An Overview of Random Matrix Theory Applications in Organic Electronics
Dan Dougherty (NCSU Physics)
Disorder is prevalent in all organic electronic devices in the form of structural defects, chemical impurities, and random interfaces with external structures like electrodes or gate dielectrics. Many of our most important engineering challenges are associated with controlling and properly characterizing disorder. In this seminar I want to step back from the applied and ask: What important basic questions about complex condensed matter systems can be addressed through the unique materials systems arising in organic electronics. I focus attention on the implications of the random matrix theory approach to observables in semiconducting polymer and small molecule systems.
Random matrix theory has been called “a new kind of statistical mechanics”  where the plan is to consider not the the detailed solution to a specific many-body Hamiltonian, but rather the universal properties of an ensemble of random Hamiltonians with appropriate symmetry constraints. Remarkably, the statistical distributions of eigenvalues, eigenvalue spacings, and correlations functions can have simple generic forms that are the same for vastly different physical systems. After giving some background on disorder in organic semiconductors, I will give an overview of some of the key results in Random Matrix Theory. These will be motivated by organic electronic materials and I will mention the few examples where random matrix tools have already been explicitly used [2,3,4] and give my thoughts about experiments that might reveal whether these tools are useful more broadly.
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Rivnay et al., Phys. Rev. B 83, 121306R (2011).
Noriega et al., Nat. Materials 12, 1038 (2013).
Welborn et al., Phys. Rev. B 88, (2013).