Ballistic graphene offers a promising platform for electron optical devices. We have developed a versatile technology that allows to suspend graphene and complement it with arbitrary bottom and top-gate structures.1 Using current annealing we demonstrated exceptional high nobilities approaching 102 m2/Vs. These suspended devices are ballistic over micrometer length scales and display intriguing interference patterns in the electrical conductance when different gate potentials and magnetic fields are applied.2 There are great similarities between the propagation of light in a dielectric and electrons in graphene, but also differences. In particular, a negative refractive index is straightforward to realize in graphene, but hard in optics. We have used pn junctions to define an electron waveguide by electrostatics3 and guide electrons in snake-states due to alternating cyclotron motion in a small magnetic field,4 to realized mirrors and momentum filters,2 beam splitters5 and Fabry-Perot-like cavities as well as more complex interferometers.

Bilayer graphene is an exciting material, widely extending the range of phenomena compared to monolayer graphene, due its massive nature and much larger interaction parameter. In bilayer graphene a gap can be opened by applying a potential difference between the two layers, for example. Furthermore, the eight-fold ground-state degeneracy of the zero-energy Landau level provides a large Hilbert space, where interaction is expected to lift the degeneracy resulting in novel composite particles. We have discovered that the ground-state in undoped ultraclean high-mobility bilayer graphene is gapped in the absence of magnetic and electric field.6 The new phase, which spontaneously appears driven by interactions, was latter assigned to an antiferromagnetic one. We have also seen recently that a gap appears, albeit much weaker, for graphene with four layers, but it is absent in graphene with a odd layer number.

In current projects we use high-quality h-BN encapsulated graphene and study superlattice effects induced by lattice of the substrate.7 We further work extensively on superconducting graphene devices with side contacts. We have realized Josephson junctions with sputter superconducting films. We also explore isospin currents due to valley effects using pn junctions and suspended graphene where we aim to control the strain in latter with the goal to realize a valley physics with a pseudomagnetic field.

Funding: NCCR-QSIT, SNI

1. R. Maurand, P. Rickhaus, P. Makk, S. Hess, E. Tovari, C. Handschin, M. Weiss and CS, Carbon 79, 486 (2014).
2. P. Rickhaus, R. Maurand, M. H. Liu, M. Weiss, K. Richter and CS, Nat. Commun. 4, 2342 (2013).
3. P. Rickhaus, M. H. Liu, P. Makk, R. Maurand, S. Hess, S. Zihlmann, M. Weiss, K. Richter and CS, Nano Lett. 15 (9), 5819-5825 (2015).
4. P. Rickhaus, P. Makk, M. H. Liu, E. Tovari, M. Weiss, R. Maurand, K. Richter and CS, Nat. Commun. 6, 6470 (2015).
5. P. Rickhaus, P. Makk, M. H. Liu, K. Richter and CS, Appl. Phys. Lett. 107 (25), 251901 (2015).
6. F. Freitag, J. Trbovic, M. Weiss and CS, Phys. Rev. Lett. 108 (6), 076602 (2012).
7. C. Handschin, P.Makk, P. Rickhaus, M.-H. Liu, K. Watanabe, T. Taniguchi, K. Richter, C. Schönenberger, Nano Lett. 17, 328 (2016).

Relevant papers (keyword: GRAPHENE):

### 2018

• GHz nanomechanical resonator in an ultraclean suspended graphene p-n junction
Minkyung Jung, P. Rickhaus, S. Zihlmann, A. Eichler, P. Makk, and C. Schönenberger.
submitted, dec 2018. arXiv:1812.06412
• Non-equilibrium properties of graphene probed by superconducting tunnel spectroscopy
S. Zihlmann, P. Makk, S. Castillas, J. Gramich, K. Thodkar, S. Caneva, R. Wang, S. Hofmann, and C. Schönenberger.
submitted, nov 2018. arXiv:1811.08746
[Abstract]

