Uncertainties in Gapped Graphene

TL;DR

This paper investigates how energy gaps in monolayer graphene influence quantum uncertainties, revealing effects like spreading and zitterbewegung, and discusses how these uncertainties can be controlled by tuning the gap parameter.

Contribution

It provides a detailed analysis of the time-dependent uncertainties in gapped graphene and highlights the role of the energy gap and Compton-like wavelength in controlling quantum fluctuations.

Findings

Uncertainties are affected by spreading and zitterbewegung phenomena.

Energy gap influences uncertainties via the Compton-like wavelength.

Uncertainties can be controlled by adjusting the gap parameter.

Abstract

Motivated by graphene-based quantum computer we examine the time-dependence of the position-momentum and position-velocity uncertainties in the monolayer gapped graphene. The effect of the energy gap to the uncertainties is shown to appear via the Compton-like wavelength $\lambda_c$. The uncertainties in the graphene are mainly contributed by two phenomena, spreading and zitterbewegung. While the former determines the uncertainties in the long-range of time, the latter gives the highly oscillation to the uncertainties in the short-range of time. The uncertainties in the graphene are compared with the corresponding values for the usual free Hamiltonian $\hat{H}_{free} = (p_1^2 + p_2^2) / 2 M$. It is shown that the uncertainties can be under control within the quantum mechanical law if one can choose the gap parameter $\lambda_c$ freely.