Topological Insulators are new states of matter. At first sight, these are just ordinary band insulators : an energy gap separates the energy of states occupied by electrons from unoccupied states. However, the ensemble of occupied electronic states possesses a non-intuitive property, known in mathematics as a topological property. Its existence is at the origin of the main physical characteristics of topological insulators: the existence of metallic states at their surface. Hence from a phenomenological point of view the topological insulators are insulating materials surrounded by a metallic surface. Moreover these surface metals are rather unique: their electrons behave as if they were massless relativistic particles. More precisely their motion is described by a Dirac equation usually associated with relativistic particles. This leads to several unique physical properties, some of them reminiscent of those of graphene. Recently, this relation between relativistic excitations and topological property triggered a large amount of work to identify other phases with analogous properties. Excitations described by a Dirac or Weyl equation of motion have now been found in bulk materials and not only at the surface of insulators.

Novel nanoelectronic devices provide fantastic opportunities for electronic systems, offering new features in an energy efficient way. However, they also possess less desirable features like high variability and low reliability. Interestingly, Biology has to face similar issues, as the brain has to compute exploiting largely imperfect nanodevices. In this talk, I will show how Biology can therefore be an inspiration for novel circuits that leverage the physics of nanoelectronics, with examples based on three physical systems:
- emerging memory devices ("memristors") used as synapses in learning systems
- stochastic nanodevices from spin electronics used for low power computation
- stochastic resonance-based nanocircuits that work by exploiting thermal noise.

I will show that these ideas could allow systems capable of complex cognitive tasks in a power efficient way. They could thus ideally complement traditional microelctronics, for the tasks where it is the least efficient.

Producing a magnetic resonance (MR) probe with single spin sensitivity and imaging capabilities would provide great insight into the nanoscale workings of interesting scientific samples, with applications ranging from healthcare to quantum information. In this talk I will give an overview of the significant progress in recent years in both ESR and NMR measurements using the nitrogen vacancy (NV) centre in diamond. In particular, I will discuss recent work done at the University of Melbourne to achieve nanoscale MR via monitoring the relaxation rate of the NV centre. In addition to potentially giving significant sensitivity improvements, this is a vastly simpler technique than previous protocols, eliminating the requirement for highly precise control of the NV centre. This opens up the prospects of high sensitivity NMR in challenging environments such as within living cells.

Surface plasmon polaritons (SPPs) are bosonic quasiparticles. As such, they show specific quantum properties, some of which have already been observed. Here we report experimental results from two sets fundamental tests on SPPs : a clear observation of the wave-particle duality of a single SPP, and a first direct experimental evidence of entanglement between a SPP and a single photon. Both our experimental setups are based on a plasmonic platform that can convert photon into plasmon, and separate or recombine them on a plasmonic beamsplitter. This platform is used as output beamsplitter of a Mach-Zehnder (MZ) interferometer. We use a source of photon pairs in order to shine the platform with a single photon α, heralded by the second photon of the pair, β. In the first experiment, the polarization of α is chosen so that it excites either one single arm, or both arms of the MZ with equivalent probabilities, thus exhibiting either antibunching (particle-like behaviour) or interferences (wave-like behaviour). In the second experiment, α and β are entangled. By carrying out a projective measurement of the polarization of β, we show that we can control the interference state of the single SPP on the plasmonic platform, and make fringes appear or disappear in the interferograms, thus demonstrating entanglement between both particles.

Recently, there has been observed several connections of integrable models to supersymmetric gauge theories. One of such connections is a correspondence between supersymmetric quiver gauge theories and integrable lattice models such that the integrability emerges as a manifestation of supersymmetric dualities. Particularly, partition functions of three-dimensional N = 2 supersymmetric quiver gauge theories on different manifolds can be identified with partition functions of two-dimensional exactly solvable statistical models. Using this relationship one can obtain new solutions of the star-triangle relation and other forms of the Yang-Baxter equation.

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