Normal Dirac Semimetal Phase and Zeeman-Induced Topological Fermi Arc in PtSr5

Abstract

Pt-Sr binary intermetallics encompass a broad range of stoichiometries and crystal structures, stabilized by complex bonding and multivalent chemistry. The Sr-rich end member, PtSr5, is recently identified via artificial-intelligence-guided materials design as a body-centered tetragonal compound (I4/m). Using first-principles calculations, we show that PtSr5 hosts a Dirac semimetal phase with trivial Z2 topology, classified as a normal Dirac semimetal. A symmetry-indicator analysis based on parity eigenvalues at the eight time-reversal-invariant momenta confirms that all Z2 invariants-evaluated on time-reversal-invariant two-dimensional subspaces of momentum space with a direct band gap-are trivial, thereby establishing the topologically trivial nature of the Dirac semimetal phase. Nonetheless, our calculations reveal that applying an external Zeeman magnetic field along the z-axis drives the system into a Weyl semimetal phase, as corroborated by characteristic changes in the computed surface states. This work demonstrates the tunability of topological phases in PtSr5 via external perturbations and highlights the effectiveness of AI-based materials exploration in discovering new quantum materials.

Figures (6)

• Figure 1: (a) Topological Dirac semimetal (DS) with a nontrivial $\mathbb{Z}_2$ topological invariant ($\mathbb{Z}_2=1$) defined on the $b_3=0$ sub-plane. Such a phase is realized in materials like Na$_3$Bi and Cd$_3$As$_2$. (b) Normal Dirac semimetal with a trivial $\mathbb{Z}_2$ invariant ($\mathbb{Z}_2=0$) on the $b_3=0$ sub-plane, as demonstrated for PtSr$_5$ in this work.
• Figure 2: Crystal structure and Brillouin zone (BZ) of PtSr5. (a)–(c) Primitive unit cell and lateral views, with red and blue arrows indicating the primitive cell vectors and Cartesian axes, respectively. Pt and Sr atoms are shown as distinct spheres. (d) First BZ, including high-symmetry points (red) and a projected two-dimensional (2D) BZ for the [001] surface orientation.
• Figure 3: Electronic energy bands of PtSr5. (a) Band structures of PtSr5 with and without spin-orbit coupling (SOC) are shown in color and black, respectively. Blue and red indicate the occupied and unoccupied SOC bands. (b) Magnified view of two Dirac points (green circles) along the $\Gamma$--$Z$ line, as highlighted by the green box in (a). (c) Magnified view of the small anti-crossing gap (35.8 meV) along the $N$--$\Gamma$ path, illustrating the SOC-induced band splitting.
• Figure 4: Dirac points and Weyl transitions in PtSr5. (a) Schematic illustration of the Dirac points (green dots) and possible Weyl points in momentum space. The black shape represents the first BZ, and the red line highlights the high-symmetry $\Gamma$--$Z$ axis. A blue cube indicates one-eighth of the BZ (comprising four TRIMs). (b) Parity eigenvalue signs ($+$ or $-$) for the eight TRIMs at the corners of a conceptual cube. (c) The $k_z = 0$ plane used for the Wannier charge center (WCC) analysis, where the blue-shaded face denotes the $k_x \ge 0$ half-plane and the blue arrow indicates the string direction ($k_y$). (d) Evolution of the WCCs obtained by shifting the $k_y$ string along $k_x$ from $\Gamma$ to $X$, revealing a well-defined spectral gap (red dashed line) without any winding of charge centers, demonstrating that both the $\mathbb{Z}_2$ topological invariant and the mirror Chern number on this plane are trivial. (e) Band structure along $\Gamma$--$Z$ under a $B = 50$ T field applied along $z$, showing each Dirac point splitting into two Weyl points with Chern numbers $+1$ (red) and $-1$ (blue). (f) Locations of these Weyl points in the first BZ, with chiralities indicated by red and blue dots.
• Figure 5: Surface energy spectra revealing the Dirac-to-Weyl transition. (a) and (b) Surface band dispersions along the $\overline{\Gamma}$--$\overline{Z}$ line, calculated with (a) and without (b) an external magnetic field $B = 50$ T. Red (blue) circles indicate the Weyl points with Chern numbers $+1$ ($-1$), while green circles denote the Dirac points in the zero-field case. The color scale represents the spectral weight projected onto the surface, with red corresponding to stronger surface localization. Black arrows in (a) mark the surface states (SS) responsible for the surface Fermi arcs shown in (c) and (e). (c) Surface spectral map in the projected 2D BZ at the average energy $E_1 = 35$ meV of the Weyl points in (a), where the momenta of the $+1$ and $-1$ Weyl points are highlighted by red and blue dots. (d) Surface spectrum at the Dirac point energy $E_3 = 18$ meV for the zero-field case, with the magnified inset highlighting the Dirac point (green circle). (e) and (f) show surface spectra at $E_2 = -47$ meV and $E_4 = -48$ meV, respectively, under $B = 50$ T. (g) Schematic energy–momentum diagram illustrating the four constant-energy planes corresponding to panels (h)–(k), where (h) $E=20$ meV, (i) $E=30$ meV, (j) $E=40$ meV, and (k) $E=50$ meV. The progression from (h) to (k) visualizes the continuous Fermi arc connecting the $-1$ Weyl node to the $+1$ Weyl node. The black arrow traces the topological SS Fermi arc.