Quantifying the Charge Carrier Interaction in Metallic Twisted Bilayer Graphene Superlattices

Abstract

The mechanism of charge carrier interaction in twisted bilayer graphene (TBG) remains an unresolved problem, where some researchers proposed the dominance of the electron–phonon interaction, while the others showed evidence for electron–electron or electron–magnon interactions. Here we propose to resolve this problem by generalizing the Bloch–Grüneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch–Grüneisen equation power-law exponent, p, exhibits exact integer values for certain mechanisms. For instance, p = 5 implies the electron–phonon interaction, p = 3 is associated with the electron–magnon interaction and p = 2 applies to the electron–electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as p→1, which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch–Grüneisen equation, where we propose that p is a free-fitting parameter. We found that TBGs have a smoothly varied p-value (ranging from 1.4 to 4.4) depending on the Moiré superlattice constant, λ, or the charge carrier concentration, n. This implies that different mechanisms of the charge carrier interaction in TBG superlattices smoothly transition from one mechanism to another depending on, at least, λ and n. The proposed generalized Bloch–Grüneisen equation is applicable to a wide range of disciplines, including superconductivity and geology.

Classifying Charge Carrier Interaction in Highly Compressed Elements and Silane

“…For instance, deduced ( Figure 2 a) has a very clear physical interpretation. At the same time, the deduced value ( Figure 2 c) has no any meaningful interpretation, as recently showed in Reference [ 46 ]. Moreover, since our primary purpose is to reveal the dominant charge carrier interaction mechanism, it cannot be revealed when p = 5 (fixed), because this condition means that the data analysis is performed with assumption of pure electron–phonon charge carrier interaction.…”

“…Jiang et al [ 45 ] and later Talantsev [ 44 , 46 ] proposed to reveal the type of the charge carrier interaction in metallic substances using a generalized version of the Bloch–Grüneisen equation [ 44 , 45 , 46 ]: where is the characteristic temperature and p is a free-fitting parameter. It should be noted that for some R ( T ) curves analyzed below we used a fixed p = 5 value in Equation (2), and for these cases the designation of is kept for the Debye temperature designation.…”

“…However, pure electron–phonon cases for elemental copper and silver, and also high-entropy alloy (ScZrNb) 0.65 [RhPd] 0.35 (i.e., free-fitting ), for which deduced is very close to the values measured by independent techniques, and pure electron–magnon cases for elemental iron and Sr 2 Cr 3 As 2 O 2 (i.e., free-fitting ) can be found in Refs. [ 44 , 45 , 46 ].…”

“…Thus, the dominant charge carrier interaction mechanism in the given materials can be determined from the comparison of the deduced free-fitting parameter p with the theoretical values for pure cases ( Table 1 ). Because all considered R ( T ) datasets were measured for superconductors, we used the recently proposed equation in [ 44 , 46 ] to fit the full R ( T ) curve, including the superconducting transition: where is the free-fitting parameter of the onset of superconducting transition, R norm is the sample resistance at the onset of the transition, is the Heaviside step function, I 0 (x) is the zero-order modified Bessel function of the first kind, and F is a free-fitting dimensionless parameter. R ( T ) data-fits to Equations (2) and (3) have been performed by using the Levenberg–Marquardt algorithm in the non-linear fitting package of the Origin software (version Origin2017, OriginLab Corp., Northampton, MA, USA) package.…”

“…Jiang et al [42] and later Talantsev [41,43] proposed to reveal the type of the charge carrier interaction in metallic substances using a generalized version of the Bloch-Grüneisen equation [41][42][43]:…”