We report on non-equilibrium properties of graphene probed by superconducting tunnel spectroscopy. A hexagonal boron nitride (hBN) tunnel barrier in combination with a superconducting Pb contact is used to extract the local energy distribution function of the quasiparticles in graphene samples in different transport regimes. In the cases where the energy distribution function resembles a Fermi-Dirac distribution, the local electron temperature can directly be accessed. This allows us to study the cooling mechanisms of hot electrons in graphene. In the case of long samples (device length L much larger than the electron-phonon scattering length le−ph), cooling through acoustic phonons is dominant. We find a cross-over from the dirty limit with a power law T3 at low temperature to the clean limit at higher temperatures with a power law T4 and a deformation potential of 13..3 eV. For shorter samples, where L is smaller than le−ph but larger than the electron-electron scattering length le−e, the well-known cooling through electron out-diffusion is found. Interestingly, we find strong indications of an enhanced Lorenz number in graphene. We also find evidence of a non-Fermi-Dirac distribution function, which is a result of non-interacting quasiparticles in very short samples

• Wideband and on-chip excitation for dynamical spin injection into graphene
D. I. Indolese, S. Zihlmann, P. Makk, C. Jünger, K. Thodkar, and C. Schönenberger.
Phys. Rev. Appl., 10:44053, oct 2018. arXiv:1806.09356
[Abstract]

Graphene is an ideal material for spin transport as very long spin relaxation times and lengths can be achieved even at room temperature. However, electrical spin injection is challenging due to the conductivity mismatch problem. Spin pumping driven by ferromagnetic resonance is a neat way to circumvent this problem as it produces a pure spin current in the absence of a charge current. Here, we show spin pumping into single layer graphene in micron scale devices. A broadband on-chip RF current line is used to bring micron scale permalloy (Ni80Fe20) pads to ferromagnetic resonance with a magnetic eld tunable resonance condition. At resonance, a spin current is emitted into graphene, which is detected by the inverse spin hall voltage in a close-by platinum electrode. Clear spin current signals are detected down to a power of a few milliwatts over a frequency range of 2 GHz to 8 GHz. This compact device scheme paves the way for more complex device structures and allows the investigation of novel materials.

• Signatures of van Hove singularities probed by the supercurrent in a graphene – hBN superlattice
D. I. Indolese, R. Delagrange, P. Makk, J. R. Wallbank, K. Wanatabe, T. Taniguchi, and C. Schönenberger.
Phys. Rev. Lett., 121:137701, sep 2018. arXiv:1805.10184
[Abstract]

The bandstructure of graphene can be strongly modified when it is aligned with its Boron Nitride substrate. A moiré superlattice forms, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we present supercurrent measurements in a Josephson junction made from such a graphene superlattice in the long and diffusive transport regime, where the supercurrent depends on the Thouless energy. We can then estimate the specific density of states of the graphene superlattice from the combined measurement of the critical current and the normal state resistance. The result matches with theoretical predictions and highlights the strong increase of the density of states at the van Hove singularities. By measuring the magnetic field dependence of the supercurrent, we find the presence of edge currents at these singularities. We explain it by the reduction of the Fermi velocity associated with the flat band at the van Hove singularity, which suppresses the supercurrent in the bulk while the electrons at the edge remain less localized, resulting in an edge supercurrent. We attribute this different behavior of the edges to defects or chemical doping.

• Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in WSe2/Gr/hBN heterostructures
S. Zihlmann, A. W. Cummings, J. H. Garcia, M. Kedves, K. Watanabe, T. Taniguchi, C. Schönenberger, and P. Makk.
Phys. Rev. B, 97:75434, feb 2018. arXiv:1712.05678
[Abstract]

Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of spin-orbit coupling and its relaxation mechanism remained unknown. We show for the first time an increased spin-orbit coupling close to the charge neutrality point in graphene, where topological states are expected to appear. Single layer graphene encapsulated between the transition metal dichalcogenide WSe2 and hBN is found to exhibit exceptional quality with mobilities as high as 100 000 cm2/Vs. At the same time clear weak anti-localization indicates strong spin-orbit coupling and a large spin relaxation anisotropy due to the presence of a dominating symmetric spin-orbit coupling is found. Doping dependent measurements show that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman spin-orbit coupling and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation. The strong spin-valley coupling opens new possibilities in exploring spin and valley degree of freedoms in graphene with the realization of new concepts in spin manipulation.

