Diﬀerent types of Rashba spin-split surface states on Ge(111)
Tetsuya Aruga
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

Abstract
In this review article, after a brief account of the early history of the study of the surface Rashba eﬀect is given, a survey
is made on an exploration of the Rashba spin-split surface states on a Ge(111) surface. First, the studies on Pb/Ge(111)is shown, which was the first surface with Rashba spin-split metallic surface state on a semiconductor established byexperiments and first-principles calculation. Second example is Tl/Ge(111), which exhibits valley-like conduction band
minimum at the K̄ points in the surface Brilouin zone. Due to the symmetry of this surface, spins at the bottom of thevalleys are completely polarized parallel to the surface normal. In these two cases, the spin splitting is due to the strong
spin-orbit interaction (SOI) in the close proximity to the heavy nuclei at the surfaces. On the other hand, the third
example demonstrates that a significant Rashba spin splitting is possible also by SOI at the nuclei of the subsurface Ge
atoms. This type of spin-split surface states are believed to be ubiquitous on any types of Ge surfaces as well as at theinterfaces between Ge and other materials. A personal view of coming developments in this field is given.
Keywords: Rashba eﬀect, spin orbit interaction, ARPES, SARPES

1. Introduction
The Rashba eﬀect refers usually to a spin orbit interaction (SOI) for electrons moving in a two-dimensional(2D) plane with an electric field perpendicular to it, as described by the Rashba Hamiltonian [1, 2], HR = αR (⃗σ ×p⃗∥ ) · êz , where ⃗σ = (σx , σy , σz ) denotes the vector of thePauli spin matrices, p⃗ = (px , py , pz ) the momentum operator, êz the unit vector directed normal to the plane, andαR the Rashba parameter which describes the strengthof SOI. Experimentally the Rashba eﬀect was first observed in two-dimensional electron gas (2DEG) confinedat GaAs/AlGaAs heterojunctions [3, 4]. The ideas suchas that utilizing the Rashba eﬀect to control the spin precession of electrons in 2DEG by electric field [5] have been
proposed since then and driving the exploration of thesemiconductor-based spin electronics, or, semiconductor
spintronics [6].
For the ideal 2D electrons in an electric field perpendicular to the plane, Ez , the Rashba parameter αR =
ℏ2 Ez /(4m2e c2 ) amounts only to ∼ 10−3 meV Å−1 . However, typical magnitude of αR for semiconductors such as
GaAs and InSb is on the order of 100 meV Å−1 . This
clearly indicates that the magnitude of the Rashba SOI
is not quantitatively described by the ideal view of 2D
free electrons moving in electric field, but is goverened byatomic SOI of the constituent atoms of the material that
supports the 2D electrons [7, 8]. Since the Fermi wavevector for 2DEG is ∼10−2 Å−1 , the spin splitting at EF is a
few meV, which is much smaller than kB T at room temperature. Thus the spin-dependent phenomena in these
semiconductor heterojunctions can be observed only atvery low temperatures. Semiconductor quantum wells ofheavier elements such as HgTe/HgCdTe have Rashba spin
splittings up to 30 meV [9].
In 1996, the Γ̄ surface state on Au(111), which had
been known for a decade, was found to be split into two
branches [10]. The splitting at EF was as large as 110
meV, which was ascribed to Rashba SOI. This conclusion
was later confirmed by a higher resolution measurement[11], a calculation by full-potential linearized augmented
plane wave (LAPW) method [12] and spin- and angleresolved photoelectron spectroscopy (SARPES) [13]. The
work initiated the search for Rashba spin splitting at various surfaces, yielding works on Li/W and Li/Mo(110)[14], H/W(110) [15], the (111), (110) and (100) surfacesof Bi [16], and Gd(0001) [17]. Among them, the surfacesof Bi, which is the heaviest of non-radioactive elements,
exhibit spin splittings as large as 300 meV. This splitting
may be considered as very large as compared with thosein semiconductor heterojunctions. However, the atomic
spin-orbit splitting of Bi 6p is 2.0 eV, which suggests thatthe spin splitting on the order of 1 eV should be possible
also for conduction bands composed of Bi 6p.
In 2007, Bi monolayers on Ag(100) surface was foundto have a Bi 6p-derived surface resonance band, which exhibits Rashba-type splitting on the order of 1 eV [18]. The
magnitude of αR amounts to 3.6 eV Å−1 , which was anorder of magnitude larger than those at the surfaces of elemental Bi. This finding indicated that the magnitude of
the Rashba spin splitting depends on precise atomic structure of the interface, where the surface state wavefunction
is localized, and can be as large as the atomic spin-orbit

