspectroscopyhasbeenperformedonSb(111)toelu-
0
cidatetheoriginofanomalouselectronicpropertiesingroup-Vsemimetalsurfaces. Thesurfacewas
2
found to be metallic despite the semimetallic character of bulk. We clearly observed two surface-

n derived Fermi surfaces which are likely spin split, demonstrating that the spin-orbit interaction
a playsadominantroleincharacterisingthesurfaceelectronicstatesofgroup-Vsemimetals. Univer-
J sality/disimilarity of the electronic structure in Bi and Sb is discussed in relation to the granular

7 superconductivity,electron-phonon coupling, and surface charge/spin density wave.

] PACSnumbers: 71.18.+y,73.20.-r,73.25.+I,79.60.-i
r
e
h
t Bi- and Sb-based nanostructure materials have gener- V semimetals [9, 10]. Comparative study by Sb, which
o
ated a considerable interest since they show variety of is a homologous element and has similar structural pa-
.
t physical properties such as superconductivity in Bi clus- rameters to those of Bi [9, 11, 12], would open a way
a
m ters [1], semimetal-semiconductor transition and quan- to better and comprehensive understanding of the ori-
tum size effect in thin films [2]. These materials are ginoftheanomalouselectronicpropertiesofBi/Sb-based
-
d also useful in devise application since their alloys and nanostructure materials.
n
heterostructures are used for a highly efficient thermo- InthisLetter,wereporthigh-resolutionARPESresult
o
c electric converter [3]. These interesting properties owe ofSb(111). WeshowthatSb(111)surfaceismetallicand
[ to the characteristic electronic structure inherent to the possesses FSs qualitatively similar to those of Bi(111)

semimetals, such as low carriernumber and its high mo- [4], but remarkably different in the volume and symme-
1
v bility. To understand the origin of these intriguing be- try. Direct observation of the degeneracy of two sur-
3 haviors,theelectronicstructureofBihasbeenintensively facebandsexactlyatthezonecenterestablishesthatthe
3 studied[4,5,6,7,8]. ThebanddispersionandtheFermi space-inversionsymmetrybreaksatthesurface,andsug-
1 surface (FS) were determined by angle-resolved photoe- geststhatthebandsarespin-splitduetoSOC.Wefound
1
mission spectroscopy (ARPES) [4, 5, 6, 7, 8], which re- no evidence for the gap opening at low temperature in
0
6 vealedthat the surface electronic structure is metallic in contrasttothereportonBi(111)[6]. Alltheseresultsare
0 contrast to the semimetallic nature of bulk. Two differ- wellexplainedintermsofthe anisotropicSOC,theweak
/ ent surface-derivedanisotropic FS sheets are reportedin electron-phonon(e-p)interaction,andthesmalleffective
t
a Bi(111), a small hexagonal electron pocket centered at mass of quasiparticle bands.
m
the Γ point and six elongated hole pockets [4]. In spite
ARPES measurements were performed using a SES-
- ofintensiveARPESstudiesonBisurfaces,thereisacon-
d 2002 spectrometer with a high-flux discharge lamp and
n siderablecontroversyonthenatureofsurfacebandsnear a toroidal grating monochromator. We used the He Iα
E . AstandHo¨chstreportedthe nestedcharacterofthe
o F (21.218eV) resonanceline to excite photoelectrons. The
c hexagonalFS and observedthe gap-opening at low tem-
energy and angular resolutions were set at 3.5-12 meV
v: peratures and interpreted it in terms of the formation and 0.2◦, respectively. The angular resolution was 0.2◦.
Xi of the surface charge density wave (CDW) [6]. On the Acleansurfaceofsamplewasobtainedbyinsitucleaving
other hand, Koroteev et al. concluded that the FS orig- inavacuumof2×10−11Torralongthe(111)plane. Band
r inates in the spin-split bands due to the spin-orbit cou-
a calculation was performed by the linearized augmented
pling (SOC) [8], and suggested the formation of surface
planewavemethodusingthelocaldensityapproximation
spin density wave (SDW). These apparently contradict-
[13] including the spin-orbit interaction.