• Charge transport in a single molecule transistor probed by scanning tunneling microscopy
S. Bouvron, R. Maurand, A. Graf, P. Erler, L. Gragnaniello, M. Skripnik, D. Wiedmann, C. Engesser, C. Nef, W. Fu, C. Schönenberger, F. Paulya, and M. Fonin.
Nanoscale, 10:1487-1493, jan 2018.
[Abstract]

We report on the scanning tunneling microscopy/spectroscopy (STM/STS) study of cobalt phthalocyanine (CoPc) molecules deposited onto a back-gated graphene device. We observe a clear gate voltage (Vg) dependence of the energy position of the features originating from the molecular states. Based on the analysis of the energy shifts of the molecular features upon tuning Vg, we are able to determine the nature of the electronic states that lead to a gapped differential conductance. Our measurements show that capacitive couplings of comparable strengths exist between the CoPc molecule and the STM tip as well as between CoPc and graphene, thus facilitating electronic transport involving only unoccupied molecular states for both tunneling bias polarities. These findings provide novel information on the interaction between graphene and organic molecules and are of importance for further studies, which envisage the realization of single molecule transistors with non-metallic electrodes.

• Quantum-Confined Stark Effect in a MoS2 Monolayer van der Waals Heterostructure
J. G. Roch, N. Leisgang, G. Froehlicher, P. Makk, K. Watanabe, T. Taniguchi, C. Schönenberger, and R. J. Warburton.
Nano Letters, 18:1070−1074, jan 2018. arXiv:1710.09750
[Abstract]

The optics of dangling-bond-free van der Waals heterostructures containing transition metal dichalcogenides are dominated by excitons. A crucial property of a confined exciton is the quantum confined Stark effect (QCSE). Here, such a heterostructure is used to probe the QCSE by applying a uniform vertical electric field across a molybdenum disulfide (MoS2) monolayer. The photoluminescence emission energies of the neutral and charged excitons shift quadratically with the applied electric field, provided that the electron density remains constant, demonstrating that the exciton can be polarized. Stark shifts corresponding to about half the homogeneous linewidth were achieved. Neutral and charged exciton polarizabilities of (7.8 ± 1.0) × 10−10 and (6.4 ± 0.9) × 10−10 D m V−1 at relatively low electron density (~10^12 cm−2) have been extracted, respectively. These values are one order of magnitude lower than the previously reported values but in line with theoretical calculations. The methodology presented here is versatile and can be applied to other semiconducting layered materials.

• Spin transport in two-layer-CVD-hBN/graphene/hBN heterostructures
M. Gurram, S. Omar, S. Zihlmann, P. Makk, Q. C. Li, Y. F. Zhang, C. Schönenberger, and B. J. van Wees.
Phys. Rev. B, 97:45411, jan 2018. arXiv:1712.00815
[Abstract]

We study room-temperature spin transport in graphene devices encapsulated between a layer-by-layer-stacked two-layer-thick chemical vapor deposition (CVD) grown hexagonal boron nitride (hBN) tunnel barrier, and a few-layer-thick exfoliated-hBN substrate. We find mobilities and spin-relaxation times comparable to that of SiO2 substrate-based graphene devices, and we obtain a similar order of magnitude of spin relaxation rates for both the Elliott-Yafet and D’Yakonov-Perel’ mechanisms. The behavior of ferromagnet/two-layer-CVDhBN/ graphene/hBN contacts ranges from transparent to tunneling due to inhomogeneities in the CVD-hBN barriers. Surprisingly, we find both positive and negative spin polarizations for high-resistance two-layer-CVDhBN barrier contacts with respect to the low-resistance contacts. Furthermore, we find that the differential spininjection polarization of the high-resistance contacts can be modulated by dc bias from −0.3 to +0.3 V with no change in its sign, while its magnitude increases at higher negative bias. These features point to the distinctive spin-injection nature of the two-layer-CVD-hBN compared to the bilayer-exfoliated-hBN tunnel barriers.

