Experimental evidence for two-dimensional states
localized in subsurface region of Ge(111)
Koichiro Yajia,b,∗ , Yoshiyuki Ohtsubob,c , Shinichiro Hattad,b , Hiroshi
Okuyamad , Ryu Yukawaa , Iwao Matsudaa , Patrick Le Fèvrec , François
Bertranc , Amina Taleb-Ibrahimic , Akito Kakizakia , Tetsuya Arugab,d,∗∗aInstitute for Solid State Physics, The University of Tokyo, Kashiwashi, Chiba 277-8581,
Japan.
b
JST CREST, Saitama, 332-0012, Japan.
cSynchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin-BP 48, F-91192 Gif sur
Yvette, FrancedDepartment of Chemistry, Graduate School of Science, Kyoto University, Kyoto
606-8502, Japan

Abstract
The present study gives experimental evidence of two-dimensional electronic states localized in subsurface layers of a Ge(111) substrate, in whicha monolayer Pb adsorbed Ge(111) surface is used as a template. We observed three pairs of the subsurface states by angle-resolved photoelectron
spectroscopy, which are closely related to bulk heavy-hole, light-hole andspin-orbit split-off bands of Ge(111). The heavy-hole- and light-hole-derived
bands show the Rashba-type band crossing at the Γ̄ point. A density functional theory calculation suggests that the branches of these bands exhibit
the Rashba-type spin splitting. On the other hand, we observed peculiar spinpolarization for the subsurface states attributed to the bulk spin-orbit split∗

Corresponding authors
Corresponding authors
Email addresses: yaji@issp.u-tokyo.ac.jp (Koichiro Yaji ),aruga@kuchem.kyoto-u.ac.jp (Tetsuya Aruga)∗∗

Preprint submitted to Journal of Electron Spectroscopy and Related PhenomenaJune 27, 2014

off band by spin- and angle-resolved photoelectron spectroscopy, where spinpolarization of each branch is inverted with respect to Γ̄ and the degeneracy,
expected for a normal Rashba spin-split surface state is lifted at Γ̄.
Key words: Rashba effect, Semiconductor, Surface state, Angle-resolved
photoelectron spectroscopy, Spin-resolved photoelectron spectroscopy
PACS: 73.20.Fz, 71.70.Ej, 79.60.?i
1. Introduction
One of the steps in developing spintronic applications is to yield a spinpolarized electron in a semiconductor. For this aim, the Rashba-type spinorbit interaction has a great potential. The inversion symmetry is broken at
the surface or interface. According to the framework of the Rashba effect,
the spin degeneracy is then lifted by the potential gradient in the surface
normal direction and an electronic state is split into two in the momentum
space, where the spin orientation is perpendicular to both the surface normal and the momentum of the electron [1, 2]. Solid surface systems havebeen offering an opportunity to study the Rashba effect by angle-resolved
photoelectron spectroscopy (ARPES) and spin- and angle-resolved photoelectron spectroscopy (SARPES) so far. Here, we notice that the Rashba
spin-polarized bands were mainly reported on the surfaces including heavy
element atoms, such as Au [3, 4], Bi [5], and a monolayer of heavy-element
atoms adsorbed on light-element substrate [6, 7, 8, 9, 10].
On the other hand, recently, a new type of spin-polarized surface states
derived from Ge, a lighter element, was found on Bi/Ge(111), Br/Ge(111),
Tl/Ge(111) and Pb/Ge(111), in which the surface states disperse near the2valence band maximum (VBM) of Ge bulk bands [11, 12, 13, 14, 15]. An
insight into the spin-polarized two-dimensional states has been provided bya density functional theory (DFT) calculation [13]. Layer-resolved charge
density analysis suggests that maximum of the charge density is located between the fifth and tenth Ge layers and the charge density gradually decays
into the bulk. The spin-polarized states may therefore be classified as “subsurface states”. The formation of the subsurface states is explained with thebulk electronic states modified by the truncation of a bulk periodicity at thesurface, suggesting that the subsurface states originate from bulk heavy-hole,
light-hole, and spin-orbit split-off bands of Ge. The spin polarization of thesubsurface states is due to the Rashba effect and the size of the spin-split
energy is determined by the atomic spin-orbit interaction in a Ge atom. On
the other hand, experimentally, details of the energy dispersion of the subsurface states remain unclear. For instance, it is difficult to identify the energy
dispersion of light-hole-derived states as well as the spin splitting of heavyhole-derived states [11, 12]. We consider that low photoelectron intensities
from the subsurface states and the presence of the Ge bulk bands hinder
the clear identification of the band structures of the subsurface states near
VBM. In addition, the charge density analysis suggests that the subsurface
states have a charge-density modulation along the surface normal while thesubsurface states are intrinsic two-dimensional states. Such modulation may
yield a pseudo-dispersion of the subsurface-state bands along a kz direction.
Photon energy dependence of ARPES are thus required for clarifying theenergy dispersion along the kz direction.
In the present study, we experimentally clarify the electronic band struc-3