ing conclusions strongly request the necessity for further
Figure 1 shows the ARPES intensity plot at E of
investigation. To clarify this issue is important not only F
Sb(111)as a function of two-dimensional(2D) wavevec-
in understanding the mechanism of anomalous physical
tor. We notice three different FSs, a small ring-like FS
properties in group-V semimetals, but also opens up the
centered at the Γ point, six lobes with three-fold inten-
waytotheapplicationofnewdevises[8]. However,there
sity variation, and an oval-shaped FS centered at the
is nofirmexperimentalevidencesofar tosettle this con-
M point. The ring-like FS has no counterpart in the
troversy, since all the previous high-resolution ARPES
band calculation, suggesting the surface-derived charac-
studies were focused on Bi, but few on the other group-
ter. ThisdemonstratesthattheSb(111)surfaceismetal-
2
(a) (b) (a) K G K (b)
0.8 Sb(111) M 0.2 EF
)
K V0.1
e
(
0.4 0.1 y 0.2
g
r
-1A)0 G yk Ene0.3
(ky M G high 0 (A)-1 ding 0.4 high
-0.4 K LUH WT X -0.1 Bin00..56 low kx=0 . 0A-1 k0x.=03 5A-1
-0.8
L low -0.1 0 0.1 -0.1 0 0.1
-0.8 -0.4 0 0.4 0.8 -0.1 0 0.1 k (A-1) k (A-1)
y y
k (A-1) k (A-1) (c) (d)
x x
kx(A-1) B A
fFuInGc.tio1n: o(af)twAoR-dPimESenisniotnenaslitwyavpelovteacttorE,FtoogfetShbe(r1w11it)hasthae nits) 0.04 nits) C
cisalicnutelagtreadteFdSovperrojtehceteedneorngythrean(1g1e1o)fp2l0anmee.VAcRePntEeSreidntaetnEsiFty. arb. u 0.02 arb. u A
Inset shows the bulk BZ and corresponding surface BZ. (b) y ( 0.0 y (
Expansion of (a) in thevicinity of the Γ point. nsit -0.02nsit B
Inte -0.04 Inte T = 7 K C
Au
licasBi(111)[4,5,6,7,8]. Theobservedstrongintensity
nearthe Γpointinthe sixelongatedFSs isnotexpected 0.25 0.15 0.0520 10 E -10 -20
F
fromthebandcalculation,suggestingthatthisFSisalso Binding Energy (eV) Binding Energy (meV)
of surface origin. The three-fold symmetry of spectral
intensity indicates that the surface state is not simply FIG.2: ARPESspectralintensityplotofSb(111)aroundthe
confined within the surface bilayer with six-fold symme- Γ as a function of ky and binding energy for (a) kx = 0.0
try [4]. As for the six elongated FS away from the Γ ˚A−1 and (b) kx = 0.035 ˚A−1. Calculated bands along the
point, the intensity shows an excellent agreement with Γ-K direction projected on the (111) plane are also shown
by red curves in (a). (c) ARPES spectra measured around
the calculated FS which originates in the hole pocket at
the zone center to show the degeneration of two bands. The
theHpointofthebulkBrillouinzone(BZ)[11,12]. This
spectrum at thezone centeris indicated byabluecurve. (d)
feature is broad and subtle as compared to the ring-like
Ultrahigh-resolution (∆E= 3.5 meV) ARPESspectra in the
FS, indicative of admixture of surface and bulk states close vicinity of EF at 7 K measured at three kF points (A,
whichareessentiallyindistinguishabledue tothe surface B, and C, in inset), compared with Au.
resonance. As seen in Fig. 1(a), the oval-shaped feature
at the M point is well reproduced by the projection of
the calculated electron pocket centered at the L point Ontheotherhand,the twobandsnearE whichappear
F
[11,12]. AsseeninFig. 1,thesmallFSlookshexagonal- withinthegapofprojectedbulkbandsareassignedtothe
like rather than circle-like and possesses parallel regions surface states. We found that the two surface bands de-
indicative of a good nesting condition. We estimated generateonlyattheΓpoint(Fig. 2(c)),andtheyarewell
the Fermi momenta (kF’s) by tracing the intensity max- separated at other k-points, as seen in the cut for kx =
ima and found that the FS is six-fold in contrast to the 0.035˚A−1(Fig. 2(b)). Wenowdiscusstheoriginofthese
trigonal-symmetric behavior of the elongated FSs. bands to resolve the controversy in the Bi surface [6, 8].
