Electron-Hole Crossover in Graphene Quantum Dots

We investigate the addition spectrum of a graphene quantum-dot in the vicinity of the electron-hole crossover as a function of perpendicular magnetic field. Coulomb-blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the $n=0$ Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.

Figure 1

(a) SFM image of the graphene QD device with source (S) and drain (D) leads, and lateral plunger gate (PG). (b) Schematic level structure of the QD device highlighting the constriction induced tunneling barriers and the electron-hole crossover. (c) Back-gate (BG) dependent conductance at $V_b=4\mathrm{mV}$, where transport is tuned from the hole ($h$) to the electron ($e$) regime. (d) Conductance as a function of bias and BG voltages exhibiting the energy gap of the tunneling barriers [see panel (b)]. (e) Source-drain current as a function of PG and BG at $V_b=100\mu \mathrm{V}$. The slope of the dashed line corresponds to the relative PG-BG lever arm ([A] and [B] mark regions studied in more detail below).

Figure 2

(a) Evolution of Coulomb-blockade resonances in perpendicular magnetic field. The conductance is plotted as a function of plunger gate voltage $V_{\mathrm{pg}}$ and magnetic field $B$ ($V_b=100\mu \mathrm{V}$). (b) Coulomb diamond measurements at $B=0\mathrm{T}$. (c) Close-up of the box in (b) highlighting the rich excited state spectra. (d) Close-up of Fig. 1e (see box therein) showing (Coulomb) resonances (with lever arms ${\alpha }_{1,2}$; dashed lines) as a function of PG and BG ($V_b=100\mu \mathrm{V}$). The solid line [A] at $V_{\mathrm{bg}}=-0.9\mathrm{V}$ marks the regime where (a) and (b) have been measured [see also [A] in Fig. 1e].

Figure 3

(a) Calculated levels of a graphene QD (see inset) as a function of magnetic field. Arrows mark the lowest Landau level ($E_0$), i.e., the electron-hole crossover at $n=0$. (b) Close-up of dashed box in panel (a), where spin, Zeeman splitting and a constant charging energy of 18 meV are included. (c) Experimental data. The peak positions are extracted from the measurements shown in Fig. 2a. The scale bar corresponds to 100 meV. (d) Average peak-to-peak spacing as a function of $B$ for the two different regimes [A] (circles) and [B] (triangles) highlighted in Fig. 1e, solid [A] and dashed [B] are calculated from (b).