Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties.

Imagine a world in which damaged parts of the body - an arm, an eye, and ultimately a region of the brain - can be replaced by artificial implants capable of restoring or even enhancing human performance. The associated improvements in the quality of human life would revolutionize the medical world and produce sweeping changes across society. In this chapter, we discuss several approaches to the fabrication of fractal electronics designed to interface with neural networks. We consider two fundamental functions - stimulating electrical signals in the neural networks and sensing the location of the signals as they pass through the network. Using experiments and simulations, we discuss the favorable electrical performances that arise from adopting fractal rather than traditional Euclidean architectures. We also demonstrate how the fractal architecture induces favorable physical interactions with the cells they interact with, including the ability to direct the growth of neurons and glia to specific regions of the neural-electronic interface.

Experimental investigation of the breakdown of the Onsager-Casimir relations.

We use magnetoconductance fluctuation measurements of phase-coherent semiconductor billiards to quantify the contributions to the nonlinear electric conductance that are asymmetric under reversal of magnetic field. We find that the average asymmetric contribution is linear in magnetic field (for magnetic flux much larger than 1 flux quantum) and that its magnitude depends on billiard geometry. In addition, we find an unexpected asymmetry in the power spectrum of the magnetoconductance with respect to reversal of magnetic field and bias voltage.

Symmetry of two-terminal nonlinear electric conduction.

The well-established symmetry relations for linear transport phenomena cannot, in general, be applied in the nonlinear regime. Here we propose a set of symmetry relations with respect to bias voltage and magnetic field for the nonlinear conductance of two-terminal electric conductors. We experimentally confirm these relations using phase-coherent, semiconductor quantum dots.