Advances in Condensed Matter Physics

Research Article

Electronic Structure of Single-Wall Silicon Nanotubes and Silicon Nanoribbons: Helical Symmetry Treatment and Effect of Dimensionality

Table 1

Calculated basic physical parameters of selected [( , ), 91]-types of SWSiNTs.
Helicity ( , )SWSiNT diameter [Å]Gap [eV]Excitation energy: allowed direct [eV]Excitation energy: lowest spin-flip [eV]Energy of folding/Si [eV]
(3,0)3.756metallic 1.002 0.995 1.355
(3,3)3.756metallic 0.342 0.317 0.811
(5,0)6.260metallic 1.996 1.993 0.495
(5,3)5.4572.547 (indirect) 2.766 2.763 0.634
(5,5)6.2602.938 (indirect) 3.564 3.652 0.482
(7,0) 8.7643.526 (indirect) 3.384 3.382 0.220
(7,3) 7.6173.857 (direct) 3.552 3.550 0.295
(7,5) 7.8193.752 (indirect) 3.386 3.385 0.280
(7,7) 8.7643.238 (direct) 2.669 2.667 0.222
(9,0) 11.2681.455 (direct) 0.913 0.912 0.134
(9,3) 9.9371.661 (direct) 1.157 1.156 0.173
(9,5) 9.7781.575 (direct) 1.075 1.074 0.178
(9,7) 10.2481.232 (direct) 0.719 0.717 0.164
(9,9) 11.2681.276 (direct) 0.736 0.734 0.181
(11,0) 13.7722.355 (direct) 1.838 1.837 0.086
(11,3) 12.3312.267 (direct) 1.799 1.798 0.109
(11,5) 11.9442.301 (direct) 1.832 1.831 0.116
(11,7) 12.0742.376 (direct) 1.902 1.901 0.113
(11,9) 12.7062.521 (direct) 2.025 2.024 0.102
(11,11) 13.7722.678 (direct) 2.162 2.161 0.086
(13,0) 16.2762.499 (direct) 2.004 2.003 0.061
(13,3) 14.7612.465 (direct) 1.993 1.992 0.074
(13,5) 14.2202.451 (direct) 1.987 1.986 0.079
(13,7) 14.1092.409 (direct) 1.947 1.946 0.081
(13,9) 14.4392.314 (direct) 1.846 1.845 0.077
(13,11) 15.1792.198 (direct) 1.718 1.717 0.070
(13,13) 16.2762.110 (direct) 1.615 1.614 0.061
(15,0) 18.7800.806 (direct) 0.329 0.328 0.047
(15,3) 17.2120.973 (direct) 0.513 0.512 0.056
(15,5) 16.5621.092 (direct) 0.642 0.641 0.060
(15,7) 16.2761.154 (direct) 0.707 0.706 0.062
(15,9) 16.3721.117 (direct) 0.669 0.668 0.062
(15,11) 16.8440.991 (direct) 0.537 0.536 0.058
(15,13) 17.6620.765 (direct) 0.301 0.299 0.053
(15,15) 18.7800.749 (direct) 0.272 0.271 0.047
(17,0) 21.2841.763 (direct) 1.301 1.301 0.035
(17,3) 19.6771.693 (direct) 1.247 1.246 0.042
(17,5) 18.9461.648 (direct) 1.209 1.208 0.045
(17,7) 18.5291.621 (direct) 1.187 1.186 0.047
(17,9) 18.4431.625 (direct) 1.191 1.191 0.047
(17,11) 18.6971.663 (direct) 1.227 1.226 0.046
(17,13) 19.2751.726 (direct) 1.285 1.284 0.043
(17,15) 20.1491.798 (direct) 1.348 1.347 0.039
(17,17) 21.2841.860 (direct) 1.399 1.399 0.035
(19,0) 23.7881.756 (direct) 1.309 1.308 0.028
(19,3) 22.1511.748 (direct) 1.314 1.313 0.032
(19,5) 21.3581.742 (direct) 1.314 1.313 0.035
(19,7) 20.8341.734 (direct) 1.311 1.310 0.037
(19,9) 20.6111.719 (direct) 1.298 1.297 0.038
(19,11) 20.6871.692 (direct) 1.270 1.269 0.037
(19,13) 21.0621.653 (direct) 1.228 1.228 0.036
(19,15) 21.7221.610 (direct) 1.180 1.799 0.034
(19,17) 22.6401.571 (direct) 1.133 1.133 0.031
(19,19) 23.7881.541 (direct) 1.094 1.904 0.028
(21,0) 26.2920.531 (direct) 0.096 0.095 0.024
(21,3) 24.6300.616 (direct) 0.191 0.190 0.027
(21,5) 23.7880.678 (direct) 0.261 0.260 0.029
(21,7) 23.1870.736 (direct) 0.323 0.323 0.030
(21,9) 22.8470.773 (direct) 0.363 0.363 0.031
(21,11) 22.7780.777 (direct) 0.368 0.365 0.031
(21,13) 22.9840.741 (direct) 0.330 0.330 0.031
(21,15) 24.4570.657 (direct) 0.243 0.242 0.029
(21,17) 24.1810.497 (direct) 0.077 0.077 0.028
(21,19) 25.1340.406 (direct) 0.020 0.021 0.026
(21,21) 26.2920.459 (direct) 0.026 0.025 0.023
(23,0) 28.7961.538 (direct) 1.115 1.114 0.019
(23,3) 27.1141.497 (direct) 1.084 1.083 0.022
(23,5) 26.2331.466 (direct) 1.058 1.058 0.023
(23,7) 25.5671.437 (direct) 1.034 1.033 0.024
(23,9) 25.1341.415 (direct) 1.014 1.014 0.025
(23,11) 24.9461,405 (direct) 1.006 1.006 0.025
(23,13) 25.0091.411 (direct) 1.011 1.011 0.026
(23,15) 25.3211.431 (direct) 1.030 1.029 0.025
(23,17) 25.8721.462 (direct) 1.058 1.057 0.024
(23,19) 26.6481.498 (direct) 1.089 1.088 0.022
(23,21) 27.6291.533 (direct) 1.118 1.118 0.021
(23,23) 28.7961.563 (direct) 1.143 1.141 0.019
(31,0) 38.8121.101 (direct) 0.718 0.718 0.011
(31,17) 33.6651.079 (direct) 0.714 0.714 0.014
(31,31) 38.8121.002 (direct) 0.622 0.622 0.011
(45,0) 56.3410.314 (direct) 0.001 0.001 0.005
(45,13) 50.2210.344 (direct) 0.020 0.020 0.006
(45,35) 51.2410.344 (direct) 0.020 0.020 0.006
(45,45) 56.3410.332 (direct) 0.003 0.003 0.005
(51,0) 63.8530.314 (direct) 0.038 0.038 0.004
(51,23) 55.3870.347 (direct) 0.040 0.040 0.005
(51,51) 63.8530.329 (direct) 0.018 0.018 0.003