Tunable flat bands and their signatures in electronic specific heat of an Aharonov-Bohm triangular quantum network
Quantum networks composed of loop-like structures provide a rich platform for exploring electronic transport phenomena and have been widely studied in various contexts. However, their thermal response remains relatively unexplored, motivating us to investigate it in the present work. We consider a tight-binding (TB) quantum network composed of a finite number of triangular plaquettes, where neighboring plaquettes are connected through single bonds and each triangular loop is threaded by an Aharonov-Bohm (AB) flux $ϕ$. The interplay of nonuniform site coordination, hopping asymmetry, and quantum interference gives rise to both dispersive and completely flat energy levels. We derive an analytical condition involving the TB parameters under which one of the energy branches becomes independent of the electronic momentum. We further show that the AB flux $ϕ$ provides a direct means of tuning the position of the flat band. The characteristic features of the energy spectrum associated with this quantum geometry are reflected in the thermal response, which we investigate through the electronic specific heat (ESH). In particular, we demonstrate that the position of the flat band manifests itself as a distinct feature in the ESH, establishing a direct connection between the flat-band formation and the thermal response of the system. Thus, the ESH provides an alternative route for identifying the presence of a flat band, consistent with the analytical condition and the corresponding energy dispersion. Moreover, the AB flux allows the ESH to be selectively regulated through the tuning of the flat-band position. The proposed approach provides a simple complementary means of identifying momentum-independent energy levels and may be extended to other simple and complex quantum networks supporting flat bands.