Spin–orbit–controlled flat-band transition, thermodynamic and magnetic response in a disordered Lieb-5 lattice

Abstract

Flat-band (FB) systems are characterized by strongly localized electronic states and can therefore exhibit unconventional thermodynamic and magnetic responses. Nevertheless, the role of disorder and impurity scattering in the extended Lieb-5 lattice has received limited attention. Here, we investigate how intrinsic spin–orbit coupling (ISOC) and nonmagnetic disorder jointly modify the electronic properties of this lattice within a tight-binding Green’s function approach. Disorder effects are incorporated through a self-consistent Born approximation (SCBA) treatment of the electronic self-energy. Our results demonstrate that ISOC progressively reconstructs the FB spectrum, weakening the associated spectral features and ultimately transforming the two FB structure of the pristine lattice into a single FB centered at zero energy. Disorder further reshapes the low-energy spectrum through spectral broadening and redistribution of states. These modifications strongly influence the thermodynamic and magnetic responses, leading to tunable heat capacity peaks and a paramagnetic susceptibility with disorder- and coupling-dependent amplitude. Our results demonstrate that the interplay of flat-band physics, ISOC, and impurity scattering provides an effective mechanism for engineering the spectral and magnetic characteristics of the Lieb-5 lattice, opening new perspectives for controllable FB quantum materials.