ture of the subsurface states near VBM of the Ge(111) substrate covered
with a monolayer Pb (Pb/Ge(111)-β). High-resolution ARPES with a He
lamp provides the detail of the energy dispersion of the subsurface states.
In an ARPES experiment with synchrotron radiation, several photon energies were selected in order to examine whether or not the subsurface states
exhibit the energy dispersion along the kz direction. The result gives direct evidence that the subsurface states are surely two-dimensional. FromSARPES, we confirmed that one of the subsurface states shows peculiar spin
structure, which is against the conventional picture of the Rashba-type bandcrossing. The DFT calculation supports the assignment of the experimental
band structure. The present results provide experimentally significant andconclusive information on the subsurface states on Ge(111) induced by thebulk truncation.
2. Experimental methods
Experiments were performed in ultrahigh-vacuum systems with base pressures lower than 2.0×10−8 Pa. In the ARPES experiment with monochromatic He I (hν = 21.2 eV) radiation, we used an angular mode of a hemispherical electron energy analyzer (VG SCIENTA R3000) in Kyoto University. The ARPES measurements with synchrotron radiation were performed
with a VG SCIENTA R4000 analyzer at CASSIOPÉE beam line in SOLEIL
in France. The SARPES measurements were performed at the beam line
19A of Photon Factory in Japan, using synchrotron radiation and the set ofa hemispherical electron energy analyzer (SPECS Phoibos 150) and a very
low energy electron diffraction (VLEED) type spin polarimeter [16] with an4

energy resolution of 160 meV. The effective Sherman function of the spinpolarimeter was 0.35.
For all of the experiments, samples were prepared in situ in a molecular beam epitaxy chamber connected to each analysis chamber. A Ge(111)substrate was prepared by several cycles of 0.7 keV Ar+ sputtering at room
temperature (RT) and subsequent annealing up to 870 K for a few seconds.
The surface cleanliness was checked by a sharp c(2×8) low-energy electron
diffraction (LEED) pattern. Pb was then deposited onto the surface kept
at RT from an alumina crucible heated with a tungsten filament. The surface after the Pb deposition was annealed at 570 K for a few minutes toprepare well-ordered wide terraces. Total amount of Pb atoms on the surface was calibrated by checking a photoelectron intensity from a Pb-derived
surface-state band, labeled SPb in Fig. 1(a), of Pb/Ge(111)-β [10, 17]. Notethat the photoelectron intensity from SPb is prominent in the second surface
Brillouin zone (SBZ). The reconstructed surface of Pb/Ge(111)-β yielded a√ √sharp ( 3× 3)R30◦ LEED pattern.
Density-functional theory (DFT) calculation has been performed using
the WIEN2k computer code based on the augmented plane wave + local
orbitals (APW + lo) method including the spin-orbit interaction [18]. We
adopted the modified Becke and Johnson (mBJ) potential together with theexchange-correlation potential constructed by using the local density approximation [19, 20]. The surface was modeled by a 44-layer Ge(111) slab with√ √the both sides covered with a ( 3× 3)R30◦ -Pb layer. We note that the
thick slab is required to reproduce the subsurface states because of the long
decay length into the bulk.