### 2017

• Giant Valley-Isospin Conductance Oscillations in Ballistic Graphene
C. Handschin, P.Makk, P. Rickhaus, R. Maurand, K. Watanabe, T. Taniguchi, K. Richter, Ming-Hao Liu, and C. Schönenberger.
Nano Letters, 17:5389-5393, aug 2017. arXiv:1708.09614
[Abstract]

At high magnetic fields the conductance of graphene is governed by the half-integer quantum Hall effect. By local electrostatic gating a p−n junction perpendicular to the graphene edges can be formed, along which quantum Hall channels copropagate. It has been predicted by Tworzidło and co-workers that if only the lowest Landau level is filled on both sides of the junction, the conductance is determined by the valley (isospin) polarization at the edges and by the width of the flake. This effect remained hidden so far due to scattering between the channels copropagating along the p−n interface (equilibration). Here we investigate p−n junctions in encapsulated graphene with a movable p−n interface with which we are able to probe the edge configuration of graphene flakes. We observe large quantum conductance oscillations on the order of e2/h which solely depend on the p−n junction position providing the first signature of isospin-defined conductance. Our experiments are underlined by quantum transport calculations.

• Restoring the Electrical Properties of CVD Graphene via Physisorption of Molecular Adsorbates
K. Thodkar, D-. Thompson, F. Lüönd, L. Moser, F. Overney, L. Marot, C. Schönenberger, B. Jeanneret, and M. Calame.
ACS Appl. Mater. Interfaces, 9(29):25014-25022, july 2017.
[Abstract]

Chemical vapor deposition (CVD) is a powerful technique to produce graphene for large-scale applications. Polymer-assisted wet transfer is commonly used to move the graphene onto silicon substrates, but the resulting devices tend to exhibit p-doping, which decreases the device quality and reproducibility. In an effort to better understand the origin of this effect, we coated graphene with n-methyl-2-pyrrolidone (NMP) and hexamethyldisilazane (HMDS) molecules that exhibit negligible charge transfer to graphene but bind more strongly to graphene than ambient adsorbents. Using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), electrical transport measurements, and quantum mechanical computer simulations, we show that the molecules help in the removal of p-doping, and our data indicate that the molecules do this by replacing ambient adsorbents (typically O2 and water) on the graphene surface. This very simple method of improving the electronic properties of CVD graphene by passivating its surface with common solvent molecules will accelerate the development of CVD graphene-based devices

• Contactless Microwave Characterization of Encapsulated Graphene p-n Junctions
V. Ranjan, S. Zihlmann, P. Makk, K. Watanabe, T. Taniguchi, and C. Schönenberger.
Phys. Rev. Applied, 7(5):54015, may 2017. arXiv:1702.02071
[Abstract]

Accessing intrinsic properties of a graphene device can be hindered by the influence of contact electrodes. Here, we capacitively couple graphene devices to superconducting resonant circuits and observe clear changes in the resonance-frequency and -widths originating from the internal charge dynamics of graphene. This allows us to extract the density of states and charge relaxation resistance in graphene p-n junctions without the need of electrical contacts. The presented characterizations pave a fast, sensitive and non-invasive measurement of graphene nanocircuits.

• Fabry-Pérot Resonances in a Graphene/hBN Moiré Superlattice
C. Handschin, P.Makk, P. Rickhaus, M. -H. Liu, K. Watanabe, T. Taniguchi, K. Richter, and C. Schönenberger.
Nano Letters, 17:328-333, jan 2017. arXiv:1701.09141
[Abstract]

While Fabry-Pérot (FP) resonances and Moiré superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moiré superlattice. First, we address the effect of the smoothness of the confining potential on the visibility of the FP resonances and carefully map the evolution of the FP cavity size as a function of densities inside and outside the cavity in the absence of a superlattice, when the cavity is bound by regular pn-junctions. Using a sample with a Moiré superlattice, we next show that an FP cavity can also be formed by interfaces that mimic a pn-junction but are defined through a satellite Dirac point due to the superlattice. We carefully analyze the FP resonances, which can provide insight into the band-reconstruction due to the superlattice.