In Fig. 2, we show ARPES intensity maps around the Important is whether the bands are spin-split or not. In
Γpointasafunctionofk andbindingenergyfortwodif- bothbulkandsurface,thetime-reversalsymmetryholds,
y
ferentk values. At k = 0.0˚A−1(Fig. 2(a)), we observe requiringtheconstraintofspin-dependentenergydisper-
x x
a highly-dispersive electronlike band with the bottom at sion, E(k, ↑) = E(-k, ↓). In addition, the space-inversion
∼0.2 eV at Γ point. Another band disperses in the en- symmetry in the bulk requests that E(k, ↑) = E(-k, ↑).
ergyregionof0.1-0.2eV.Theformerproducesthesmall Combination of these requirements results in E(k, ↑) =
hexagonal-like electron pocket at the Γ point, while the E(k, ↓). This does not lead to lifting of the spin de-
latterproducesthesixelongatedholepockets. Thesetwo generacy, hence the bands are doubly degenerate in the
bands degenerate at the zone center (Γ point). We also bulk. However, on the surface where the space-inversion
find another relatively broad feature dispersing around symmetry usually breaks, the time-reversal symmetry
0.2 - 0.6 eV. This band overlaps with the projection of alone determines the character of bands. Therefore, if
the calculated 5p band, demonstrating the bulk origin. the two bands arespin-split onthe surfaceas inthe case
3
70 EF (a) 10 (b) ually goes to zero at the binding energy higher than 20
V) 50
60 B. E (me20 T = 7 K 8 mtheeVb,arreeflbeacntidn.gImthΣe(rωe)cokveeerpysonfeatrhleyecnonersgtayndtibspuetrssliiognhttlyo
)meV50 4-00.065ky(A-1)-0.060 46ReS ()meV40 decreases in the binding energy region of 40 - 15 meV,
m while it shows a relatively steep drop at lower binding
S (Im40 2eV)S (Im30 l = 0.22 0.03 energy. Thecharacteristicenergydependenceintheself-
0 energy indicates that surface electrons are coupled to a
30 -2 certain excitation, most likely phonon, since the Debye
40 30 20 10 0 200 50 100 150 200 250 temperature of bulk Sb (211 K = 18 meV [17]) has a
Binding Energy (meV) Temperature (K)
similar energy scale. Figure 3(b) shows the temperature
dependence of ImΣ(0), which exhibits almost linear be-
FIG. 3: (a) Imaginary (filled circles) and real (open circles)
part of the self-energy at 7 K, ImΣ(ω) and ReΣ(ω), deter- havior up to 250 K. Estimated coupling constant λ by
mined by the Lorentzian fitting of MDC on the electronlike using the approximationImΣ(0;T) = πλkBT [18] is 0.22
band. Solid lines show the result of fitting by the bulk De- ± 0.03, which is classified into a weak-coupling regime.
bye model which satisfies a Kramers-Kronig relation. The This value is much smaller than that of Bi(111)which is
finite electron-electron scattering term is taken into account ashighasλ= 0.7[5,8]. Itisnotedthatthe estimatedλ
in ImΣ(ω). Inset shows the MDC peak position (solid cir- forω = 20and40 meVis 0.20± 0.03ineach,indicating
cles) together with extrapolated parabolic bare-band disper-
that the coupling constant is independent of energy, at
sion (solid line). (b) Temperature dependence of ImΣ(0).
least within 40 meV. This implies that the bulk density
Solidlinerepresentstheresultofleast-squarefittingbylinear
function. λ is the e-pcoupling constant. ofstates (DOS) does not showdiscernible modulation in
the close vicinity of E [7]. We fit the experimentally
F
obtained self-energy by both the surface and the bulk
ofAu(111)[14,15],thebandshouldshowthedegeneracy Debye models with Debye energy (ωD) and λ as free
exactly at the Γ point because E(0, ↑) = E(0, ↓). This parameters, and found that the best fit by the surface
behaviorisindeedobservedinthepresentARPESexper- model gives an anomalously high λ (1.8), while the bulk
iment, suggesting that the two surface bands in Sb(111) model (solid lines) produces the value (λ = 0.3) roughly
are produced by SOC. The strong anisotropy of the FSs consistent with the value estimated from the tempera-
/ bands demonstrates that the spin-orbit interaction is ture dependence. Since the bulk model also reproduces
quite anisotropic. Clear observation of the degeneracy the ωD (14 meV) close to the known bulk Debye energy
of the surface bands at the Γ point in Sb(111) is due to (18 meV), these suggestthat electrons atthe surface are
no overlapping between the surface and the bulk bands substantially coupled to the bulk phonon.