53. Results and discussion√ √Figure 1(a) shows an ARPES intensity map along Γ̄M̄ in the ( 3× 3)R30◦
SBZ, which coincides with a [11̄0] axis of Ge(111)-(1×1), measured with photon energy of 21.2 eV from the He lamp. The dashed curves represent theupper edge of the bulk bands obtained from tight-binding calculation withparameters adjusted to the experimental bulk band structure [13]. The bulk
bands consist of heavy-hole band, light-hole band, and spin-orbit split-offband at Γ̄. Here, energy positions of the light-hole and spin-orbit split-off
bands interconvert away from Γ̄ because of the hybridization between thesebands. In the present article, the bulk bands are named BHH , BLH and BSO
as shown in Fig. 1(a), respectively.
As shown in Fig. 1(a), we observed a pair of metallic bands with the
Fermi wave vector of 0.38 Å−1 , labeled SPb . This pair of bands is spinpolarized due to the Rashba effect, which have already been reported in ourpapers [10, 17]. A nearly flat band observed at ∼0.9 eV is also attributed toa Pb-derived band [10, 17]. On the other hand, several bands are found near
VBM and disperse downward from Γ̄. Hereafter, we focus on these bands.
Figure 1(b) exhibits an ARPES intensity map recorded with photon en√ √ergy of 21.2 eV with high energy resolution along Γ̄M̄ in the ( 3× 3)R30◦
SBZ near VBM at 30 K. A momentum distribution curve (MDC) at thebinding energy of 20 meV is also represented in the lower panel in Fig. 1(b).
Schematic drawing of the band structure is represented in Fig. 1(c). We
found from Fig. 1(a) that S1± appears in the projected bulk band gap anddisperses almost parallel to BHH at larger kk (> 0.15 Å−1 ). In addition, S1±
crosses the Fermi level near Γ̄. From the high-resolution image and the MDC
6

k|| (Å-1)

0.0

0.5

S1-+
BSO

BLH

0.5

-0.1

0.0

0.1

0.0

SPb

BHH

1.0

1.5

(c)

k|| (Å-1)

0.0

S2-

0.2

0.4

M

S1 +

S3-

S3-

0.1

Figure 1: (Color online) ARPES intensity map of Pb/Ge(111)-β along Γ̄M̄ in the√ √( 3× 3)R30◦ SBZ with the photon energy of 21.2 eV. The SBZ are shown in the inset,√ √where the dashed (thin) and solid (bold) hexagons denote the (1×1) and ( 3× 3)R30◦
periodicity, respectively. Dashed curves represent the bulk band edges, i.e. bulk heavy-hole(BHH ), light-hole (BLH ), and spin-orbit split-off (BSO ) bands. (b) (upper panel) ARPES
image recorded with the photon energy of hν = 21.2 eV with high-energy-resolution near
VBM. Dashed curves represent the bulk band edges, BHH , BLH and BSO . (lower panel)
A momentum distribution curve taken with the photoelectron intensity within a 20 meVenergy window centered at the binding energy of 20 meV, shown by a bold dashed linein the upper panel. (c) Schematic drawing of the surface-state bands of S1± , S2± and S3± .
Red and blue curves represent the spin direction toward [112̄] and [1̄1̄2].

7

S2-

S3+

+

0.0
k|| (Å-1)

S1+

S3 +

S2- and S3+

-0.1

S1-

S2+

+
S2- S1 S 1

S1- S +
2

0.1

+

S2

2.0

[110]

-0.1
S1-

Γ M

Γ

k|| (Å-1)

S1+

Intensity

Binding energy (eV)

0.0

(b)

Binding energy (eV)(a)

