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<p>The occurrence of a topological phase transition can be demonstrated by a direct observation of a change in the topological invariant. For holographic topological semimetals, a topological Hamiltonian method needs to be employed to calculate the topological invariants due to the strong coupling nature of the system. We calculate the topological invariants for the holographic Weyl semimetal and the holographic Weyl-<i>Z</i><sub>2</sub> semimetal, which correspond to the chiral charge and the spin-Chern number, respectively. This is achieved by probing fermions within the system and deriving the topological Hamiltonian from the zero-frequency Green’s function. In both cases, we have identified an effective band structure characterized by an infinite number of Weyl or <i>Z</i><sub>2</sub> nodes, a distinctive feature of holographic systems different from weakly coupled systems. The topological invariants of these nodes are computed numerically and found to be nonzero, thereby confirming the topologically nontrivial nature of these nodes.</p>

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Topological invariant for holographic Weyl-Z2 semimetal

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月6日

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  • Xiantong Chen,
  • Xuanting Ji,
  • Ya-Wen Sun

摘要

The occurrence of a topological phase transition can be demonstrated by a direct observation of a change in the topological invariant. For holographic topological semimetals, a topological Hamiltonian method needs to be employed to calculate the topological invariants due to the strong coupling nature of the system. We calculate the topological invariants for the holographic Weyl semimetal and the holographic Weyl-Z2 semimetal, which correspond to the chiral charge and the spin-Chern number, respectively. This is achieved by probing fermions within the system and deriving the topological Hamiltonian from the zero-frequency Green’s function. In both cases, we have identified an effective band structure characterized by an infinite number of Weyl or Z2 nodes, a distinctive feature of holographic systems different from weakly coupled systems. The topological invariants of these nodes are computed numerically and found to be nonzero, thereby confirming the topologically nontrivial nature of these nodes.