Symmetry-constrained quantum coupling in non-Fermi-liquid transport

Finding the common origin of non-Fermi liquids (NFLs) transport in high-temperature superconductors (HTSCs) has proven to be fundamentally challenging due to the prominence of various collective fluctuations. Here, we propose a comprehensive non-Hermitian Hamiltonian (NHH) for quantum coupling of multiple scattering mechanisms associated with four types of order fluctuations. It predicts that the anticommutation symmetry of the spinor fermions constrains the scattering rate to a unified quadrature scaling, i.e., $\Gamma ={\Gamma }_{\mathrm{I}}+\sqrt{{\Gamma }_{\mathrm{Q}}^2+{(\mu k_{\mathrm{B}}T)}^2+{(\nu {\mu }_{\mathrm{B}}B)}^2+{({\gamma }_{E}E)}^2}$. This scaling yields a comprehensive and accurate description of two widespread NFL behaviors in HTSCs, i.e., a temperature-scaling crossover between quadratic and linear laws and the quadrature magnetoresistance, validated by several dozens of data sets for broad phase regimes. It reveals that the common origin of these behaviors is the spinor-symmetry-constrained quantum coupling of spin-wave and topological excitations of mesoscopic orders. Finally, we show that this NHH can be easily extended to other complex quantum fluids by specifying the corresponding symmetries. It is concluded that this work uncovers a critical organization principle (i.e., the spinor symmetry) underlying the NFL transport, thus providing a novel theoretical framework to advance the transport theory of correlated electron systems.