Transmission Lines and Metamaterials Based on Quantum Hall Plasmonics

Abstract

The characteristic impedance of a microwave transmission line is typically constrained to a value Z0 = 50 Ω, in-part because of the low impedance of free space and the limited range of permittivity and permeability realizable with conventional materials. Here we suggest the possibility of constructing high-impedance transmission lines by exploiting the plasmonic response of edge states associated with the quantum Hall effect in gated devices. We analyze various implementations of quantum Hall transmission lines based on distributed networks and lumped-element circuits, including a detailed account of parasitic capacitance and Coulomb drag effects, which can modify device performance. We additionally conceive of a meta-material structure comprising arrays of quantum Hall droplets and analyze its unusual properties. The realization of such structures holds promise for efficiently wiring-up quantum circuits on chip, as well as engineering strong coupling between semiconductor qubits and microwave photons.

Transmission lines and resonators based on quantum Hall plasmonics: Electromagnetic field, attenuation, and coupling to qubits

“…From a microwave engineering perspective, the complicated structure of the fields means that the choice of the reference potential is not unique, and so the definition of the characteristic impedance Z 0 of the device can vary [16]. For example, the characteristic impedance can be defined from the microwave S-parameters [11,15,45] by setting it equal to the values of the impedance of the external circuit that minimizes reflection at the electrodes. Using this approach in capacitively coupled QH devices, one obtains [15]…”

“…Materials in the QH regime have another interesting property, which was sometimes overlooked, that is they exhibit a large voltage drop between opposite edges when a low current is applied. This high voltage to current ratio is related to the large value of the quantum of resistance, h/e 2 ∼ 25kΩ; for this reason, it was pointed out that the QH effect can be exploited to manufacture low-loss transmission lines and resonators with a high characteristic impedance [15]. The characteristic impedance of these devices was estimated to be proportional to the resisitance quantum, and so orders of magnitude higher than the typical value ∼ 50Ω of microwave circuits [16].…”

“…The physics of EMPs has been studied in depth in a variety of different cases [36][37][38][39][40][41][42][43][44][45][46][47]. We use here a semiclassical model that captures the main features of these excitations and we adapt it to describe actual devices, such as the ones in [15]. In particular, we study in detail the electromagnetic field propagating in these devices, with a particular focus on the effect of the metal electrodes and of the externally applied AC voltage sources.…”

“…We also consider the effect of the Coulomb drag between EMPs propagating at different edges of a nanowire. With this analysis, we are able to justify the model of EMP propagation used in [15], and to quantify its phenomenological parameters.…”

“…In Subsec. II A, we introduce a simple approximation scheme, which allows to find a solution for the electromagnetic field that is accurate sufficiently far from the edge of QH material; we then use this solution to describe the physics of capacititively coupled QH effect devices and to justify the treatment used in [15]. In Subsec.…”