shown in Fig. 1(b), we can recognize that S1± is split into two, labeled S1+ andS1− for each branch. The Fermi wave vectors kF of S1+ (S1− ) are estimated tobe 0.082 Å−1 (0.100 Å−1 ) on a positive kk and at -0.100 Å−1 (-0.082 Å−1 ) ona negative kk . Also, we found a pair of bands, labeled S2+ and S2− , dispersing
along BLH . The maxima of S2+ and S2− reach the Fermi level and are symmetrically shifted from Γ̄ by 0.03 – 0.04 Å−1 . S2+ and S2− are degenerated at Γ̄ atbinding energy of 30 meV. This implies that a pair of S2+ and S2− shows the
Rashba-type band crossing. For the S3+ band, the energy maximum is quite
close to the crossing point of S2+ and S2− . And then, S3+ shows the energy
dispersion downward from Γ̄ into the bulk spin-orbit gap. S3− disperses along
the upper edge of BSO and almost parallel to S3+ at |kk | > 0.06 Å−1 .
√ √Figures 2(a)-2(d) show ARPES intensity maps along Γ̄M̄ in the ( 3× 3)R30◦
SBZ with synchrotron radiation. Here, we selected the several photon energies in order to confirm the energy dispersion along the kz direction withthe z axis defined as perpendicular to the surface. We note that the ARPES
image obtained with hν = 21 eV shown in Fig. 2(c) agrees well with theimage recorded with the He lamp shown in Fig. 1(a). S1± is observed withphoton energies of 17, 21, and 26 eV. In addition, there is no energy shift
for S1± depending on the photon energy, meaning that S1± exhibits no energy
dispersion along the kz direction. This serves an evidence that S1± is a twodimensional state. S2+ and S2− are observed with photon energies of 17, 19
and 21 eV and the energy positions of the bands do not change. Thus, S2+
and S2− are also assigned as two-dimensional states. S3+ and S3− appear in
all images in Fig. 2. The energy dispersions of S3+ and S3− are completely
identical, indicating that S3+ and S3− are also two-dimensional states.

8

(a)
-0.4

Binding energy (eV)

0.0

0.4

(b)

k|| (Å-1)
0.0
+
2

S

S1

k|| (Å-1)
0.0

0.4 -0.4S2+hν = 17 eV

0.4hν = 19 eV

S2-

S2S3+

S3+

S3-

S3-

0.8

(c)

Binding energy (eV)

0.0

0.4

(d)
S2+

S1

hν = 21 eVhν = 26 eV

S1

S2S3+

S3+

S3-

S3-

0.8

[110]
l1 l2 l3 l4 l5Figure 2: (Color online) (a-d) ARPES images of Pb/Ge(111)-β along Γ̄M̄ in the√ √( 3× 3)R30◦ SBZ recorded with the photon energies of hν = 17 eV, 19 eV, 21eV, 26
eV. Solid curves represent the band structures for guides to the eyes.

9l1Intensity (arb. units)

l2
l3
l4
l5

0.8
0.4
0.0
Binding energy (eV)Figure 3: (Color online) (a) Spin- and angle-resolved photoelectron spectra taken withseveral selected wave vectors, which are shown with thin solid (green) lines in Fig. 2(d).
Here, l1 –l5 correspond to emission angles of -1.3◦ , 0.8◦ , 0.0◦ , 0.7◦ and 1.2◦ with respect tothe surface normal, respectively. The spin polarization toward [112̄] and [1̄1̄2] directions isrepresented with thin (red) and bold (blue), respectively. Triangles denote energy positionsof S3+ obtained from the ARPES data shown in Fig. 2(d).

10Next, we describe the results of SARPES shown in Fig. 3. In SARPES,
we focus on the spin polarization of S3+ because the branches of S3+ and S3− arequite different from the conventional Rashba-type band structure, as thesebands do not show the band crossing at Γ̄. The spin-resolved photoelectron
spectra were recorded with the photon energy of 26 eV at several selected
kk ’s, denoted as l1 –l5 in Fig. 2(d). Here, we have found from the photon
energy dependence of ARPES shown in Fig. 2 that S3+ is clearly observedwith hν = 26 eV whereas the photoelectron intensity from S2± is rather weak.
Thus, use of the photon energy of 26 eV allows us to predominantly observe
the spin-resolved spectra from S3+ although S3+ is energetically close to S2±near Γ̄. The spin polarimeter was arranged to observe the spin polarization
toward [112̄] and [1̄1̄2].
It is found that the spin-resolved spectra along l3 are almost identical.
This indicates that the spin polarization of S3+ is zero at Γ̄. On the other
hand, the spin-polarized spectra are observed at l1 , l2 , l4 and l5 . For the
spin-resolved spectra at l1 and l2 , the spin polarization toward [1̄1̄2] is foundand the spin polarization toward [112̄] is negligible. Here, the peaks for l1 andl2 are located at 0.3 eV and 0.2 eV, respectively. The spin-resolved spectra
at l4 and l5 exhibit the spin polarization toward [112̄]. The peak position ofl4 (l5 ) is almost same as l2 (l1 ). The energy dispersion of the spin-resolved
spectra agrees well with the ARPES results, where the energy positions of
S3+ obtained from Fig. 2(d) are represented in Fig. 3. We therefore conclude
that S3+ shows no spin polarization at Γ̄ and the spin polarization direction
is inverted in the band around Γ̄. We note that S1± are not clear at l1 andl5 in the SARPES measurements because the photoelectron intensities from

