Thermal signature of a helical molecule: Beyond nearest-neighbor electron hopping

We investigate, for the first time, the thermal signature of a single-stranded helical molecule that is described beyond usual nearest-neighbor electron hopping, by analyzing electronic specific heat. Depending on the hopping of electrons, two different kinds of helical systems are considered. In one case the hopping is confined within a few neighboring lattice sites which is referred to as short-range hopping helix, while in the other case, electrons can hop in all possible sites making the system a long-range hopping one. These two helices accurately emulate the structures of single-stranded DNA and protein molecules, respectively. Each helix geometry is exposed to a transverse electric field applied perpendicular to the helix axis. Due to this field, the system transforms into a correlated disordered one, resembling the well-known Aubry-Andr\'e-Harper (AAH) model. The interplay among the helicity, higher-order hopping, and the electric field has significant impact on thermal response. Our comprehensive theoretical analysis reveals that, under low-temperature conditions, the short-range hopping helix exhibits greater sensitivity to temperature compared to the long-range hopping helix system. Conversely, the scenario reverses in the high-temperature limit. The thermal response of the helices can be modified selectively by means of the electric field, and the difference between the specific heats of the two helices gradually decreases with increasing the field strength. The molecular handedness, whether left-handed or right-handed, on the other hand does not have any appreciable effect on the thermal signature. In addition, we also explore a significant application of electronic specific heat (ESH). If the helix contains a point defect, then by comparing the results of perfect and defective helices, one can estimate the location of the defect, which might be useful in diagnosing bad cells and different diseases. Finally, we discuss the results of ESH by considering the spin degree of freedom and in the context of real biological helical systems.