### 2016

• Gate-controlled conductance enhancement from quantum Hall channels along graphene p-n junctions
E. Tovari, P. Makk, Ming-Hao Liu, P. Rickhaus, Z. Kovas-Krausz, C. Schönenberger, and S. Csonka.
Nanoscale, 8(47):19910-19916, dec 2016. arXiv:1606.08007
[Abstract]

The formation of quantum Hall channels inside the bulk of graphene is studied using various contact and gate geometries. p-n junctions are created along the longitudinal direction of samples, and enhanced conductance is observed in the case of bipolar doping due to the new conducting channels formed in the bulk, whose position, propagating direction and, in one geometry, coupling to electrodes are determined by the gate-controlled filling factor across the device. This effect could be exploited to probe the behavior and interaction of quantum Hall channels protected against uncontrolled scattering at the edges.

• Microwave Photodetection in an Ultraclean Suspended Bilayer Graphene p–n Junction
M. Jung, P. Rickhaus, S. Zihlmann, P. Makk, and C. Schönenberger.
Nano Letters, 16(11):6988-6993, nov 2016. arXiv:1702.01529
[Abstract]

We explore the potential of bilayer graphene as a cryogenic microwave photodetector by studying the microwave absorption in fully suspended clean bilayer graphene p–n junctions in the frequency range of 1–5 GHz at a temperature of 8 K. We observe a distinct photocurrent signal if the device is gated into the p–n regime, while there is almost no signal for unipolar doping in either the n–n or p–p regimes. Most surprisingly, the photocurrent strongly peaks when one side of the junction is gated to the Dirac point (charge-neutrality point CNP), while the other remains in a highly doped state. This is different to previous results where optical radiation was used. We propose a new mechanism based on the phototermal effect explaining the large signal. It requires contact doping and a distinctly different transport mechanism on both sides: one side of graphene is ballistic and the other diffusive. By engineering partially diffusive and partially ballistic devices, the photocurrent can drastically be enhanced.

• Comparative study of single and multi domain CVD graphene using large-area Raman mapping and electrical transport characterization
K. Thodkar, El M. Abbassi, F. Lüönd, F. Overney, C. Schönenberger, B. Jeanneret, and M. Calame.
physica status solidi (RRL) – Rapid Research Letters, 10(11):807-811, sep 2016.
[Abstract]

We systematically investigate the impact of granularity in CVD graphene films by performing Raman mapping and electrical characterization of single (SD) and multi domain (MD) graphene. In order to elucidate the quality of the graphene film, we study its regional variations using large-area Raman mapping and compare the G and 2D peak positions of as-transferred chemical vapor deposited (CVD) graphene on SiO2 substrate. We find a similar upshift in wavenumber in both SD and MD graphene in comparison to freshly exfoliated graphene. In our case, doping could play the dominant role behind the observation of such upshifts rather than the influence due to strain. Interestingly, the impact of the polymer-assisted wet transfer process is the same in both the CVD graphene types. The electrical characterization shows that SD graphene exhibits a substantially higher (a factor 5) field-effect mobility when compared to MD graphene. We attribute the low sheet resistance and mobility enhancement to a decrease in charge carrier scattering thanks to a reduction of the number of grain boundaries and defects in SD graphene.

• Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime
E. Tovari, P. Makk, P. Rickhaus, C. Schönenberger, and S. Csonka.
Nanoscale, 8(22):11480-11486, may 2016. arXiv:1601.01628
[Abstract]

We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that form in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system’s signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.

• Spin transport in fully hexagonal boron nitride encapsulated graphene
M. Gurram, S. Omar, S. Zihlmann, P. Makk, C. Schönenberger, and B. J. van Wees.
Physical Review B, 93(11):115441, mar 2016. arXiv:1603.04357
[Abstract]

We study fully hexagonal boron nitride (hBN) encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes: thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from Si_{O2}/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Further, even with the multiple electrodes in-between the injection and the detection electrodes which are in conductivity mismatch regime, we observe spin transport over 12.5 $\mu$m-long distance under the thin-hBN encapsulated graphene channel, demonstrating the clean interface and the pinhole-free nature of the thin hBN as an efficient tunnel barrier.