aroundtheΓpoint. ThisisagreatadvantageofSb(111), We now discuss the surface states on Sb(111) in rela-
becausethesurfaceresonance,whichsignificantlybroad- tion to the previous reports on Bi(111) [4, 5, 6, 8]. The
ens and weakens the surface-state emission as observed hexagonal-likeelectronpocketandthesixelongatedhole
in Bi(111), does not take place in Sb(111). Moreover, pockets are commonly seen in both surfaces. The main
similarity of the overall FS topology and band disper- differenceisthattheE -intensityprofileoftheholepock-
F
sion between Sb and Bi [4], in return, suggests that the ets in Sb is three-fold while that of Bi is six-fold. This
twosurfacebandsinBi(111)arealsocausedbySOC.To is understood in terms of the difference of the location
examine the possibility of gap opening on the electron of bulk valence-band maximum, which is at T point in
pocket, we performed ultrahigh-resolution measurement Bi while it is between T and W points (H point) in Sb
atthreerepresentativekF points. AsshowninFig. 2(d), [9, 11, 12]. When these bands are projected onto the
the leading-edge midpoint at 7 K for all kF points coin- surface BZ, a small FS is produced inside the surface-
cides wellwith that of Au, demonstratingthe absence of derived hexagonal-like FS in Bi [8] while that is outside
an energy gap. This is in sharp contrast to the leading- in Sb and overlaps with the surface-derived elongated
edge shift (4-7.5 meV) for Bi(111) [6]. hole pocket. Since bulk bands have a three-fold sym-
Figure 3 shows the result of numerical analysis on the metry, considerableoverlappingbetween the surface and
electron band near E indicated by a white rectangle in bulk bands would give rise to the observedthree-fold in-
F
Fig. 2(a). AsseenintheinsettoFig. 3(a),thedispersion tensity variation for the six hole pockets in Sb(111). We
shows a weak kink at about 10 meV. The estimated real also find that the electron pocket is bigger in Sb. Es-
and imaginaryparts of self-energy,ReΣ(ω) and ImΣ(ω), timated k points in Sb are 0.065 ˚A−1 and 0.071 ˚A−1
F
are plotted in Fig. 3(a). ReΣ(ω) was obtained by as- for Γ-K and Γ-M directions, respectively, while those of
suming a parabolic bare band dispersion, and ImΣ(ω) Bi are 0.053 ˚A−1 and 0.061 ˚A−1 [4]. The correspond-
was derived from the width of momentum distribution ing electroncarriernumber is 8.7×1012 cm−2 for Sb and
curves (MDC) as in the previous work [16]. ReΣ(ω) 5.5×1012 cm−2 for Bi. The difference in the volume is
shows a maximum around 10 meV which corresponds to directlyconnectedtothebandwidthinanoccupiedside;
the sudden velocity change in the dispersion, and grad- bottom of the band at the Γ point is 0.22 eV in Sb (Fig.
4
2(a)) while that of Bi is 0.03 - 0.07 eV [4, 8]. This leads unlike the overall six-fold symmetry in Bi may degrade
to a fairly light electron mass of 0.09 ± 0.01m0 in Sb, the CDW stability on the electron pocket by the scat-
which is 2.5 times smaller than that of Bi [4]. tering between the hole and electron FSs. We note here
The quantitative difference between Sb and Bi de- thatalthoughformationofthe surfaceCDWis quiteun-
scribedabovewouldbedirectlyrelatedtothestrengthof likely,the possibilityofsurfaceSDWisnotexcludeddue
SOC.Ingeneral,themagnitudeofSOCcanbeestimated to the spin-split nature of surface bands. To elucidate
bytheenergy/momentumseparationoftwosplitbands this point, further detailed ultrahigh-resolution ARPES
as applied in Au(111) [14, 15]. In the case of Sb, it is measurement combined with spin-resolved experiments
strongly anisotropic and k-dependent, so that extraction at various locations on FSs is highly desired.
