Experimental Realization of Interfacial Fluctuations in the Kardar-Parisi-Zhang Universality Class: A Non-Orthodox Approach & Its Consequences for Kinetic-Roughening Status

The Kardar-Parisi-Zhang (KPZ) Universality Class has been helding a central, cornerstone position in the realm of non-equilibrium Physics since the seminal work of KPZ in 1986 [1]. Inspired by Landau-Ginzburg Theory from Equilibrium Statistics, KPZ proposed the simplest, local, continuum and non-linear equation to describe the dynamic of growing surfaces. Unexpectedly, since then, the KPZ class has been showing to underlie the behaviour of a rich family of equilibrium and out-of-equilibrium phenomena beyond its initial purpose. Examples touch models for protein traffic flow, global paths of random walks in random landscapes, lines in superconductors, coffe-rings' effect, besides a striking, wonderful connection to random matrices theory. While most advances have been done in $d = 1 + 1$ dimensions, tying theory, simulations and an increasing number of experiments in a KPZ triumvirate, much less attention has been paid to 2 + 1 due to the inexorable difficulties to handle mathematically, numerically and experimentally such systems. As consequence, 2D-KPZ experiments, for instance, were not convincingly demonstrated until last year [2,3]. In this talk, we show an unprecedented experimental realization of 2D-KPZ by keeping track on fluctuations at interface of CdTe thin-films grown on Si. Critical exponents are unearthed and demonstrated to agree with numerical results for 2D-KPZ models. Going further the orthodox analysis, we experimentally demonstrate that: i) An universal, rescaled Height Distribution (HD), upper dimensional counterpart of the Tracy-Widom distribution, emerge in the system. Interestingly, a non-integer Gumbel distribution seems to fit well HD data. ii) Squared Local Roughness Distributions exhibit striking agreement with numerical simulations of lattice models, revealing a new universal signature of KPZ, highlighted by its stretched exponential decay. iii) Connection with statistics of extremes provide other universal distribution for 2D-KPZ systems. In the last part, we show how to use i-iii) to uncover the possible KPZ universality in fluctuating surfaces when poor statistics and strong finite-time effects are unavoidable, a common experimental situation. We use this scheme to analyse the temperature effect on our experimental KPZ system. Finally, consequences of i-iii) into the current Kinetic-Roughening Status are addressed. \newline

The authors acknowledge support from FAPEMIG and CAPES. \newline

[1] M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. \textbf{56}, 889 (1986). \newline
[2] R. A. L. Almeida, S. O. Ferreira, T. J. Oliveira, and F. D. A. Aar?o Reis, Phys. Rev. B \textbf{89}, 045309 (2014).
[3] R. A. L. Almeida, \textit{et al.}, Europhys. Lett. \textbf{109}, 46003 (2015).