Frustrated supercritical collapse in tunable charge arrays on graphene

Jiong Lu,Alex Zettl,Vitor M Pereira,Takashi Taniguchi,Sebastian Wickenburg,Dillon Wong,Arash A Omrani,Alpin N Tatan,Alexander Riss,Erik Piatti,Hsin-Zon Tsai,Kenji Watanabe,Michael F Crommie

doi:10.1038/s41467-019-08371-2

Abstract

The photon-like behavior of electrons in graphene causes unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential. We report bottom-up synthesis of atomically-precise one-dimensional (1D) arrays of point charges on graphene that allow exploration of a new type of supercritical confinement of graphene carriers. The arrays were synthesized by arranging F4TCNQ molecules into a 1D lattice on back-gated graphene, allowing precise tuning of both the molecular charge and the array periodicity. While dilute arrays of ionized F4TCNQ molecules are seen to behave like isolated subcritical charges, dense arrays show emergent supercriticality. In contrast to compact supercritical clusters, these extended arrays display both supercritical and subcritical characteristics and belong to a new physical regime termed “frustrated supercritical collapse”. Here carriers in the far-field are attracted by a supercritical charge distribution, but their fall to the center is frustrated by subcritical potentials in the near-field, similar to trapping of light by a dense cluster of stars in general relativity.

Highlights

The photon-like behavior of electrons in graphene causes unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential
Our FET devices were fabricated by placing a CVDgrown graphene monolayer on top of a hexagonal boron nitride (h-BN) flake resting on an SiO2 layer covering a doped Si wafer, the latter providing an electrostatic back-gate
The template consists of electronically inert 10,12-pentacosadiynoic acid (PCDA), a linear chain molecule that self-assembles into monolayer-high islands on graphene with perfectly straight edges[17] (Fig. 1a)

Summary

Introduction

The photon-like behavior of electrons in graphene causes unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential. Trapping electrons by placing point charges on graphene is formally analogous to trapping light by a gravitational field: something only possible near extremely dense matter[4] Such localization, is possible for graphene around very strong Coulomb centers in the so-called supercritical regime[5,6,7,8,9,10], which allows a degree of localization otherwise impossible to achieve in pristine graphene. For intermolecular separations less than the screening length, our simulations reveal the emergence of a new type of collective supercritical state with energy near the Dirac point This frustrated supercritical state is seen theoretically even for systems composed of only twopoint charges and the wavefunction spread scales with intercharge separation. This behavior is shown to be nearly equivalent to a general relativistic treatment of trapped light

Methods

Results

Conclusion