In this work, we present a general and direct procedure to reproduce the peculiar physics of graphene within a very simple acoustic metamaterial: a double lattice of soda cans resonating at two different frequencies. The first triangular sub-lattice generates a bandgap at low frequency, which induces a tight-binding coupling between the resonant defects of the second honeycomb one, hence allowing us to obtain a graphene-like band structure. We show that this procedure generates a lattice where both the Dirac cone and the tight-binding interaction are obtained, from a triangular configuration. We also prove the relevance of this approach by showing that both numerical and experimental dispersion relations exhibit the requested Dirac cone. We also demonstrate the straightforward monitoring of the coupling strength within the crystal of resonant defects. This work shows that crystalline metamaterials are very promising candidates to investigate tantalizing solid-state physics phenomena with classical waves.
Recent technological progress has opened new ways of exploring the quantum physics of graphene. One of them is by studying exotic quantum Hall effects observed in graphene. These effects are strictly related to the Dirac electrons in the material, with a conductance that changes dramatically in the presence of a magnetic field. The explanation of these effects relies on the Berry phase, the phase acquired by the wave function of electrons around a closed path in the Brillouin zone. This phase can be related to the winding number of a vector field on a two-dimensional space. In this case, the Berry phase quantitatively describes how much the electron wave function changes when the magnetic field is varied. In the language of solid-state physics, the Berry phase corresponds to the Aharonov-Bohm effect. Experiments have been performed to measure the Berry phase of an electron in a magnetic field, but the challenge is to insert the electron in the material. Recent progress in the fabrication of graphene have enabled the creation of a quasi-permanent magnetic field in graphene by surrounding it with a superconducting loop15. This technique could allow to measure the Berry phase of an electron in graphene. In this work, we show that such a measurement would not be easy to perform because the Berry phase is very small. We also discuss the possibility to measure the Berry phase in a different way by adding an electric field in the material through a gate electrode. Interestingly, the Berry phase depends on the relative position between the magnetic field and the electric field.
These tools are powerful, and plenty of people use them. One very simple way to create a spreadsheet is to use Microsoft Excel. This tutorial shows you how to get a couple of useful functions to help you with your spreadsheets.
The next function is called RAND(). This is a useful way to randomly select numbers to use in your spreadsheet. For example, if you wanted to create a list of numbers to make a random password or generate a random phone number then you could use this function. For more information about the RAND() function you can use the following link: Find out more . 827ec27edc