Preprint submitted to Journal of Electron Spectroscopy and Related Phenomena

December 25, 2014

splitting. Subsequently, a similar Bi-derived surface band
was found for Bi-Ag surface alloy monolayer on Ag(111)with a very similar αR value of 3.1 eV Å−1 [19]. It waslater∫ pointed out that the Rashba parameter approximetesto ρ(r)(∂V /∂z)dr, and therefore the asymmetric chargedensity distribution along the surface normal in the vicinity of the nuclei of surface heavy atoms is crucial because
the potential gradient ∂V /∂z is anti-symmetric with respect to the nuclei and is most prominent near the nuclei[8].
These findings suggested that the large Rashba SOI
could be realized on the surfaces of semiconductors suchas Si and Ge by covering them with a monolayer of heavy
elements, which would have significant implications toward
the semiconductor spintronics. The possibility was immediately examined for Tl-covered Ge(111) surfaces. Fullpotential LAPW method, which had been used in successfully reproducing Rashba spin-split surface state on
Au(111) [12], was applied to Ge(111)-(1 × 1)-Tl [20] [Fig.
1(c)] and Ge(111)-(3×1)-Tl surfaces [21], which showed
the large Rashba spin splitting of the Tl-derived surface
states on Ge(111) surface. Experimentally, it was shownin 2009 that the√Si(111)√ [22] and Ge(111) [23] surfaces
covered with a ( 3 × 3)R30◦ -Bi monolayer [Fig. 1(d)]have Rashba spin-split surface states at M̄ of the surface
Brillouin zone (SBZ). The dispersion and spin splittingof the surface state was again precisely reproduced by afull-potential LAPW calculation [23]. The correspondence
between the magnitude of the Rashba parameter and theasymmetry of the charge density distribution along thesurface normal in the closest proximity to the Bi nuclei
was also verified [23].
√√The surface state on Si, Ge(111)-( 3 × 3)R30◦ -Bi
surfaces is not metallic, because the surface Bi atoms forma trimer structure with saturated valence bonds on thesesurfaces as shown in Fig. 1(d) [24]. The surfaces, therefore, were not adequate for spin-transport experiment suchas intrinsic spin Hall eﬀect (SHE) [25, 26, 27]. However,the finding clearly indicated the possibility of Rashba spinsplit surface states on Si and Ge surfaces, which initiated the subsequent studies on the Rashba eﬀect in heavyelement-covered Si and Ge surfaces. While there have been
a number of quality works, let us concentrate in this review
on some topics related to the Ge(111) surface.
Before going into details of the surface electronic structure, let us show the atomic structures of some of theadsorbate-covered Ge(111) surfaces. Some of them arealso formed on Si(111). Clean surfaces of Si(111) andGe(111) reconstructs into complicated (7×7) and c(2 × 8)
strucutures. Figure 1(a) shows ideal (1×1) structure. The
high-symmetry adsorption sites T1 (atop), H3 , and T4 areshown. Figure 1(b) shows (1×1)-Br surface [28], in which
each dangling bond of the topmost Ge atom is terminatedby a 4p orbital of the Br adatom. On the (1×1)-Tl surface
shown in Fig. 1(c) [20], Tl adatoms occupy H3 sites. Since
the 6s2 electrons of Tl forms an inert pair, the half-filledsurface dangling bonds and the 6p1 electrons of Tl atoms