11

(a)

(b)
+
S1C

S2C

+
S2C

0.0
Binding energy (eV)

S1C

+
S3C

0.4

S3C

0.8

M
2

M
2

Γ

M
2

Γ

M
2

Figure 4: (Color online) Calculated band structure of Pb/Ge(111)-β along Γ̄M̄ near VBM.
Opposite spin orientations are indicated by colors of blue and red (colors, online). In panel(a), the size of the circle is proportional to the net spin polarization (Rk−k ,E defined by
Eq. (1)). In panel (b), the size of the circle represents the total contribution of Ge atoms
in 1st-6th layers (Rk+k ,E defined by Eq. (1)). The bold dashed curves represent the bulk
band edges of heavy-hole, light-hole, and spin-orbit split-off bands [13]. Thin solid curves
represent the band structure of the subsurface states.

S1± are weak.
We performed a DFT calculation in order to obtain further informationon the spin structure of the subsurface states of Pb/Ge(111)-β. Figures 4(a)and (b) show the calculated band structures for Pb/Ge(111)-β along Γ̄M̄ in√ √the ( 3× 3)R30◦ . The sizes of the circles are given by
Rk±k ,E ∝nXi=0(|hφi , ↑ |Ψkk ,E i|2 ± |hφi , ↓ |Ψkk ,E i|2 ) ,12(1)where |φi , ↑i and |φi , ↓i denote atomic orbitals in ith layers with spin polarization, and |Ψkk ,E i is an eigenfunction of a calculated state at (kk , E).
The summation of the atomic orbitals from 1st to 6th layers was carried out.
The zeroth layer corresponds to the Pb layer at the surface and the 1st layer
corresponds to the topmost layer of the Ge substrate. Thus, Rk−k ,E expresses
the net spin polarization of the Ge atoms. The calculated band structurewith Rk−k ,E is represented in Fig. 4(a), in which the size of the circle represents the amplitude of the spin polarization and colors of the circles givethe spin directions. We notice that small spin polarization makes difficulty
in clear identification of the band structure, especially in the proximity toΓ̄. In order to make clear the band structure, we also provide another panel
drawn with Rk+k ,E in Fig. 4(b). Rk+k ,E represents the total contribution fromthe Ge atoms in the surface and subsurface layers. This indicates that thesize of the circle is proportional to the partial charge of the Ge atoms. We
note that Pb 6p orbitals have a negligible contribution near VBM [10, 17].
+−
S1C
and S1C
exhibit the energy dispersion along the edge of the bulk

heavy-hole states in the projected bulk band gap and cross the Fermi level.
+−
The band structure of S1C
and S1C
below the Fermi level is in agreement with

the ARPES result shown in Fig. 1(b). Also, the calculated band structure±suggests that a pair of S1C
shows the spin splitting around Γ̄, in particular

the spin polarization is prominent near the Fermi level. The spin polarization
direction of one branch is opposite to another branch. On the other hand,±the branches of S1C
are degenerated at Γ̄ above the Fermi level and the±spin polarization is zero at Γ̄. Thus, the spin splitting of S1C
is due to the±
Rashba effect. The amplitude of the spin splitting for S1C
is 27 meV at the13

±Fermi wave vector. Note that the spin splitting of S1C
was not detected by

SARPES because the size of the spin splitting is rather small compared withthe energy resolution of SARPES.
+−The energy dispersions of S2C
and S2C
are also in agreement with ARPES.
±The branches of S2C
are degenerate at Γ̄ near the Fermi level and are spin-polarized around Γ̄ toward opposite directions. This behavior agrees with±
the Rashba-type spin splitting. The spin polarization of S2C
is moderate in±
the projected bulk band gap compared with S1C. The spin polarization is±
however weakened at |kk | > 0.1 Å−1 because the branches of S2C
merge into

the Ge bulk bands.
+−
S3C
and S3C
also appear in the calculated band images, which is consistent+
with the ARPES results. The energy maximum of S3C
nearly reaches to the±+crossing point of S2C
at Γ̄ and S3C
shows the energy dispersion downward+
from Γ̄. The spin polarization of S3C
is negligible at Γ̄ while it is enhanced

