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What are the theoretical foundations for the existence of Weyl semimetal phases in materials? 


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The theoretical foundations for the existence of Weyl semimetal phases in materials lie in the breaking of either time-reversal or inversion symmetry, leading to unique electronic structures. Various materials like MoTe, RuO2, CeAlSi, and porous Ge and SiGe structures exhibit Weyl semimetal states based on first-principles calculations and experimental verifications. MoTe, for instance, transitions from nodal loop states to Weyl points under the influence of spin-orbit coupling and strain, showcasing tunable topological properties . RuO2 is predicted to host Weyl points and nodal loops due to its collinear antiferromagnetic nature, offering a platform for studying Weyl semimetal states in antiferromagnets . Additionally, noncentrosymmetric 2D structures like porous Ge and SiGe are identified as Weyl semimetals with unique topological features, expanding the family of Weyl materials in condensed matter physics . These diverse examples highlight the rich theoretical underpinnings supporting the emergence of Weyl semimetal phases in various materials.

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Theoretical foundations for Weyl semimetals include breaking time-reversal or inversion symmetry, leading to non-trivial band crossings near the Fermi level, as seen in InMnTi2.
Theoretical foundations for Weyl semimetals lie in breaking inversion or time-reversal symmetry, leading to emergent Weyl fermions. Magnetic Weyl semimetals offer insight into magnetism-topology interplay.
Theoretical foundations for Weyl semimetal phases include collinear antiferromagnetic structures, small magnetocrystalline anisotropy energy, and the ability to transform between Weyl points and nodal loops.
Theoretical foundations for Weyl semimetal phases include breaking time-reversal or inversion symmetry, leading to gapless electronic excitation in non-centrosymmetric materials like MoTe demonstrated in this study.
Theoretical foundations for Weyl semimetals in materials include noncentrosymmetric structures with broken inversion symmetry, resulting in nontrivial topological phases, protected by specific symmetries, and featuring edge Fermi-arcs.

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