Figure 1: Top and side views of (a) ideal Si(111)- and Ge(111)-(1×1),(b) Si(111)- and Ge(111)-(1×1)-Br, and (c) Si(111)- and Ge(111)√(1×1)-Tlsurfaces. Top views√of (d)Si(111)- and Ge(111)-( 3 ×√√3)R30◦ -Bi and (e) Ge(111)-( 3 × 3)R30◦ -Pb surfaces. Rhombi
indicate the unit meshes. Dashed lines indicate mirror planes. The
structures shown in (a-c) belongs to p3m1, while those shown inpanels (d, e) belongs to p31m plane group. In panel (a), adsorption
sites T1 , T4 and H3 are shown.

form semi-metallic surface states, which will be discussed
in Section 3. The Si(111) and Ge(111)covered√ surfaces√
with 1 monolayer of Bi atoms form ( 3 × 3)R30◦ structure as shown in Fig. 1(d) [24]. While each Bi atom has
6p3 valence electrons, one of them are used to terminate
the dangling bonds and two others are used form covalent bonds with neighboring Bi atoms, thus forming Bi3
trimers . As a result, √the surface
states becomes insulat√
ing. On the Ge(111)-( 3 × 3)R30◦ -Pb surface, three Pb
atoms per unit cell terminates the surface dangling bonds
and a remaining Pb atom per unit cell occupies H3 sites[36]. It will be shown in Section 2 that this structure gives
rise to a nearly-free-electron surface state localised in the
Pb monolayer. In Fig. √1 are√also shown mirror planes onthese surfaces. In the ( 3 × 3)R30◦ structures shown in
Fig. 1(d,e), the mirror planes are parallel with the sidesof the unit mesh, while the mirror planes are not parallelwith the sides in the (1×1) structures shown in Fig. 1(ac). This has an interesting relevance to the spin splitting
on these surfaces, which will be discussed in Section 3.
2. Nearly-free-electron surface states on
Pb/Ge(111)In order to establish metallic surface state spin-splitby the Rashba eﬀect on semiconductor surfaces, the Si
and Ge(111) surfaces covered with heavy elements such as
2

a

b
1.0

0.0

Binding energy (eV)c

1.5Energy relative to valence band maximum (eV)

0.5

1.0

2.0

1.0

0.0

U1

U1

S1

S1

SGe

-1.0
S3

S2

S3

S2

-2.0
MM

M
M1

M

M2
Spin polarizationpx, pypz√√
Figure 2: Measured and computed energy-band structure of Ge(111)-β( 3 × 3)R30◦ -Pb. (Reproduced from Ref. [34].) (a) Experimental
energy-band dispersion measured by angle-resolved photoelectron spectroscopy (ARPES)√√ at 30 K. The dashed line indicates the upper edgeof the bulk bands of Ge. (b) Computed energy-band structure for the Ge(111)-β( 3 × 3)R30◦ -Pb surface. The radii of the blue (red) circles
are proportional to the net contribution of the Pb 6p with spin up (down). (c) Computed energy-band structure with relative contributionof Pb 6px py and 6pz shown by color scale. The sizes of the circles are proportional to the total contribution of Pb 6p.

