Quantized conductance of a suspended graphene nanoconstriction

Abstract

at integer multiples of 2e 2 /h at zero magnetic field in a high mobility suspended graphene ballistic nanoconstriction. This quantization evolves into the typical quantum Hall effect for graphene at magnetic fields above 60 mT. Voltage bias spectroscopy reveals an energy spacing of 8 meV between the first two subbands. A pronounced feature at 0.6 × 2e 2 /h present at a magnetic field as low as ∼0.2 T resembles the '0.7 anomaly' observed in quantum point contacts in a GaAs-AlGaAs two-dimensional electron gas, possibly caused by electron-electron interactions 11 . Conductance quantization in zero magnetic field in graphene ribbons is expected to strongly depend on the type of edge termination 6,7,[12][13][14] . In the case of ideal non-disordered armchair edges the valley degeneracy is lifted, leading to a quantization sequence 0 (for a semiconducting ribbon), 1,2,3,... × G 0 , when the Fermi energy is raised or lowered from the charge neutrality point. Here G 0 = 2e 2 /h, with e the electron charge, h the Planck constant and the factor two is due to the spin degeneracy. For zigzag edges on the other hand, theory predicts a quantization in odd multiples 1,3,5,... × G 0 , reflecting the presence of both spin, as well as valley degeneracy. However, realistic devices have a finite (edge) disorder which will dominate the electronic transport in long and narrow ribbons, making the experimental observation of conductance quantization very challenging. Signatures of the formation of one-dimensional subbands because of quantum confinement have been reported for nanoribbons fabricated on a silicon oxide (SiO 2 ) substrate 15,16 . However, those devices are not in the ballistic regime because they have the characteristics of a diffusive, disordered system and lack uniform doping owing to strong interaction with the substrate. In such a narrow and long ribbon an edge disorder of typically only a few per cent of missing carbon atoms will prevent the observation of quantum ballistic transport and conductance quantization [17][18][19] . A way to circumvent this problem is to prepare a constriction with a length comparable or shorter than the width, for which conductance quantization is theoretically possible for an edge disorder of 10% or even higher [18][19][20] . To investigate quantum ballistic 1 Molecular Electronics, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747AG Groningen, The Netherlands, 2 Physics of Nanodevices, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh, NL-9747AG Groningen, The Netherlands. *e-mail: n.tombros@rug.nl. No current annealing was applied to region C. b, A schematic cross-section of the device. The graphene layer is suspended about 1 µm above the 500 nm thick SiO 2 and the electrodes are kept in place by pillars of LOR polymer. The n+ doped silicon substrate is used as a back gate electrode to control the charge-carrier density.transport and conductance quantization in graphene it is therefore crucial to prepare a narrow, short...

Superballistic flow of viscous electron fluid through graphene constrictions

“…Deviations become larger for our smallest constrictions, suggesting that they are effectively narrower, possibly because of edge defects. Although we focus here on classical PCs with a large number of transmitting modes, we note that our devices with w < 0.2 µm exhibit certain signs of conductance quantization, fairly similar to those reported previously 25,26 , but they are rapidly washed out upon raising T above 30 K. The central result of our study is presented in Fig. 1e.…”

Transport gap in suspended bilayer graphene at zero magnetic field

“…24,25 We deposited highly ordered pyrolytic graphite on an n ++ Si/SiO 2 wafer (500 nm thick) which is covered with a lift-off organic resist: LOR (1.15 μm). A standard lithography procedure is performed in order to contact bilayer graphene flakes (determined by their contrast in an optical microscope) with 80 nm of Ti/Au contacts.…”

“…We repeat this procedure until the appearance of a sharp resistance maximum at the CNP located close to zero V g . More details on the current annealing procedure can be found in Tombros et al 25 The studied device was 2 μm long and 2.3 μm wide. All measurements were performed in four-probe geometry (with contacts across the full width of graphene) at temperatures from 4.2 K down to 300 mK.…”

Spin Transport in High-Quality Suspended Graphene Devices

“…Before the quality improvement via the current annealing procedure (described in the next paragraph), the devices typically show high p-doping and only a small change of the resistance as a function of V g is observed. 28,31 To improve the quality of our suspended graphene devices we perform current annealing 32 in vacuum (at a pressure better than 10 −6 mbar) at a base temperature of 4.2 K (see Supporting Information). Since the contact resistance of the spin injector and detector in our samples has to be kept at high values (>10 kΩ) to avoid the impedance mismatch and contact induced spin relaxation, 4,7,33 we use the outer electrodes to apply the high current densities capable of heating the graphene flake to high temperatures ( Figure 1c).…”