• Role of hexagonal boron nitride in protecting ferromagnetic anostructures from oxidation
S. Zihlmann, P. Makk, C. A. F. Vaz, and C. Schönenberger.
2D Materials, 3(1):11008, feb 2016. arXiv:1509.03087
[Abstract]

Ferromagnetic contacts are widely used to inject spin polarized currents into non-magnetic materials such as semiconductors or 2-dimensional materials like graphene. In these systems, oxidation of the ferromagnetic materials poses an intrinsic limitation on device performance. Here we investigate the role of ex situ transferred chemical vapour deposited hexagonal boron nitride (hBN) as an oxidation barrier for nanostructured cobalt and permalloy electrodes. The chemical state of the ferromagnets was investigated using x-ray photoemission electron microscopy because of its high sensitivity and lateral resolution. We have compared the oxide thickness formed on ferromagnetic nanostructures covered by hBN to uncovered reference structures. Our results show that hBN reduces the oxidation rate of ferromagnetic nanostructures suggesting that it could be used as an ultra-thin protection layer in future spintronic devices.

### 2015

• Gate tuneable beamsplitter in ballistic graphene
P. Rickhaus, P. Makk, M. -H. Liu, K. Richter, and C. Schönenberger.
Applied Physics Letters, 107(25):251901, dec 2015. arXiv:1511.03044
[Abstract]

We present a beam splitter in a suspended, ballistic, multiterminal, bilayer graphene device. By using local bottomgates, a p-n interface tilted with respect to the current direction can be formed. We show that the p-n interface acts as a semi-transparent mirror in the bipolar regime and that the reflectance and transmittance of the p-n interface can be tuned by the gate voltages. Moreover, by studying the conductance features appearing in magnetic field, we demonstrate that the position of the p-n interface can be moved by 1μm. The herein presented beamsplitter device can form the basis of electron-optic interferometers in graphene

• Point contacts in encapsulated graphene
C. Handschin, B. Fülöp, P. Makk, S. Blanter, M. Weiss, K. Watanabe, T. Taniguchi, S. Csonka, and C. Schönenberger.
Applied Physics Letters, 107(18):183108, nov 2015. arXiv:1509.04137v1.pdf
[Abstract]

We present a method to establish inner point contacts on hexagonal boron nitride (hBN) encapsulated graphene heterostructures with dimensions as small as 100 nm by pre-patterning the top-hBN in a separate step prior to dry-stacking. 2 and 4-terminal field effect measurements between different lead combinations are in qualitative agreement with an electrostatic model assuming point-like contacts. The measured contact resistances are 0.5-1.5 k$\Omega$ per contact, which is quite low for such small contacts. By applying a perpendicular magnetic fields, an insulating behaviour in the quantum Hall regime was observed, as expected for inner contacts. The fabricated contacts are compatible with high mobility graphene structures and open up the field for the realization of several electron optical proposals.

• Electron optics: Turn the other way
Péter Makk.
Nature Physics, 11(11):894-895, nov 2015.
• Guiding of Electrons in a Few-Mode Ballistic Graphene Channel
P. Rickhaus, M. -H. Liu, P. Makk, R. Maurand, S. Hess, S. Zihlmann, M. Weiss, K. Richter, and Schönenberger Richter (Uni. C. -. in cooperation with group Regensburg).
Nano Letters, 15(9):5819-5825, sep 2015. arXiv:1509.02653
[Abstract]

In graphene, the extremely fast charge carriers can be controlled by electron-optical elements, such as waveguides, in which the transmissivity is tuned by the wavelength. In this work, charge carriers are guided in a suspended ballistic few-mode graphene channel, defined by electrostatic gating. By depleting the channel, a reduction of mode number and steps in the conductance are observed, until the channel is completely emptied. The measurements are supported by tight-binding transport calculations including the full electrostatics of the sample.