79 Au, 81 Tl, 82 Pb and 83 Bi were considered as candidates.

band dispersion and the spin polarization quantitatively.
As already mentioned, Bi/Si(111) and Bi/Ge(111) at a
Moreover, the calculation revealed the orbital character ofcoverage of 1 have qualitatively the same atomic structhe surface states as shown in Fig. 2(c). The S1 band
ture and exhibit almost identical, semiconducting surface
is composed mostly of Pb 6px py and confined in the Pb
states. On the other hand, the structural phases of Pb/Ge(111)monolayer. The S2 band is essentially of a bonding charand Pb/Si(111) are diﬀerent. The Pb-covered Si(111) suracteer between the dangling bonds of the topmost Ge atoms
face was known to exhibit a variety of structural phases
and the Pb atoms near the atop (T1 ) sites. The unoccuwhich are often very complicated, in particular, at coverpied U1 band around Γ̄ corresponds to the 6pz orbital ofages near and higher than 1 [29, 30, 31, 32]. The electronic
the Pb atoms at H3 sites [36].
structure of some of the high-coverage phases were found
The Rashba spin-split metallic states on semiconducto be metallic, but the Fermi contours were complicatedtor surface is interesting with respect not only to the spin
[33].
transport phenomena such as SHE, but also to usual elecAt coverages higher
than
1,
the
Pb/Ge(111)
surfacetric conductance since the large Rashba spin splitting may√√
forms only the β( 3 × 3)R30◦ phase at a coverage ofalter the scattering process of conduction electrons. A re4/3 [Fig. 1e)]. The first experimental identification of thecent experiment indicated unusual electrical transport on
metallic surface state that is√spin√split by Rashba SOI wasthis surface [37], which probably is related to the large
achieved for the Ge(111)-β( 3 × 3)R30◦ -Pb surface [34].
Rashba spin splitting of the metallic surface state.
Figure 2 shows the measured andcomputedenergy√band structure of the Pb/Ge(111)-β 3 surface. The ex3. Uniaxially spin-polarized K̄ surface states on
perimental band suggests that a nearly-free-electron paraTl/Ge(111)bolic band is hybridized with a almost flat band (S2 ) toyield a upper (S1 ) and a lower (S3 ) branch. The S1 band
The Rashba spin-split states are always degenerated
was found to be split into two branches, which was studat Γ̄, which gives rise to the characteristic band crossing
ied by SARPES and was found to be spin-polarized toof the spin-split pair at Γ̄. Similar band crossing is also
the directions opposite to each other as expected fromobserved√ at M̄ of the hexagonal lattice such as Ge(111)√
the Rashba Hamiltonean [34]. The Rashba parameter was( 3 × 3)R30◦ -Bi [23], because√ of the√ time reversal symslightly energy dependent and was 0.35 eV Å at EF . The
metry of this point. For the ( 3 × 3)R30◦ surface, thespin splitting at EF amounted to 200 meV, which is an orband crossing is also observed at K̄ point whereas there is
der of magnitude larger than the thermal energy at roomno time reversal symmetry [38]. The crossing in this casetemperature.
is due√to the√ C3v point-group symmetry of the K̄ point for
The calculation, which was carried out by using fullthe ( 3 × 3)R30◦ structure that belongs to p31m planepotential LAPW code [35], reproduced the experimental
3

