Mirror-Selective Quasiparticle Interference in Bilayer Nickelate Superconductor

Abstract

The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates has garnered significant attention. In this study, inspired by recent STM experiments on thin films, we investigate the quasiparticle interference (QPI) characteristics of bilayer nickelates in both normal and superconducting states to identify their Fermiology and pairing symmetry. We demonstrate that the mirror symmetry inherent in the bilayer structure induces mirror-selective quasiparticle scattering by establishing selection rules based on the mirror properties of impurities and the mirror eigenvalues of electronic wavefunctions. This mirror-selective scattering allows for the differentiation of distinct Fermiologies, as QPI patterns vary markedly between scenarios with and without the $d_{z^2}$-bonding Fermi surface (FS). Furthermore, it enables the separate detection of sign changes in superconducting gaps both within the same FS and between different FSs. Crucially, if the mirror-symmetry-enforced selection rules are ignored, the QPI response of an $s_\pm$-wave state can masquerade as that of a conventional $s$-wave state, leading to a misidentification of the pairing symmetry. When combined with field-dependent and reference QPI measurements, this approach facilitates the precise determination of pairing symmetry, even in the presence of FS-dependent gaps and gap anisotropy. Additionally, we discuss practical considerations for STM measurements to effectively identify the pairing symmetry. Our findings demonstrate that mirror-selective QPI is a powerful tool for distinguishing between different Fermiologies and pairing states, which is helpful in pinning down pairing symmetry and revealing the pairing mechanism in bilayer nickelates.

Figures (5)

• Figure 1: Bilayer structure and Fermi surface for bilayer nickelates. (a) The mirror-symmetric bilayer structure. Each site hosts two $3d$ orbitals $d_{x^2-y^2}$ and $d_{z^2}$ of the nickel atom. (b) The band structure of the Hamiltonian described in Eq. \ref{['main_eq_Hamiltonian']}. $\mu_1$ and $\mu_2$ represent pristine filling $n=3.0$ and filling $n=2.7$, respectively. (c)-(d) Two types of Fermiologies with $\mu_1=0$ and $\mu_2=-0.1433$. The corresponding vector ${\bf{{q}}}_{i,j}$ means $j$-th vectors at Fermi level $\mu_i$. In (b)-(d), red and blue mean the states are the bonding and antibonding states. From the $\Gamma$ to the M, the Fermi surfaces are labeled as $\alpha$, $\beta$, and $\gamma$, respectively. Red arrows and Blue arrows represent vectors connecting FS segments with same and different mirror eigenvalues.
• Figure 2: FT-QPI intensity $|\delta\rho({\bf{{q}}},\omega=0)|$ in Eq. \ref{['main_eq_normalQPI']} of normal state for three types of impurities. (a)-(c) QPI patterns for $V_1$, $V_2$, and $V_3$ without the $\gamma$-FS. For mirror-odd impurity $V_2$, we calculate the layer-dependent QPI. (d)-(f) Same quantities as (a)-(c), but with the $\gamma$-FS. In calculation, we adopt a $1001\times 1001$ lattice sites and $v_0=0.25$.
• Figure 3: QPI intensity for three types of pairing symmetries and nonmagnetic impurities without the $\gamma$-FS. (a) The $s$-wave gap amplitude on the Fermi surface. (b)-(d) the QPI intensity $|\delta\rho^{\text{odd}}({\bf{{q}}},\omega)|$ for three types impurities measured at the superconducting gap $\Delta_0$. (e)-(h) and (i)-(l) are the same quantities as (b)-(d), but for $s_\pm$-wave and $d_{x^2-y^2}$-wave. (f)-(h) are measured at $\omega=\Delta_0$, and (i)-(l) are measured at $\omega=\Delta_0/2$. The strength of impurity is set to be $v_0=0.25$.
• Figure 4: The QPI intensity $Z({\bf{{q}}},\omega)$ on the top layer with renormalized impurities potential $T_t(\omega)$. (a)-(c) $Z({\bf{{q}}},\omega)$ for three representative pairing symmetries without the $\gamma$-FS. For $s$ and $s_\pm$-wave pairing, the QPI are measured at $\omega=\Delta_0$. For $d_{x^2-y^2}$-wave pairing, the QPI are measured at $\omega=\Delta_0/2$. (d)-(f) the same quantities but for the case with the $\gamma$-FS.
• Figure 5: Field dependent and reference QPI (a)-(b) Magnetic field-induced change in QPI pattern $|Z_{B=B_0}({\bf{{q}}},\omega)|-|Z_{B=0}({\bf{{q}}},\omega)|$ for $s_\pm$-wave and $d_{x^2-y^2}$-wave pairing. The strength of the nonmagnetic impurity is $v_0=0.25$, and the strength ratio between the vortex impurity and the nonmagnetic impurity is $2$. (c) The PR-QPI intensity $\delta \rho_{\text{PR}}({\bf{{q}}},\omega=-|\Delta_\alpha|)$ induced by top layer nonmagnetic impurity in Eq. \ref{['main_eq_PRQPI']} for $s_\pm^*$-wave pairing without hole doping. (d) The integrated QPI intensity $\delta\rho^{\text{odd}}$ around ${\bf{{q}}}_{1,2}$ for for $s^*_{++}$-wave and $s_\pm^*$-wave pairing. The parameters are set to be $\{\Delta_\alpha,\Delta_\beta\}=\{0.6\Delta_0,\Delta_0\}$.