Thermal stability of pair density wave in a $d$-wave altermagnetic superconductor

Abstract

We study finite-momentum superconductivity in a two-dimensional $d$-wave altermagnetic superconductor using a non-perturbative Monte Carlo approach beyond mean-field theory. We show that altermagnetism stabilizes a pair density wave (PDW) state without external magnetic fields and enables its survival at finite temperatures with robust phase coherence. Our results establish altermagnetism as a promising route to realizing thermally stable PDW superconductivity and identify clear thermodynamic and spectroscopic signatures.

Figures (5)

• Figure 1: Ground state phase diagram of $d$-wave altermagnetic superconductor in the $t_{am}-h$-plane showing the BCS, QBP, PDW, LO and PFL phases along with the corresponding transition scales (solid lines with points).
• Figure 2: Mean field estimates of the thermodynamic and spectroscopic quantities at selected $t_{am}-h$ cross sections. (a) Pairing field amplitude ($\vert \Delta\vert$), (b) pairing momentum ($q=\sqrt{q_{x}^{2}+q_{y}^{2}}$), (c) magnetic polarization ($m$), (d) real space maps of the pairing field amplitude at representative fields corresponding to BCS, PDW, 1D-LO and 2D-LO phases, (e)-(f) spin resolved low energy spectral weight distribution ($A_{\sigma}({\bf k}, 0)$) mapping out the underlying Fermi surface, (g) single particle DOS ($N(\omega)$) at the representative $t_{am}-h$ cross sections.
• Figure 3: Thermodynamic and spectroscopic signatures in the BCS and PDW phases at representative $t_{am}-T$ cross sections and $h=0$. (a), (c), (e) real space maps corresponding to the thermal evolution of the pairing field amplitude $\vert \Delta_{ij}\vert$ at the selected values of $t_{am}=0$, $t_{am}=1t$ and $t_{am}=1.4t$, respectively. (b), (d), (f) thermal evolution of the phase correlation ($\cos(\phi_{0}^{x}-\phi_{ij}^{x})$) at $t_{am}=0$, $t_{am}=1t$ and $t_{am}=1.4t$, respectively. (g)-(i) corresponding single particle DOS as a function of temperature. (j)-(k) real space maps for the thermal evolution of $\vert \Delta_{ij}\vert$ and $\cos(\phi_{0}^{x}-\phi_{ij}^{x})$ at a Zeeman field of $h=1.0t$ and $t_{am}=1.0t$.
• Figure 4: Thermal phase diagram as obtained from the variational mean field theory, showing the BCS and PDW phases and the corresponding thermal scales $T_{c}^{BCS}$ and $T_{c}^{PDW}$. Note that while the thermodynamic phases and the order of phase transitions are well captured by MFT, the thermal scales are overestimated.
• Figure 5: The thermal evolution of the PDW state at $t_{am} = 1.0t$ and $h = 0.0$. Top row: Spatial maps corresponding to the pairing amplitude $\vert \Delta_{ij}\vert$. Bottom row: Zero-energy spectral weight distributions $A({\bf k}, 0)$ that demonstrate the reconstruction of the Fermi surface.