group [See Fig. 1(d)]. On the other hand, the (1 × 1)Tl structure belongs to p3m1 plane group [Fig. 1(c)], inwhich case the K̄ point has a C3 point-group symmetry.
In this case, the spin-split pair is not degenerated [39].
The Pauli spin-orbit interaction is decomposed into two
terms:⃗ × p⃗)
HSO ∝ ⃗σ · (∇V()∂V⃗ ∥ V × p⃗∥ σz ,=(px σy − py σx ) + ∇∂z⃗ ∥ = ⃗ex (∂/∂x)−where V denotes the Coulomb potential, ∇⃗ey (∂/∂y), and p⃗∥ = (px , py , 0). The first term corresponds
to the usual Rashba term, which describes the surface parallel spin polarization induced by surface normal potential
gradient. The second term describes the surface-normal
spin polarization due to the in-plane potential gradient.
At the K̄ points in the 2D Brillouin zone of the hexagonal lattice, the first term vanishes and only the second
term, which corresponds to the surface normal spin polarization, is expected. Therefore, the spin polarization along
the surface normal should be realized at the K̄ point on
the (1 × 1)-Tl surfaces.
The Tl-adsorbed Ge(111) surface exhibits one-dimensional (3×1) structure [21, 40] as well as isotropic (1×1)
structure [20]. For the (1×1)-Tl surface, the breakdown of
the degeneracy was first acknowledged in 2007 by a LAPW
calculation [20].
Experimentally, it was found that the adsorption of asmall amount of Tl on top of the ideal (1×1)-Tl surface results in doping of electrons to the surface electronic states,
and converts the Fermi surface from the hole pocket at Γ̄to the electron pockets at K̄ [41]. The ideal and Tl-doped
surfaces were denoted as α(1×1) and β(1×1), respectively.
Figure 3(a) shows the band structure of Ge(111)-α(1×1)Tl computed by the LAPW method. Two pairs of surface
states, A and B, are found. The surface state A forms ahole pocket around Γ̄, which was confirmed by ARPES experiment [41]. The A band disperses downward from Γ̄ toK̄. It has strong in-plane spin orientation, characteristic
to the normal Rashba spins, near the Γ̄ point, but changes
its spin orientation to the surface normal upon approacing
K̄. Note that the size of the circles in Fig. 3(a) is proportional to the contribution of Tl with spin oriented normal
to the surface. The unoccupied surface state B is foundaround K̄ and is spin polarized completely along the surface normal at K̄. The electron doping by addition of asmall amount of Tl causes the disappearance of the hole
pocket at Γ̄ and the concomitant appearance of electron
pockets at the K̄ points in the β(1 × 1) surface as shownin Fig. 3(b).
Fermi contour for the β(1×1)-Tl surface measured by
ARPES is shown in Fig. 4(a). Also, a schematic of the Bband in the α and β phases is shown in Fig. 4(b). The spinpolarization at a pair of opposite K̄ points with respect toΓ̄ is reversed. The overall spin texture is as shown in Fig.
4(b). The spin structure of the α(1 × 1) surface resembles

Figure 3: Measured and computed energy-band structure of Ge(111)(1 × 1)-Tl. (Reproduced from Ref. [41].) (a) Computed energy-bandstructure for the as-prepared Ge(111)-α(1×1)-Tl surface. The radiiof the red (blue) circles are proportional to the net contribution ofTl with spin oriented parallel (anti-parallel) to the surface normal.
(b) Experimental energy-band dispersion of the Tl-doped Ge(111)β(1×1)-Tl measured by ARPES.

Figure 4: (a) The Fermi contour around K̄ for the β(1 × 1) surface
measured by ARPES. (Reproduced from Ref. [41].) (b) Schematic
structure of the Bup and Bdn bands in the α and β phases.

