Supplementary Information
Supplementary Information
Encapsulated silicene: A robust large-gap topological insulator Liangzhi Kou1*,Yandong Ma2, Binghai Yan3, Xin Tan1, Changfeng Chen4 and Sean Smith1* 1
Integrated Materials Design Centre (IMDC), School of Chemical Engineering, University of New SouthWales,
Sydney, NSW 2052, Australia 2
School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
3
Max Planck Institute for Chemical Physics of Solids, NoethnitzerStr. 40, 01187 Dresden, Germany
4
Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of
Nevada, Las Vegas, Nevada 89154, United States
Email: [email protected], [email protected]
S1
Figure S-1. The electronic band structures of the MoTe2/Silicene/MoTe2 QWs in (a) AB and (b) AA stacking. The red (black) lines represent the results without (with) the SOC effect.
Table S-1. Parities of all 22 occupied spin-degenerate bands at the four TRIM points of the ABstacked QW structure reported in the main text. Their product at each TRIM point is indicated at the end in parentheses. Γ + 3M +
-
+ +
-
+ -
+
+ +
-
+ +
-
+ -
+
+ -
+
+ -
+
-
+ +
+ -
+
+ +
+ -
(+) (-)
Figure S-2. (a) Top and (b) side view of the AB-stacked QW armchair nanoribbon with a width of 55 angstroms, which is used in the edge-state calculations reported in the main text.
S2
Figure S-3. The variation of the nontrivial band gap at the K point for the (a) AA and (b) MA stacked WTe2/Silicene/WTe2 QW as a function of the increased interlayer distance.
Figure S-4. The initial and final structure used to construct a series of WTe2/Silicene/WTe2 QWs in MA stacking. In the Initial QW, each Si atom is on top of either a W or Te atom of the upper WTe2 layer, while either on top of a W atom or a hexagonal centre of the lower WTe2 layer. With the WTe2 layers fixed, we slide the silicene layer in the direction indicated by the red arrow in six steps over a total distance of √3/3a (where a is the lattice constant) to generate the intermediate MAtacked structures shown in Figure S5. In the final QW, each Si atom is either on top of a W atom or a hexagonal centre of the WTe2 layers. These MA stacking patterns are generated differently from that in Figure 2(c), but their band gaps (see Figure S5) show similar behaviour, demonstrating that proximity-SOC driven large nontrivial band gap is a common phenomenon in the MA-stacked QWs.
S3
Figure S-5. (a)-(e): Five MA-stacked WTe2/Silicene/WTe2 QWs generated as described in Figure S4, their electronic band structures and the corresponding edge states calculated using the same ribbon model shown in Figure S1 except for the difference in the stacking pattern. All the MA-stacked structures have topologically nontrivial edge states, indicating their TI character. The QWs with larger formation energy Ef have larger nontrivial band gaps, suggesting that experimentally synthesized QW structures are likely to possess large band gaps on the order of 100 meV.
S4
Figure S-6. The band structures of the H-terminated (left panel) and OH-terminated (right) silicene. A large gap is opened when silicene is passivated with hydrogen while OH-silicene becomes metallic.
Figure S-7. (a) The gap variation at the K point as a function of the vertical applied electric field. (b) The band structure of the AB-stacked QW at the electric field of 0.04 V/Å.
POSCAR for AB stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.6666667075679886 0.3333333214320170 0.7960034787059138 0.3333332924320110 0.6666666485679873 0.2039965212940864 -0.0000001666910301 0.0000001666910300 0.7243050326921272 -0.0000001850770832 0.0000001850770832 0.8680173800274221 0.0000001666910300 -0.0000001666910301 0.2756949673078729 0.0000001850770832 -0.0000001850770832 0.1319826489725767 0.3333336273467913 0.6666664016532077 0.9838097703284827
S5
0.6666664016532077 0.3333336273467913 0.0161901996715150
POSCAR for AA stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.1666675292393584 0.3333324707606415 0.2147714455773166 0.8333324707606414 0.6666675292393586 0.7852285544226836 0.8333334340937630 0.6666665959062323 0.1438102430886177 0.8333332597180321 0.6666667702819633 0.2856386125256488 0.1666665359062342 0.3333334040937680 0.8561897719113802 0.1666667102819656 0.3333332297180365 0.7143613874743511 0.8333336530678859 0.6666663469321141 0.9855910125122429 0.1666663469321142 0.3333336530678859 0.0144089874877574
POSCAR for Random stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.6741054731149784 0.3482100345545305 0.2071334023819756 0.3258945268850218 0.6517899654454694 0.7928665976180246 0.3407314448017351 0.6814612398468886 0.1361955899991943 0.3393111183832159 0.6786209286566686 0.2780120124102414 0.6592685251982626 0.3185387601531117 0.8638044250008035 0.6606888516167820 0.3213790713433315 0.7219879875897585 0.8339336100542070 0.6678679169594386 0.9849687177336353 0.1660663899457931 0.3321320830405612 0.0150312822663646
S6
Encapsulated silicene: A robust large-gap topological insulator Liangzhi Kou1*,Yandong Ma2, Binghai Yan3, Xin Tan1, Changfeng Chen4 and Sean Smith1* 1
Integrated Materials Design Centre (IMDC), School of Chemical Engineering, University of New SouthWales,
Sydney, NSW 2052, Australia 2
School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
3
Max Planck Institute for Chemical Physics of Solids, NoethnitzerStr. 40, 01187 Dresden, Germany
4
Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of
Nevada, Las Vegas, Nevada 89154, United States
Email: [email protected], [email protected]
S1
Figure S-1. The electronic band structures of the MoTe2/Silicene/MoTe2 QWs in (a) AB and (b) AA stacking. The red (black) lines represent the results without (with) the SOC effect.
