Electronic Fractals in Quantum Materials

Forrest Simmons, Purdue University

Abstract

Surface probes are producing a huge variety of spatially resolved images of materials during phase transitions. These images have complex pattern formation present across a variety of length scales. Here, I apply image cluster scaling analysis and machine learning to several such images, First, I apply cluster analysis techniques to charge stripe orientations in Bi2−zPbzSr2−yLayCuO6+x. Our experimental collaborators observe stripes with period 4a0 in Bi2−zPbzSr2−yLayCuO6+x. [1] The local orientation of these stripes forms complex patterns from which we extract relationships involving cluster sizes. We compare these experimental exponents to those computed at a phase transition in the following models: 2D percolation and the 2D and 3D clean and random field Ising models. We find that only the 3D clean and random field Ising models are consistent with the data. Combined with the stability of these exponents across the superconducting region, we conclude that the system is in the random field Ising model universality class. We apply these same cluster techniques to period-4 antiferromagnet order in NdNiO3. [2] Our experimental collaborators observed the intensity for 2 of 8 possible directions for period-4 antiferromagnetic order in NdNiO3 and find complex pattern formation that remains after a temperature cycle past the hysteresis loop. We threshold this experimental data and extract cluster exponents for this system. We then compare these models to the 4-state clean and random field clock models. This exponent comparison shows that the 4-state random field clock model is a match for the experimental data. We then train a convolutional neural network to distinguish the 4-state clean and random field clock models. The fit neural net is capable of labeling our entire testing dataset of 16000 images with 100% accuracy. This gives us a 95% confidence interval of (0.9998, 1) by the rule of three. [3] We then split the field of view into 52 sliding windows of the original experimental data which we feed into the trained model. The model classifies every input window as a 2D random field clock model which gives us a 95% confidence interval of (0.94, 1). The observed hysteresis in the experimental data, the cluster analysis and the machine learning prediction clearly show the observed patterns are in the random field 4-state clock model universality class.

Degree

Ph.D.

Advisors

Carlson, Purdue University.

Subject Area

Artificial intelligence|Mathematics

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