4

it is clear that the heavy elements that cover the surface
are not essential to the spin polarization observed on thesesurfaces.
Figure 5 shows the ARPES data around Γ̄ for the
Bi/Ge(111), Br/Ge(111) and Tl/Ge(111) [44, 28, 45]. For
all the three cases, the band denoted S3 is running along
the bulk SO band edge at k∥ >0.05 Å−1 . The S3 band disperses into the bulk spin-orbit gap at k∥ <0.05 Å−1 , indicating that this is a surface state. Also the bands runningslightly below the HH band edge, denoted S2 , is found on
Bi/Ge(111) and Tl/Ge(111). The S1 band observed only
on Tl/Ge(111) is due to the weak hybridization between
Ge 3pz dangling bonds and the 6pz orbitals of Tl occupying the T4 sites. SARPES experiments reviealed thatthese surface states are spin polarized as indicated by red
and blue triangles. The spin polarization is reversed withrespect to Γ̄, suggesting that it is due to the Rashba SOI.
Figure 6 shows the band structure calculated by thefull-potential LAPW method [28, 45]. In the upper panels(a-c), the electronic states that have a large contributionof the subsurface Ge layers are indicated by large circles.
The surface states, S1 , S2 , and S3 , observed by ARPES
is reproduced well by the calculated states, Sa± , Sb± , and
Sc± . The lower panels (d-f) shows the spin polarization
toward the directions expected for the Rashba eﬀect isshown by large circles. The spin polarization observed by
SARPES is also well reproduced. Note that the Sa± bands
in Tl/Ge(111) are spin polarized parallel to the surface
near Γ̄ due to the normal Rashba eﬀect, while the spin orientation changes to the surface normal upon approachingK̄. Note also that the Sc+ and Sc− bands are not degenerate at Γ̄, while these two bands appear to be a spin-split
pair.
Figure 7 shows the depth profile of the partial charge
distribution of the states Sb and Sc indicated by the arrows
in Fig. 6(d) for Bi/Ge(111). The partial charge is calculated as |⟨ϕilm , ↑ |Ψk∥ ,E ⟩|2 , where |ϕilm , ↑⟩ represents eachatomic orbital in the ith layer and |Ψk∥ ,E ⟩ the eigenfunction for the calculated state at (k∥ , E). Note that, since the“atomic orbitals” are defined only within atomic spheres
and the wavefunctions in the interstitial space is describedby plane waves in the LAPW method, the partial charge
summed up for all the atoms is less than unity. Both states
has a similar distribution, which has a broad maximum ataround the fifth Ge layer and gradually decay upon going
into the bulk. The distribution implies that these surface
states, S2 (Sb ) and S3 (Sc ) are formed from the bulk states
LH and SO, respectively, due to the perturbation inducedby the truncation of the bulk translational symmetry at
the surface. The S1 (Sa ) band in Tl/Ge(111) is the sameas the A band in Fig. 3, which is formed by the weakhybridization between Ge 4pz with the 6pz orbitals of theTl atoms at H3 sites. For Bi/Ge(111) and Br/Ge(111),
since the adatoms occupy the T1 sites, the Ge 4pz orbitals
strongly interact with the pz orbitals of the adsorbates andform flat bands with bonding and antibonding characters√
Figure5: Second-derivative ARPES images for (a) Ge(111)-( 3 ×√◦3)R30 , (b) Ge(111)-(1 × 1)-Br, and (c) Ge(111)-(1 × 1)-Tl. (d)Schematic of bulk Ge band structure. ∆SO = 0.29 eV. Panel (a) was
reproduced from Ref. [44]. Panels (b), (c), and (d) were reproduced
from Ref. [45]. Dashed lines indicate the upper edges of the HH, SO,
and LH bands, which were calculated by a tight-binding method withparameters fitted to the bulk bands. Triangle markers in (a) and (b)show the spin polarization measured by SARPES [44].

those of MoS2 and WS2 , suggesting that it is possible toselectively populate the electrons with particular spin polarization by optically pumping with circularly polarized
light [42, 43]. On the other hand, the β(1 × 1) surface hasa spin-polarized metallic surface states, suggesting that it
is usable to study spin transport phenomena.
4. Γ̄ surface states derived from subsurface Ge orbitals
Since the discovery of the surface Rashba eﬀect on
Au(111) [10], eﬀorts had been paid to study the surfaces
containing heavy elements in the 6th row of the periodic
table. In 2010, however, the spin-polarized surface√ √ states
localized in subsurface layers of the Ge(111)-( 3× 3)R30◦ Bi surface [Fig. 1(d)] was discovered and the spin polarization was ascribed to the Rashba SOI at the nuclei
of subsurface Ge atoms [44]. Similar spin-polarized surface states were identified also on Ge(111)-(1 × 1)-Br [Fig.
1(b)]√ Ge(111)-(1×1)-Tl [Fig. 1(c)] [45], and Ge(111)√ [28],( 3 × 3)R30◦ -Pb surfaces [Fig. 1(e)] [46]. Since Br isin the fourth row, the same as Ge, in the periodic table,
5

