Measuring and Tuning the Potential Landscape of Electrostatically Defined Quantum Dots in Graphene

Abstract

We use Kelvin probe force microscopy (KPFM) to probe the carrier-dependent potential of an electrostatically defined quantum dot (QD) in a graphene/hexagonal boron nitride (hBN) heterostructure. We show that gate-dependent measurements enable a calibration scheme that corrects for uncertainty inherent in typical KPFM measurements and accurately reconstructs the potential well profile. Our measurements reveal how the well changes with carrier concentration, which we associate with the nonlinear dependence of graphene's work function on carrier density. These changes shift the energy levels of quasi-bound states in the QD which we can measure via scanning tunneling spectroscopy (STS). We show that the experimentally extracted energy levels closely compare with wave functions calculated from the reconstructed KPFM data. This methodology, where KPFM and STS data are simultaneously acquired from 2D materials, allows the quasiparticle response to an electrostatic potential to be determined in a self-consistent way.

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules

“…1b) avoids the 100% transmission occurring at normal incidence. This allows for the formation of quasi-bound states in graphene QDs, which have been confirmed in previous experiements 6,[8][9][10][11][12]14,15 . In zero B, the clockwise and counterclockwise quasibound states possessing the same radial quantum number (𝑛) and angular quantum numbers (±𝑚) are degenerate due to time reversal symmetry.…”

“…They have been widely studied over the last 40 years in semiconductors and have provided immense fundamental insight [3][4][5] . Recently, the confinement of massless Dirac fermions in electrostatically defined QDs has been achieved in graphene [6][7][8][9][10][11][12][13][14][15] and topological insulators 16 . Different from semiconductor QDs formed with massive Schrödinger fermions, QDs populated by massless Dirac fermions can be viewed as artificial relativistic atoms, thus offering a unique opportunity to study atomic properties in the ultra-relativistic regime.…”

Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids

“…The p-n barrier can be observed as the bright (dark) ring in the 4.5 K (77 K) measurements. The same ring feature has been determined in previous scanning tunneling spectroscopy and Kelvin probe force microscopy measurements to indicate the position of the classical turning point of the quasibound states, where there is an accumulation of quasiparticle density ( 44 , 71 – 73 ). It is not fully understood why the p-n boundary appears bright for measurements at 4.5 K but dark at 77 K. This effect was observed in multiple separate measurements, and we speculate that STP is sensitive to thermovoltages generated on the p-n boundary because of strong tip-induced resonances in the local density of states ( 72 , 74 , 75 ).…”

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

“…Since its first application in 1991 [2], there have been significant developments in the field of KPFM [6,9,10] with significant advances in both temporal [11][12][13][14] and spatial resolution [13,[15][16][17][18][19]. These advances have enabled investigations mapping light-induced surface potential dynamics [20], ferroelectric domains [19], individual quantum dots [21,22], and even submolecular charge distributions [23][24][25][26][27]. These applications demonstrate that KPFM is capable of atomic-scale spatial resolution and nanosecond time resolution under specific conditions.…”

“…OL techniques avoid the limitations and artefacts that can arise when using a feedback loop, for example, bandwidth limitations due to the time constant of the feedback loop [29], increased noise [36,37], and electrical crosstalk [38,39]. Whilst the application of DC bias is not required for OL operation it can still be utilized to allow CPD to be determined via bias sweeps [28,40] or to investigate gate-dependent potential profiles of interfaces [22,41,42]. There are a wide range of OL KPFM techniques beyond those examined in this paper, including pump-probe KPFM [13,20,43], time-resolved KPFM [11,12,[44][45][46][47], fast free force recovery KPFM (G-Mode) [14,[48][49][50], intermodulation electrostatic force microscopy (EFM) [42,51], and PeakForce tapping KPFM [52].…”