11.6 Surface Physical Properties
349
E
k
(b)
(a)
E
k
Fig. 11.16 a ‘Normal’ band structure with surface states, the valence band states are antisymmetric (‘–’) from p-states,
the conduction band states are symmetric (‘+’) from s-states. The arrows denote the electron spin orientation of the
states. b ‘Topological’ band structure with surface states crossing the gap and electrons in the two surface states having
unique spin orientations
Fig. 11.17 Density of
states for Bi 2 Se 3 (111)
surface. Adapted
from [1086]
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Energy (eV)
K
M
Bi Se
2
3
states cross the band gap (Fig. 11.16b) and are spin-polarized (Fig. 11.16c) [1085, 1086]. A review
of various systems is given in [463]. Charge transport in such spin-polarized surface states suffers no
scattering (thus these states are called ‘topologically protected’) unless by a center that breaks time
reversal symmetry (magnetic impurity). The more or less linear dispersion of these states forms a
‘Dirac cone’ (cmp. Sect. 13.1.2 for the band structure of graphene with six Dirac cones) (Fig. 11.17).
Topological surface states have been observed in various systems [463]. As an example we show
data on bulk Bi 2 Se 3 [1087] for which the surface states are found to cross the band gap (Fig. 11.18a)
and spin-polarized measurements (Fig. 11.18b) show a strong spin polarization (about 50%) of the
two branches. Another situation where topological edge states appear is the interface between two
semiconductors with bands of different topology, such as HgTe and CdTe (cf. Sect. 6.11).
349
E
k
(b)
(a)
E
k
Fig. 11.16 a ‘Normal’ band structure with surface states, the valence band states are antisymmetric (‘–’) from p-states,
the conduction band states are symmetric (‘+’) from s-states. The arrows denote the electron spin orientation of the
states. b ‘Topological’ band structure with surface states crossing the gap and electrons in the two surface states having
unique spin orientations
Fig. 11.17 Density of
states for Bi 2 Se 3 (111)
surface. Adapted
from [1086]
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Energy (eV)
K
M
Bi Se
2
3
states cross the band gap (Fig. 11.16b) and are spin-polarized (Fig. 11.16c) [1085, 1086]. A review
of various systems is given in [463]. Charge transport in such spin-polarized surface states suffers no
scattering (thus these states are called ‘topologically protected’) unless by a center that breaks time
reversal symmetry (magnetic impurity). The more or less linear dispersion of these states forms a
‘Dirac cone’ (cmp. Sect. 13.1.2 for the band structure of graphene with six Dirac cones) (Fig. 11.17).
Topological surface states have been observed in various systems [463]. As an example we show
data on bulk Bi 2 Se 3 [1087] for which the surface states are found to cross the band gap (Fig. 11.18a)
and spin-polarized measurements (Fig. 11.18b) show a strong spin polarization (about 50%) of the
two branches. Another situation where topological edge states appear is the interface between two
semiconductors with bands of different topology, such as HgTe and CdTe (cf. Sect. 6.11).