/
√
√
Figure 6: Calculated band structures for (a,d) Ge(111)-( 3 × 3)R30◦ -Bi, (b,e) Ge(111)-(1 × 1)-Br, and (c,f) Ge(111)-(1 × 1)-Tl. The radiiof the circles in panels (a-c) indicate total contribution of the subsurface layers, while those in panel (d-e) show net spin polarization. Thinlines in the left halves show bulk valence bands. Thick lines in the right halves show the upper edges of the HH, LH, and SO bands. Panel(e) was reproduced from Ref. [28] and panels (a), (b), (c), (d) and (f) were reproduced from Ref. [45].

surface states should be formed even on clean Ge(111)
surface. However, since the clean Ge(111) surface is reconstructed in c(2×8) periodicity, it is not very easy toidentify the surbsurface states and their spin polarization.
A recent full-potential LAPW calculation for a hypothetical Ge(111)-(1×1) surface and Ge(111)-(1×1)-H surface
indicates the existence of spin-polarized subsurface states[47].
The lifting of the degeneracy at Γ̄ of the Sc+ and Sc−
branches can be understood as the “partner-switching”
similar to that in topological insulators. Since these branches
are resonances within bulk continua, each of them canchange its partner at Γ̄ to another band which may be
a bulk band [45].
Figure 7: Layer- and spin-resolved
partial charges of surface states√√
Sb and Sc of Ge(111)-( 3 × 3)R30◦ at the states indicated by thearrows in Fig. 6(d). The zeroth layer corresponds to the Bi layer.
Reproduced from Ref. [45].

5. Summary
During the past decade, the electronic structure of the
Rashba spin-split states on semiconductor surfaces has
been established by spectroscopic means such as ARPES
and SARPES and by theories and computations. A next
important topic along this line will be transport phenomena, including spin transport such as SHE, spin filters [48],and spin light-emitting
diodes [49]. At the moment, the√√Ge(111)-β( 3 × 3)R30◦ -Pb surface is probably a nicecandidate to study spin transport phenomena on surfaces,
since it has a nearly-free-electron band with a large spin
splitting and a very good surface order. The surface shows

at 0.5–1.0 eV below and above EF . Hence the subsurface
states are predominantly of the Ge 4px py character as indicated in Fig. 7. All of these states are not bulk states but
are localized in the surface/subsurface region, the states
are spin-split due to the Rashba SOI.
Since the surface states localized in subsurface layers
originate from the bulk states which are perturbed by thetruncation of the bulk translational symmetry, similar sub6

no phase transition down to 10 K [37], which is important
for low temperature spin transport experiments. The peculiar spin texture of the Ge(111)-(1 × 1)-Tl surface is useful for the optoelectronic studies. Optical pumping withcircularly polarized light can be used to selectively populate the conduction band with uniquely spin-polarized
electrons.
The third topic in this review, the spin-polarized subsurface states may have a most significant implication for
the forthcoming semiconductor spintronics. Since the subsurface states are derived from the corresponding bulk
states due to the truncation of the bulk periodicity, theseare essentially interface states. This suggests that similar
spin-split states should be formed at the heterointerface
between bulk Ge with other solids such as Si. This has
an important consequence. Usually, metal-covered semiconductor surfaces prepared in ultrahigh vacuum chambers are very sensitive to the exposure to gasses. Hencetransport experiments should be conducted in vacuo. On
the other hand, if the spin-split states are formed at theheterointerface of, for instance, Ge and Si, it should bepossible to bring the sample out of the vacuum chamberand carry out spin transport experiments such as intrinsic
SHE under ambient conditions. If the interface state thatis spin-split by ∼ 100 meV is achieved at semiconductor
heterojunctions, it would bring a breakthrough toward thesemiconductor spintronics.

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