Observation of excited states in a graphene quantum dot

Abstract

We demonstrate that excited states in single-layer graphene quantum dots can be detected via direct transport experiments. Coulomb diamond measurements show distinct features of sequential tunneling through an excited state. Moreover, the onset of inelastic co-tunneling in the diamond region could be detected. For low magnetic fields, the position of the single-particle energy levels fluctuate on the scale of a flux quantum penetrating the dot area. For higher magnetic fields, the transition to the formation of Landau levels is observed. Estimates based on the linear energymomentum relation of graphene give carrier numbers of the order of 10 for our device.Graphene [1,2], the first real two-dimensional (2D) solid, consists of a hexagonal lattice of carbon atoms providing highly mobile electrons [3,4] for future applications in electronics, spintronics [5] and information processing [6]. However, confinement of charge carriers in graphene cannot be achieved as easily as in conventional two-dimensional electron gases by using electrostatic gates because of the gapless nature of graphene [2] and a relativistic phenomenon called Klein tunneling [7,8]. Cutting graphene into a desired geometry is an alternative to overcome this obstacle. Well-controlled nanostructures, such as nanoribbons [9, 10, 11], quantum interference devices [12,13,14], and single-electron transistors [15,16,17] have been created in several labs to date. Small spin-orbit and hyperfine interactions have been theoretically predicted [18], promising spin decoherence times superior to the GaAs material system in which solid-state spin qubits are most advanced today [19,20]. Therefore, the identification of individual orbital quantum states, well established in GaAs quantum dot devices, have so far remained on the wish list of physicists aiming at quantum information processing with graphene.An atomic force microscope image of our quantum dot (QD) is shown in Fig. 1a. It was fabricated with the standard procedure: Mechanical exfoliation of natural graphite led to single-layer graphene flakes. The desired structure was defined with electron beam lithography and subsequently cut using reactive ion etching based on Ar and O 2 . Contacts were also defined with electron beam lithography; then gold contacts were evaporated on top [15]. The single layer quality was experimentally verified with Raman spectroscopy [21]. The QD device consists of two about 60 nm and 70 nm wide graphene constrictions separating source (S) and drain (D) contacts from the graphene island (diameter 140 nm). The island can be tuned by a nearby plunger gate (PG), whereas the overall Fermi level is adjusted with a highly doped silicon back gate (BG). The sample was annealed for about 24 hours at 400 K directly before cool down. The experiments were carried out in a dilution refrigerator at a base temperature of 40 mK. Measuring the current I through the QD as a function of back gate voltage V bg allows us S D 200nmCurrent ( to identify a transport gap [15] extending roughly from V bg ...

Electronic Excited States in Bilayer Graphene Double Quantum Dots

“…Assuming a QD diameter of d = 50 nm, which is in reasonable agreement with the lithographically defined QD we obtain a constant (carrier number independent) level spacing of ∆ = 1.71 meV, which is in good agreement with the experimental data. The charge carrier number independent level spacing is in contrast to single-layer graphene QDs where the singleparticle level spacing, ∆(N ) =hv F /d √ N , depends on the number of carriers, N [16]. In Figure 4g we show the single-level spacing for a 50 nm diameter single-layer and bilayer graphene QD as function of the excess number of carriers on the left dot, ∆N = N − N 0 .…”

Zero-energy states of graphene triangular quantum dots in a magnetic field

“…[11][12][13] Considerable experimental effort has been made aiming at producing graphene nanostructures with desired shape and edges. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Among graphene nanostructures, nanoribbons and quantum dots are of particular interest. In graphene quantum dots, a size-dependent energy gap opens, [33][34][35] and its magnitude is determined by shape and edge termination.…”

“…[44][45][46][47] The influence of an external magnetic field on the electronic properties of the graphene quantum dots was also studied. 18,34,[50][51][52][53][54][55][56][57][58][59][60][61][62][63] The magnetic field plays the role of a tunable external parameter allowing to change electronic properties in a controllable way. Graphene quantum dots and rings with circular, square, hexagonal, triangular, and rhombus-shaped shapes with zigzag and armchair edges were investigated.…”

High-frequency gate manipulation of a bilayer graphene quantum dot

“…Graphene is expected to meet this request due to the low interaction of the electron spin with the carbon host lattice [2]. Recently, quantum confinement has been shown in graphene quantum dots [3][4][5] and spin states could be identified [6]. However, spin relaxation times in graphene nanostructures remain to be determined experimentally at present.…”