page_title: Dirac matter
section_title: Transition metal dichalcogenides (TMDCs)
hierarchical_section_title: Dirac matter / Fermionic Dirac matter / Transition metal dichalcogenides (TMDCs)
caption_attribution_description: English: While they are gapped, near the K {\displaystyle K} and K &#x2032; {\displaystyle K^{\prime }} points of their hexagonal Brilliouin zone, the dispersions of transition metal dichalcogenides can be described by a massive Dirac equation with additional spin-orbit coupling terms that lead to spin-splitting in the valance band.
context_page_description: The term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself was formulated for fermions, the quasi-particles present within Dirac matter can be of any statistics. As a consequence, Dirac matter can be distinguished in fermionic, bosonic or anyonic Dirac matter. Prominent examples of Dirac matter are Graphene, topological insulators, Dirac semimetals, Weyl semimetals, various high-temperature superconductors with -wave pairing and liquid Helium-3. The effective theory of such systems is classified by a specific choice of the Dirac mass, the Dirac velocity, the Dirac matrices and the space-time curvature. The universal treatment of the class of Dirac matter in terms of an effective theory leads to a common features with respect to the density of states, the heat capacity and impurity scattering.
context_section_description: The low-energy properties some semiconducting transition metal dichalcogenide monolayers,
  can be described by a two-dimensional massive (gapped) Dirac Hamiltonian with an additional term describing a strong spin–orbit coupling: 
  The spin-orbit coupling  provides a large spin-splitting in the valence band and  indicates the spin degree of freedom. As for graphene,  gives the valley degree of freedom - whether near the  or  point of the hexagonal Brillouin zone. Transition metal dichalcogenide monolayers are often discussed in reference to potential applications in valleytronics.
caption: While they are gapped, near the 
    
      
        
          K
        
      
      {\displaystyle K}
    
   and 
    
      
        
          
            K
            
              ′
            
          
        
      
      {\displaystyle K^{\prime }}
    
   points of their hexagonal Brilliouin zone, the dispersions of transition metal dichalcogenides can be described by a massive Dirac equation with additional spin-orbit coupling terms that lead to spin-splitting in the valence band.
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