Strain as a topological selector in altermagnetic CrSb

TL;DR

This study demonstrates that CrSb, an altermagnetic Weyl semimetal, hosts a rich strain- and correlation-driven topological landscape. By combining isotropic tensile strain with Hubbard interaction tuning $U_{ ext{eff}}$, the authors reveal symmetry-allowed Dirac crossings and emergent triple-point fermions, describable by a 3D low-energy Hamiltonian that couples sublattice mass to an exchange field. The strain-induced Dirac points are delicate, while TP fermions remain robust under strain due to $C_{3v}$ symmetry, and both bulk states are corroborated by topological surface states and nontrivial Berry phases. Overall, CrSb acts as a model system where altermagnetism and structural perturbations jointly enable controllable topological quasiparticles, suggesting practical routes to engineer altermagnetic topological phases via strain or chemical pressure.

Abstract

Altermagnetism combines fully compensated magnetic order with a magnetic symmetry that relates inequivalent spin sublattices, offering a promising, still underexplored platform for unconventional topological phases. Here we show that both isotropic tensile strain and electron localization, controlled by an effective Hubbard interaction $U_{\text{eff}}$, can act as efficient and systematic topological control parameters in the altermagnetic Weyl semimetal CrSb. While CrSb hosts Weyl fermions at equilibrium, modest tensile strain of 4-5% stabilizes additional symmetry allowed Dirac crossings and triple-point fermions, with further strain selectively favoring the triple-point phase. We propose a 3D low-energy Hamiltonian that captures the interplay between the Hubbard interaction $U$ and the sublattice symmetry of the altermagnet, giving rise to an interaction-driven Dirac crossing. Our results establish CrSb as a model altermagnet in which either strain or electron localization can selectively access and control the distinct topologies inherent to the altermagnets.

Figures (5)

• Figure 1: Electronic structure of bulk CrSb with and without spin orbit coupling. (a) The magnetic unit cell of CrSb. (b) Bulk BZ of CrSb with the high symmetry points denoted along with the (001) [red] and (010) [blue] surfaces of the BZ. (c) and (d) Without and with SOC electronic structures of bulk CrSb respectively.
• Figure 2: Electronic band structure showing the Triple points and the compatibility relations of the bands. (a) The pair of TPs along the A--$\Gamma$ (A--$\Gamma$) line produced by the four bands labeled as red dashed lines. (b) and (c) Zoomed in portion shown in blue circle and rectangluar box respectively in (a). (d) and (e) Fine tuned pair of TPs at $k_z = -0.271$ and $k_z = -0.281$ inside the BZ along the -A--$\Gamma$ line respectively. The x-axis denotes the $k_x$ line.
• Figure 3: Electronic band structures calculated with different $U_{\text{eff}}$ values and also with isotropic tensile strain. (a)--(d) The electronic band structures of CrSb calculated with $U_{\text{eff}} =$ 1 eV, 1.5 eV, 2.5 eV, and 3.5 eV respectively. It shows the evolution of the Dirac crossing from $U_{\text{eff}} =$ 1 eV to nearly 3.5 eV. (e)--(h) The calculated electronic band structure with isotropic tensile strain starting from 1%, and then 2%, 3%, and 4% respectively. In all of the above strained case we took the $U_{\text{eff}}$ value to be 1 eV. It shows the same evolution of the Dirac crossing as in the varying $U_{\text{eff}}$ case. The red circles on (d) and (h) shows the observed Dirac crossing at 3.5 eV $U_{\text{eff}}$ value and 4% isotropic tensile strain respectively.
• Figure 4: Evolution of the minimum bulk band gap along the L--A line as a function of theeffective interaction strength $U$, obtained from the low-energyBloch Hamiltonian derived in the \ref{['simplified_H']}. For small $U$, the system isinsulating due to a finite, symmetry-allowed sublattice mass. Upon increasing $U$, the interaction-generated exchange field compensates the band mass at a critical value, leading to a gap closing and the emergence of a Dirac semimetal phase. For larger $U$, the gap reopens, yielding a second insulating phase.
• Figure 5: Topological surface state of unstrained and strained CrSb. (a)--(d) The surface states of unstrained CrSb in which (a) and (c) show the bulk projected surface density of states on the (010) and (001) surfaces respectively, while (b) and (d) show the projected surface density of states for the (010) and (001) surface BZ respectively. (e)--(h) The surface states of strained (4%) CrSb in which (e) and (g) show the bulk projected surface density of states on the (010) and (001) surfaces respectively, and (f) and (h) show the projected surface density of states for the (010) and (001) surfaces of CrSb respectively. In figs. (f) and (h), the vertical white arrows indicate the clear topological surface states that are absent in the unstrained case shown in figs. (b) and (d).