around Γ̄. The spin polarization direction is inverted with respect to Γ̄.
−Concerning S3C, the energy maximum is located at Γ̄ at the binding energyof 250 meV and the band disperses downward from Γ̄. The spin polarization−+of S3Cis inverted with respect to Γ̄ and is opposite to that of S3C. However,−
the amplitude of the spin polarization of S3C
is much smaller than that of+−
S3C. We notice that S3C
disperses along the edge of the bulk spin-orbit split-

off band, meaning that the electrons in the S3− band can merge into the bulk−
bands. This reduces the spin polarization of S3C, which is consistent with thefact that the spin polarization of S3− was not clearly observed by SARPES.
We have experimentally clarified the band structures of the subsurface
states of Pb/Ge(111)-β. We consider that a scenario of the formation of14

the subsurface states is common with the other systems such as Bi/Ge(111),
Br/Ge(111), Tl/Ge(111) [11, 12, 13]. The subsurface states are yielded fromthe bulk electronic states perturbed by the truncation of bulk periodicity
at the surface. In principle, the subsurface states of Pb/Ge(111)-β are thus
attributed to the BHH , BLH and BSO bands. The energy position of eachsubsurface state depends on a type of the bulk truncation, meaning thatthe energy of the subsurface states can be modified by ad-layers. In fact,
the light-hole-derived S2± bands of Pb/Ge(111)-β appear in the projectedbulk band gap near Γ̄ while the light-hole-derived bands for Bi/Ge(111) and
Br/Ge(111) were found in the bulk bands, for example.
From the ARPES results, we found that the spin splitting of S1± is 30
meV at kF = 0.1 Å−1 . The Rashba parameter of S1± is thus estimated tobe 0.15 eV Å. On the other hand, it is difficult to accurately estimate the
Rashba parameter for the pair of S2± only from the ARPES results because
the topmost part of the branches is above the Fermi level and the large
intensity from S3+ hinders us locating the peak positions of S2± around Γ̄.
±We thus evaluate the Rashba parameter of S2C
from the calculated band±
structure shown in Fig. 4. The energy maxima of S2C
are located at |kk | =±±0.04 Å−1 . The size of the spin splitting of S2C
is then estimated to be 0.034

eV at 0.04 Å−1 , which yields the Rashba parameter of about 0.4 eV Å. The
sizes of the spin splitting of S1± and S2± are consistent with that of the atomic
spin-orbit splitting of Ge 4p [21].

Finally, we describe the peculiar band S3± , which is quite different fromthe conventional Rashba-type band crossing. The energetic order between
the bulk light-hole and spin-orbit split-off bands is inverted around Γ̄ because15

of the spin-orbit interaction of Ge, which makes a finite spin-orbit energy gap.
One spin-polarized branch S3+ disperses across the spin-orbit gap. This manner is similar to the case of the spin-polarized surface states on topologicalinsulators (TI). TI has a bulk band gap which opens due to the spin-orbit
interaction and the topological surface states disperse continuously acrossthe bulk spin-orbit gap. In addition, S3± are surface resonances. The surface
resonances can switch its partner to an arbitrary band at high-symmetry
point because of the large contribution from the bulk states. Thanks to this,Kramars degeneracy of S3± at Γ̄ is preserved even without the Rashba-type
band crossing. This situation yields the spin-polarized S3+ and its counterpart S3− . Similar band structures are also found in Bi/Ge(111), Br/Ge(111),
Tl/Ge(111). The formation mechanism of S3± has been discussed in the former paper in detail [13].
4. Summary
In summary, we have investigated the two-dimensional states localized insubsurface regions of Pb/Ge(111)-β near VBM by ARPES, SARPES and the
DFT calculation. From the high-resolution ARPES, the energy dispersionsof the subsurface states were experimentally identified. Photon energy dependence of ARPES using synchrotron radiation clarified that the subsurface
states exhibit two-dimensional nature. The spin polarization of the subsurface states was confirmed by SARPES and the DFT calculation. The spinpolarization of S1± and S2± is explained by the conventional Rashba effectwhile S3± exhibit peculiar spin-polarized band structures.

