Emergent spin-resolved electronic charge density waves and pseudogap phenomena from strong $d$-wave altermagnetism

Abstract

Inspired by recent discovery of metallic $d$-wave altermagnetism in KV$_2$Se$_2$O, we develop a self-consistent microscopic many-body calculation of density-wave order for an itinerant altermagnetic metal. We show that the strong $d$-wave spin-momentum locking inherent to the altermagnetic band structure reconstructs the Fermi surface into spin-selective quasi-1D open sheets. This unique topology of Fermi surface drives an instability toward spin-resolved electronic charge density waves (CDWs), in which the ordering wave vectors for spin-up and spin-down electrons condense along two mutually orthogonal directions, forming spin-resolved stripe phases. As a consequence, this results in pronounced gap openings near the Fermi surface, and the superposition of these spin-resolved stripe orders leads to a checkerboard CDW in the charge channel and an antiphase spin-density-wave modulation in the spin channel. Upon increasing temperature, the density-wave order melts at $T_c$ due to thermal phase fluctuation while the gap opening persists, giving rise to a robust pseudogap regime, which eventually closes at a higher temperature $T_g$. The resulting simulations quantitatively reproduce the key features observed in the spectroscopic measurements, offering a consistent and generic understanding of the reported phenomena in KV$_2$Se$_2$O and, more broadly, in metallic altermagnets with strong spin-momentum locking.

Figures (3)

• Figure 1: Atomic and electronic structure of KV$_2$Se$_2$O calculated by DFT. ( a) Crystal unit cell of KV$_2$Se$_2$O, where red arrows indicates the spin states. ( b) Fermi surface at the $k_z = 0$ plane, where the red and blue curves corresponds to spin-up and spin-down states, respectively. ( c) Band structure without spin-orbit coupling. Red, blue, and black curves denote spin-up, spin-down, and spin-degenerate bands, respectively. The circles represent results from the tight-binding model, shown in the same color scheme as the DFT bands.
• Figure 2: ( a) Self-consistently calculated spin-resolved density-wave gap magnitudes $|\Delta_{{\bf Q}_s}|$ as functions of the ordering direction $\theta_{{\bf Q}_s}$. ( b) Quasiparticle energy spectra in the density-wave state, showing the gap opening around the Fermi surface. Red (blue) curves denote the spin-up (spin-down) bands. The darker curves represent the original quasiparticle dispersion with the gap opening, whereas the lighter curves correspond to the backfolded bands arising from particle--hole mixing induced by the density-wave order. The black dashed circles highlight the gapped regions on the Fermi surface. ( c) and ( d) Real-space density modulations $\rho_{\uparrow}$ and $\rho_{\downarrow}$ associated with the spin-up and spin-down density-wave orders, respectively. ( e) Total charge-density modulation $\rho_{\uparrow}+\rho_{\downarrow}$. ( f) Spin-density modulation $\rho_{\uparrow}-\rho_{\downarrow}$ [see Sec. SVII for more details of its incommensurate nature (Fig. SI)].
• Figure 3: Temperature dependence of the spin-resolved density-wave modulation amplitude $\rho_{\rm CDW}(T)={4V^{-1}}|\Delta_s(T)| \exp({-\langle{\delta\phi^2_s(T)}\rangle}/2)$ and the gap magnitude $|\Delta(T)|=|\Delta_s(T)|$. All physical quantities are normalized by their respective $T=0$ values, showing the thermal evolution of experimentally accessible observables upon heating and across the phase transitions. Experimental data are taken from Ref. Jiang2025 and extracted from the temperature dependence of the spectral splitting observed in NMR measurements, assuming that the splitting is proportional to the spin-resolved density order $\rho_{\rm CDW}$. Specific parameters used in our calculation are presented in Sec. SIV.