394
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.17 a Schematic three-dimensional view of (unsplit) conduction band minima (grey) and spin-split valence band
maxima with opposite (red: up, blue: down) spin orientation. b Relativistic band structure of 2H-WSe 2 (red dots show
band structure without inclusion of spin-orbit splitting) with spin-splittings of conduction and valence band indicated.
Adapted from [1296], reprinted with permission, ©2011 APS
Fig. 13.18 ARPES
measurement of the band
structure of monolayer
WSe 2 . The horizontal
dashed white lines indicate
the spin-orbit splitting
SOC = 513(10) meV of
the top of the valence band.
Adapted from [1297],
reprinted with permission,
©2015 IOP Publishing
The lack of inversion symmetry results in a splitting of the electronic bands due to spin-orbit
interaction. This effect is particularly strong in the valence band. Splitting energies SOC from fully
relativistic calculations have been predicted for various 2H-MX 2 systems [1292, 1293, 1296], ranging
between about 150 meV (MoS 2 ) and 500 meV (WTe 2 ). For WSe 2 , an experimental value of about
500 meV has been found [1297] (Fig. 13.18). For the same materials, the spin-splitting in the conduction
band
5 is an order of magnitude smaller in the range of 3–50 meV [1292, 1293]. Because of time reversal
symmetry, the spin-splitting (cf. Sect. 6.2.4) of the bands at K and K’ has opposite sign as visualized
in Fig. 13.17a; this property is termed ’spin-valley coupling’.
5 The splitting is negative (positive) for MoX 2 (WX 2 ) compounds, i.e. the lowest conduction band at the K-point is spin
up (down) [1292, 1294]; the valence band maximum at K is spin up for all cases.
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.17 a Schematic three-dimensional view of (unsplit) conduction band minima (grey) and spin-split valence band
maxima with opposite (red: up, blue: down) spin orientation. b Relativistic band structure of 2H-WSe 2 (red dots show
band structure without inclusion of spin-orbit splitting) with spin-splittings of conduction and valence band indicated.
Adapted from [1296], reprinted with permission, ©2011 APS
Fig. 13.18 ARPES
measurement of the band
structure of monolayer
WSe 2 . The horizontal
dashed white lines indicate
the spin-orbit splitting
SOC = 513(10) meV of
the top of the valence band.
Adapted from [1297],
reprinted with permission,
©2015 IOP Publishing
The lack of inversion symmetry results in a splitting of the electronic bands due to spin-orbit
interaction. This effect is particularly strong in the valence band. Splitting energies SOC from fully
relativistic calculations have been predicted for various 2H-MX 2 systems [1292, 1293, 1296], ranging
between about 150 meV (MoS 2 ) and 500 meV (WTe 2 ). For WSe 2 , an experimental value of about
500 meV has been found [1297] (Fig. 13.18). For the same materials, the spin-splitting in the conduction
band
5 is an order of magnitude smaller in the range of 3–50 meV [1292, 1293]. Because of time reversal
symmetry, the spin-splitting (cf. Sect. 6.2.4) of the bands at K and K’ has opposite sign as visualized
in Fig. 13.17a; this property is termed ’spin-valley coupling’.
5 The splitting is negative (positive) for MoX 2 (WX 2 ) compounds, i.e. the lowest conduction band at the K-point is spin
up (down) [1292, 1294]; the valence band maximum at K is spin up for all cases.