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Dirac cone
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<h2 id="description">Description</h2> <p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, Dirac cones are a kind of <a href="/facts/Avoided_crossing/7VtKlQkC">crossing-point which electrons avoid</a>,<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> where the energy of the valence and conduction bands are not equal anywhere in two dimensional <a href="/facts/Reciprocal_lattice/jYCjcEpH">lattice k-space</a>, except at the zero dimensional Dirac points. As a result of the cones, electrical conduction can be described by the movement of <a href="/facts/Charge_carriers/wpjjql4x">charge carriers</a> which are massless <a href="/facts/Fermion/LEckdDsR">fermions</a>, a situation which is handled theoretically by the relativistic <a href="/facts/Dirac_equation/DzFaXS4p">Dirac equation</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> The massless fermions lead to various <a href="/facts/Quantum_Hall_effect/yK3zcCgu">quantum Hall effects</a>, magnetoelectric effects in topological materials, and ultra high <a href="/facts/Carrier_mobility/aN3bco00">carrier mobility</a>.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> Dirac cones were observed in 2008-2009, using <a href="/facts/Angle-resolved_photoemission_spectroscopy/vQW4b9Dh">angle-resolved photoemission spectroscopy</a> (ARPES) on the potassium-<a href="/facts/Graphite_intercalation_compound/FssMzW21">graphite intercalation compound</a> KC8<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> and on several bismuth-based alloys.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a><a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> </p><p>As an object with three dimensions, Dirac cones are a feature of <a href="/facts/Two-dimensional_materials/YnsFhbWg">two-dimensional materials</a> or surface states, based on a linear <a href="/facts/Dispersion_relation/oo7RM5eg">dispersion relation</a> between energy and the two components of the <a href="/facts/Crystal_momentum/GzTGXyUj">crystal momentum</a> kx and ky. However, this concept can be extended to three dimensions, where Dirac semimetals are defined by a linear dispersion relation between energy and kx, ky, and kz. In k-space, this shows up as a <a href="/facts/Hypercone/YHJS9jzq">hypercone</a>, which have doubly degenerate bands which also meet at Dirac points.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> Dirac semimetals contain both time reversal and spatial inversion symmetry; when one of these is broken, the Dirac points are split into two constituent <a href="/facts/Weyl_semimetal/FjWk1AMl">Weyl points</a>, and the material becomes a Weyl semimetal.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a><a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a><a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a><a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a><a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a><a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a><a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a>[<i>excessive citations</i>] In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal <a href="/facts/Cadmium_arsenide/eLrWjQbQ">cadmium arsenide</a>.<a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a><a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a><a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> </p> <h2 id="analog-systems">Analog systems</h2> <p>Dirac points have been realized in many physical areas such as <a href="/facts/Plasmonics/IAR0rUhe">plasmonics</a>, <a href="/facts/Phonon/tflWW6vw">phononics</a>, or <a href="/facts/Nanophotonics/f2UAn4oH">nanophotonics</a> (microcavities,<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a> photonic crystals<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a>). </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Dirac_matter/0WVIl6DC">Dirac matter</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Wehling, T.O.; Black-Schaffer, A.M.; Balatsky, A.V. (2014). "Dirac materials". <i>Advances in Physics</i>. 63 (1): 1. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/1405.5774">1405.5774</a>. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2014AdPhy..63....1W">2014AdPhy..63....1W</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1080%2F00018732.2014.927109">10.1080/00018732.2014.927109</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:118557449">118557449</a>.</li></ul> <ul><li>Johnston, Hamish (23 July 2015). <a href="http://physicsworld.com/cws/article/news/2015/jul/23/weyl-fermions-are-spotted-at-long-last">"Weyl fermions are spotted at long last"</a>. <i>Physics World</i>. Retrieved 22 November 2018.</li></ul> <ul><li>Ciudad, David (20 August 2015). <a href="https://doi.org/10.1038%2Fnmat4411">"Massless, yet real"</a>. <i>Nature Materials</i>. 14 (9): 863. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1038%2Fnmat4411">10.1038/nmat4411</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/1476-1122">1476-1122</a>. <a href="/facts/PMID_(identifier)/JlHAvMHt">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/26288972">26288972</a>.</li></ul> <ul><li>Vishwanath, Ashvin (8 September 2015). <a href="http://physics.aps.org/articles/v8/84">"Where the Weyl things are"</a>. <i>Physics</i>. 8: 84. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2015PhyOJ...8...84V">2015PhyOJ...8...84V</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1103%2FPhysics.8.84">10.1103/Physics.8.84</a>. Retrieved 22 November 2018.</li></ul> <ul><li>Jia, Shuang; Xu, Su-Yang; Hasan, M. Zahid (25 October 2016). <a href="https://www.nature.com/articles/nmat4787">"Weyl semimetals, Fermi arcs, and chiral anomaly"</a>. <i>Nature Materials</i>. 15 (11): 1140–1144. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/1612.00416">1612.00416</a>. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2016NatMa..15.1140J">2016NatMa..15.1140J</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1038%2Fnmat4787">10.1038/nmat4787</a>. <a href="/facts/PMID_(identifier)/JlHAvMHt">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/27777402">27777402</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:1115349">1115349</a>.</li></ul> <ul><li>Hasan, M. Z.; Xu, S.-Y.; Neupane, M. (2015). "Chapter 4: Topological insulators, topological Dirac semimetals, topological crystalline insulators, and topological Kondo insulators". In Ortmann, Frank; Roche, Stephan; Valenzuela, Sergio O. (eds.). <i>Topological Insulators: Fundamentals and Perspectives</i>. Wiley. pp. 55–100. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/1406.1040">1406.1040</a>. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2014arXiv1406.1040Z">2014arXiv1406.1040Z</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-527-33702-6.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Novoselov, K.S.; Geim, A.K. (2007). "The rise of graphene". Nature Materials. 6 (3): 183–191. Bibcode:2007NatMa...6..183G. doi:10.1038/nmat1849. PMID 17330084. 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