Kinetic inductance, also known as AC inductance, refers to the ability of an electrical circuit to store energy over time through the conversion of magnetic fields into electrical currents. It is a property that arises due to the interactions between charged particles in the circuit.
(what is the fundamental origin of kinetic inductance in graphene)
In graphene, a two-dimensional material made from carbon atoms arranged in a hexagonal lattice, the electrons behave differently compared to classical metals. One of the unique features of graphene is its electronic band structure, which consists of discrete energy levels along the x and y axes. This means that the electrons in graphene can move collectively or individually through the material without interacting with each other.
One way in which this property affects the behavior of charge carriers in a graphene-based circuit is through the creation of kinetic inductance. When an electron moves through a graphene sheet, it creates a voltage drop across the sheet, which in turn generates an electric current. However, this current is not directly proportional to the voltage drop, but rather depends on the relative orientation and movement of the electrons in the sheet. As the electrons become more randomly distributed throughout the sheet, the voltage drop decreases, resulting in less kinetic inductance.
This effect can be visualized by creating a simple circuit diagram where an electron moves through a graphene sheet with constant speed v and changes direction periodically in one dimension (x). The displacement vector d of the electron at any given instant is described by the position vector p, which contains information about the electron’s velocity and direction. The kinetic inductance L of the circuit can then be calculated using the formula:
L = e^2 / (4πε_0v^2) * [d^3 / (3h^2)]/dθ
where e is the elementary charge, ε_0 is the permittivity of free space, h is the Planck constant, and θ is the angle between the displacement vector d and the wavevector k. This formula shows that the kinetic inductance of the circuit increases as the spacing between the electrons becomes smaller, and decreases as the sheet becomes thicker. This behavior is similar to what occurs in many types of circuits, including metallic conductors and semiconductor devices.
(what is the fundamental origin of kinetic inductance in graphene)
In conclusion, the fundamental origin of kinetic inductance in graphene lies in its unique electronic band structure, which allows for the random movement of charge carriers through the material without direct interaction with each other. By controlling the speed and direction of these charge carriers, engineers can tailor the performance of their graphene-based circuits, from low-frequency devices to high-performance wireless networks.
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