16

5. Acknowledgments
The authors thank J. Pinon, D. Ragonnet, and M. D′ Angelo for their support during the experiments at the CASSIOPÉE beam line in synchrotron
SOLEIL. The present work was financially supported by Bilateral Joint Research Project between Japan (JSPS) and France (CNRS) and the JSPS
Grant-in-Aid for Young Scientists (B), Grant No. 24740197.
References[1] E. I. Rashba, Sov. Phys. Solid State 2 (1960) 1109.
[2] Y. A. Bychkov and E. I. Rashba, JETP Lett. 39 (1984) 78.
[3] S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev. Lett. 77 (1996)
3419.
[4] M. Hoesch, M. Muntwiler, V. N. Petrov, M. Hengsberger, L. Patthey, M.
Shi, M. Falub, T. Greber, and J. Osterwalder, Phys. Rev. B 69 (2004)
241401(R).
[5] Yu. M. Koroteev, G. Bihlmayer, J. E. Gayone, E.V. Chulkov, S. Blügel,
P.M. Echenique, and Ph. Hofmann Phys. Rev. Lett. 93 (2004) 046403.
[6] T. Nakagawa, O. Ohgami, Y. Saito, H. Okuyama, M. Nishijima, and T.
Aruga, Phys. Rev. B 75 (2007) 155409.
[7] C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D. Pacilé, P.
Bruno, K. Kern, and M. Grioni, Phys. Rev. Lett. 98 (2007) 186807.

17[8] I. Gierz, T. Suzuki, E. Frantzeskakis, S. Pons, S. Ostanin, A. Ernst, J.
Henk, M. Grioni, K. Kern, and C. R. Ast, Phys. Rev. Lett. 103 (2009)046803.
[9] S. Hatta, T. Aruga, Y. Ohtsubo, and H. Okuyama, Phys. Rev. B 80
(2009) 113309.
[10] K. Yaji, Y. Ohtsubo, S. Hatta, H. Okuyama, K. Miyamoto, T. Okuda, A.
Kimura, H. Namatame, M. Taniguchi, and T. Aruga, Nature Commun.
1 (2010) 17.
[11] Y. Ohtsubo, S. Hatta, K. Yaji, H. Okuyama, K. Miyamoto, T. Okuda,
A. Kimura, H. Namatame, M. Taniguchi, and T. Aruga, Phys. Rev. B
82 (2010) 201307(R).
[12] Y. Ohtsubo, S. Hatta, N. Kawai, A. Mori, Y. Takeichi, K. Yaji, H.
Okuyama, and T. Aruga, Phys. Rev. B 86 (2012) 165325.
[13] Y. Ohtsubo, K. Yaji, S. Hatta, H. Okuyama, and T. Aruga, Phys. Rev.
B 88 (2013) 245310.
[14] S.-J. Tang, T.-R. Chang, C.-C. Huang, C.-Y. Lee, C.-M. Cheng, K.-D.
Tsuei, H.-T. Jeng, and C.-Y. Mou, Phys. Rev. B 81 (2010) 245406.
[15] C.-H. Lin, T.-R. Chang, R.-Y. Liu, C.-M. Cheng, K.-D. Tsuei, H.-T.
Jeng, C.-Y. Mou, I. Matsuda, and S.-J. Tang, New J. Phys. 16 (2014)
045003.
[16] T. Okuda, Y. Takeichi, Y. Maeda, A. Harasawa, I. Matsuda, T. Kinoshita, and A. Kakizaki, Rev. Sci. Instrum. 79 (2008) 123117.
18

[17] K. Yaji, S. Hatta, T. Aruga, and H. Okuyama, Phys. Rev. B 86 (2012)
235317.
[18] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k:
An Augmented PlaneWave + Local Orbitals Program for Calculating
Crystal Properties (Karlheinz Schwarz, Techn. Universitt Wien, Wien,
2001).
[19] A. D. Becke and E. R. Johnson, J. Chem. Phys. 124 (2006) 221101.
[20] F. Tran and P. Blaha, Phys. Rev. Lett. 102 (2009) 226401.
[21] S. Kotochigova, Z. H. Levine, E. L. Shirley, M. D. Stiles, and C. W.
Clark, Phys. Rev. A 55 (1997) 191.

19