Table S-1. Parities of all 22 occupied spin-degenerate bands at the four TRIM points of the ABstacked QW structure reported in the main text. Their product at each TRIM point is indicated at the end in parentheses. Γ + 3M +
-
+ +
-
+ -
+
+ +
-
+ +
-
+ -
+
+ -
+
+ -
+
-
+ +
+ -
+
+ +
+ -
(+) (-)
Figure S-2. (a) Top and (b) side view of the AB-stacked QW armchair nanoribbon with a width of 55 angstroms, which is used in the edge-state calculations reported in the main text.
S2
Figure S-3. The variation of the nontrivial band gap at the K point for the (a) AA and (b) MA stacked WTe2/Silicene/WTe2 QW as a function of the increased interlayer distance.
Figure S-4. The initial and final structure used to construct a series of WTe2/Silicene/WTe2 QWs in MA stacking. In the Initial QW, each Si atom is on top of either a W or Te atom of the upper WTe2 layer, while either on top of a W atom or a hexagonal centre of the lower WTe2 layer. With the WTe2 layers fixed, we slide the silicene layer in the direction indicated by the red arrow in six steps over a total distance of √3/3a (where a is the lattice constant) to generate the intermediate MAtacked structures shown in Figure S5. In the final QW, each Si atom is either on top of a W atom or a hexagonal centre of the WTe2 layers. These MA stacking patterns are generated differently from that in Figure 2(c), but their band gaps (see Figure S5) show similar behaviour, demonstrating that proximity-SOC driven large nontrivial band gap is a common phenomenon in the MA-stacked QWs.
S3
Figure S-5. (a)-(e): Five MA-stacked WTe2/Silicene/WTe2 QWs generated as described in Figure S4, their electronic band structures and the corresponding edge states calculated using the same ribbon model shown in Figure S1 except for the difference in the stacking pattern. All the MA-stacked structures have topologically nontrivial edge states, indicating their TI character. The QWs with larger formation energy Ef have larger nontrivial band gaps, suggesting that experimentally synthesized QW structures are likely to possess large band gaps on the order of 100 meV.
S4
Figure S-6. The band structures of the H-terminated (left panel) and OH-terminated (right) silicene. A large gap is opened when silicene is passivated with hydrogen while OH-silicene becomes metallic.
Figure S-7. (a) The gap variation at the K point as a function of the vertical applied electric field. (b) The band structure of the AB-stacked QW at the electric field of 0.04 V/Å.
POSCAR for AB stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.6666667075679886 0.3333333214320170 0.7960034787059138 0.3333332924320110 0.6666666485679873 0.2039965212940864 -0.0000001666910301 0.0000001666910300 0.7243050326921272 -0.0000001850770832 0.0000001850770832 0.8680173800274221 0.0000001666910300 -0.0000001666910301 0.2756949673078729 0.0000001850770832 -0.0000001850770832 0.1319826489725767 0.3333336273467913 0.6666664016532077 0.9838097703284827
S5
0.6666664016532077 0.3333336273467913 0.0161901996715150
POSCAR for AA stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.1666675292393584 0.3333324707606415 0.2147714455773166 0.8333324707606414 0.6666675292393586 0.7852285544226836 0.8333334340937630 0.6666665959062323 0.1438102430886177 0.8333332597180321 0.6666667702819633 0.2856386125256488 0.1666665359062342 0.3333334040937680 0.8561897719113802 0.1666667102819656 0.3333332297180365 0.7143613874743511 0.8333336530678859 0.6666663469321141 0.9855910125122429 0.1666663469321142 0.3333336530678859 0.0144089874877574
POSCAR for Random stacked QW WTe2-Si 1.00000000000000 3.5999999046000002 0.0000000000000000 0.0000000000000000 -1.7999999523000001 3.1176913709999998 0.0000000000000000 0.0000000000000000 0.0000000000000000 25.0000000000000000 W Te Si 2 4 2 Direct 0.6741054731149784 0.3482100345545305 0.2071334023819756 0.3258945268850218 0.6517899654454694 0.7928665976180246 0.3407314448017351 0.6814612398468886 0.1361955899991943 0.3393111183832159 0.6786209286566686 0.2780120124102414 0.6592685251982626 0.3185387601531117 0.8638044250008035 0.6606888516167820 0.3213790713433315 0.7219879875897585 0.8339336100542070 0.6678679169594386 0.9849687177336353 0.1660663899457931 0.3321320830405612 0.0150312822663646
S6
