Measuring the inelastic scattering exponent of a two-dimensional electron system

Ching-Chen Yeh^1,2, Pin-Chi Liao², Yanfei Yang^1,3, Wei-Chen Lin^4,5, Alireza R. Panna¹, Albert F. Rigosi¹, Randolph E. Elmquist¹, Chi-Te Liang^2,6,7*

¹National Institute of Standards and Technology (NIST), Gaithersburg, Maryland, USA
²Physics, National Taiwan University, Taipei, Taiwan
³Graphene Waves, Germantown, Maryland, USA
⁴Taiwan International Graduate Program, Academia Sinica, Taipei, Taiwan
⁵Department of Engineering and System Science, National Tsing Hua University, Hsinch, Taiwan
⁶Taiwan Consortium of Emergent Crystalline Materials (TCECM), Taipei, Taiwan
⁷CQSE, National Taiwan University, Taipei, Taiwan

* Presenter:Chi-Te Liang, email:ctliang@phys.ntu.edu.tw

The quantum Hall effect is one of the most widely studied effects in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p and the universal exponent γ. Although previous research has primarily focused on measuring κ and inferring γ based on the assumption that p equals 2 and is independent of magnetic field, our study represents a significant leap forward by measuring all three exponents, κ, γ, and p, within a single graphene device as well as a conventional two-dimensional electron system. This work notably stands as the first to determine the inelastic scattering exponent p across both low and high magnetic fields in the quantum Hall regime. Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined κ, p, and γ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 in the high magnetic field quantum Hall regime. This measurement not only provides key insights into the mechanisms of electron scattering but also highlights the transition from the dirty limit to the clean limit, offering a fundamental understanding of the quantum Hall effect, its scaling behavior [1] and inelastic scattering of electrons that is strongly related to quantum dephasing [2].
References
[1] C.-C. Yeh et al., Phys. Rev. B 108, 205304 (2023).
[2] C.-C. Yeh et al., Phys. Rev. Lett. 133, 096302 (2024).

Keywords: Inelastic scattering exponent, Quantum Hall, Two-dimensional, Graphene, Critical exponent