of the accurate value is difficult. However, the momen- In conclusion, we demonstrated that the anisotropic
tum separationof two FSs along the high symmetry line spin-orbitinteractioncharacterizesthe surfaceelectronic
can be a good measure of it [8]. In this context, the nar- structure of Sb. The electron-phonon and the spin-orbit
rower separation along the Γ-M direction of the electron coupling are found to be the essential factors in under-
and hole pockets in Sb (0.056 ˚A−1) compared to that in standing the anomalous physical properties of Bi- and
Bi (0.136 ˚A−1) [4] would be a fingerprint of the weaker Sb-surfaces. Those couplings are remarkably weak in
SOC in Sb. This is supported by the experimental fact Sb(111) as compared to those of Bi(111). These experi-
thatthebottomofbandsatΓpointislocatedatahigher mentalresultstogetherwiththesmallereffectivemassof
binding energy in Sb than in Bi, which essentially tracks quasiparticle band in Sb(111) consistently explain why
the trend of the reduced SOC in the band calculation of the CDW or SDW energy gap and the granular super-
surface layers [8]. It is noted that the relatively weak conductivity are absent in Sb in contrast to Bi.
SOC in Sb is reasonable since the atomic SOC in Sb is This work is supported by grants from MEXT and
2.5 times smaller than that of Bi [11, 12]. CREST-JST of Japan. S.S. thanks JSPS for financial
Next we discuss the consequence of e-p coupling. The support.
weak e-p coupling in Sb(111) is naturally explained by
the much lighter atomic mass of Sb (51) than Bi (83).
This would lead to a larger ω , as a result a smaller λ.
D
Inaddition,theestimatedpartialDOSatE fortheelec-
F
tron pocket [19] in Sb(111) is 2 to 5.5 times as small as [1] B. Weitzel and H. Micklitz, Phys. Rev. Lett. 66, 385
thatofBi(111),sothatitwouldalsoreduceλ. We think (1991).
[2] C. A.Hoffman et al.,Phys. Rev.B 48, 11431 (1993).
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exp (-1/λ) [18], is T = 1 K in Sb, which is significantly [5] C.R.AstandH.H¨ochst,Phys.Rev.B66,125103(2002).
c
smallerthanthatdeterminedinBi(8K)[5],implyingthe [6] C. R. Ast and H. H¨ochst, Phys. Rev. Lett. 90, 016403
(2003).
considerable difference in the superconducting behavior
[7] J. E. Gayone et al.,Phys. Rev.Lett. 91, 127601 (2003).
of granular system. [8] Yu. M. Koroteev et al., Phys. Rev. Lett. 93, 046403
We think that occurrence of CDW in Sb(111) is quite
(2004).
unlikely,becausewedidnotobserveanenergygapdown [9] X. Gonze et al., Phys.Rev.B 44, 11023 (1991).
to7KorasuperlatticespotintheLEEDpattern. Inad- [10] H. H¨ochst and C. R. Ast, J. Electron Spectrosc. Relat.
dition, the excitation process which connects two nested Phenom. 137, 441 (2004).
regionshas to involvea spin flip, since the surface bands [11] J. H.Xu et al., Phys.Rev.B 48, 17271 (1993).
[12] Y. Liu and R.E. Allen, Phys.Rev.B 52, 1566 (1995).
are spin-split with opposite spins for opposite k vectors.
[13] P. Blaha, K. Schwarz and J. Luitz: WIEN2k, (Tech.
Thisspin-flipprocessisalsounfavorabletotheCDWfor-
Univ.Wien, Vienna, 2001) ISBN 3-9501031-1-2.
mation. The small value of the nesting vector Q = 0.13
[14] S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev.
˚A−1, corresponding to the long-range real-space period- Lett. 77, 3419 (1996).
icity of about 25 ˚A, may not be a goodcondition for the [15] G. Nicolay et al.,Phys. Rev.B 65, 033407 (2001).
CDW formation. Then, a question arises in why the en- [16] T. Valla et al., Phys.Rev.Lett. 83, 2085 (1999).
ergy gap is seen in Bi(111) [6] but not in Sb(111). The [17] C.Kittel,IntroductiontoSolidStatePhysics(JohnWiley
& Sons, Inc.,New York).
weakere-pcouplinginSbcomparedwiththatofBi[5,7]
[18] G. Grimvall, in The electron-phonon interaction in Met-
would remarkably reduce the CDW transition tempera-
als,edt.E.Wohlfarth(North-Holland,NewYork,1981).
ture (TCDW). In addition, the lower partial DOS at EF [19] DOS was calculated by assuming a free electron band
of the electron pocket [19] in Sb than that of Bi is also withhexagonalenergycontours.kF valueandtheenergy
unfavorabletothehighTCDW. Thethree-foldsymmetry bottom of the band reported previously [4, 8] were used
of six elongated hole pockets in Sb as seen in Fig. 1(a) as input parameters.