• Graphene spintronics: the European Flagship perspective
S. Roche, J. Akerman, B. Beschoten, J. -C. Charlier, M. Chshiev, S. P. Dash, B. Dlubak, J. Fabian, A. Fert, M. Guimaraes, F. Guinea, I. Grigorieva, C. Schönenberger, P. Seneor, C. Stampfer, S. O.Valenzuela, X. Waintal, and B. van Wees.
2D Materials, 2(3):30202, jul 2015.
[Abstract]

We review current challenges and perspectives in graphene spintronics, which is one of the most promising directions of innovation, given its room-temperature long-spin lifetimes and the ability of graphene to be easily interfaced with other classes of materials (ferromagnets, magnetic insulators, semiconductors, oxides, etc), allowing proximity effects to be harvested. The general context of spintronics is first discussed together with open issues and recent advances achieved by the Graphene Spintronics Work Package consortium within the Graphene Flagship project. Based on such progress, which establishes the state of the art, several novel opportunities for spin manipulation such as the generation of pure spin current (through spin Hall effect) and the control of magnetization through the spin torque phenomena appear on the horizon. Practical applications are within reach, but will require the demonstration of wafer-scale graphene device integration, and the realization of functional prototypes employed for determined applications such as magnetic sensors or nano-oscillators. This is a specially commissioned editorial from the Graphene Flagship Work Package on Spintronics. This editorial is part of the 2D Materials focus collection on ‘Progress on the science and applications of two-dimensional materials,’ published in association with the Graphene Flagship. It provides an overview of key recent advances of the spintronics work package as well as the mid-term objectives of the consortium.

• Snake trajectories in ultraclean graphene p–n junctions
P. Rickhaus, P. Makk, Ming-Hao Liu, E. Tovari, M. Weiss, R. Maurand, and C. Schönenberger.
Nature Communications, 6:6470, mar 2015. arXiv:1502.01935
[Abstract]

Snake states are trajectories of charge carriers curving back and forth along an interface. There are two types of snake states, formed by either inverting the magnetic field direction or the charge carrier type at an interface. The former has been demonstrated in GaAs–AlGaAs heterostructures, whereas the latter has become conceivable only with the advance of ballistic graphene where a gap-less p–n interface governed by Klein tunnelling can be formed. Such snake states were hidden in previous experiments due to limited sample quality. Here we report on magneto-conductance oscillations due to snake states in a ballistic suspended graphene p–n junction, which occur already at a very small magnetic field of 20 mT. The visibility of 30 percent is enabled by Klein collimation. Our finding is firmly supported by quantum transport simulations. We demonstrate the high tunability of the device and operate it in different magnetic field regimes.

• Scalable Tight-Binding Model for Graphene
Ming-Hao Liu, P. Rickhaus, P. Makk, E. Tovari, R. Maurand, F. Tkatschenko, M. Weiss, C. Schönenberger, and K. Richter.
Phys. Rev. Lett., 114(3):36601, jan 2015. arXiv:1407.5620
[Abstract]

Artificial graphene consisting of honeycomb lattices other than the atomic layer of carbon has been shown to exhibit electronic properties similar to real graphene. Here, we reverse the argument to show that transport properties of real graphene can be captured by simulations using “theoretical artificial graphene.” To prove this, we first derive a simple condition, along with its restrictions, to achieve band structure invariance for a scalable graphene lattice. We then present transport measurements for an ultraclean suspended single-layer graphene pn junction device, where ballistic transport features from complex Fabry-Pérot interference (at zero magnetic field) to the quantum Hall effect (at unusually low field) are observed and are well reproduced by transport simulations based on properly scaled single-particle tight-binding models. Our findings indicate that transport simulations for graphene can be efficiently performed with a strongly reduced number of atomic sites, allowing for reliable predictions for electric properties of complex graphene devices. We demonstrate the capability of the model by applying it to predict so-far unexplored gate-defined conductance quantization in single-layer graphene.

### 2014

• Large-scale fabrication of BN tunnel barriers for graphene spintronics
W. Fu, P. Makk, R. Maurand, M. Bräuninger, and C. Schönenberger.
Journal of Applied Physics, 116(20):74306, aug 2014. arXiv:1407.1439
[Abstract]

We have fabricated graphene spin-valve devices utilizing scalable materials made from chemical vapor deposition (CVD). Both the spin-transporting graphene and the tunnel barrier material are CVD-grown. The tunnel barrier is realized by Hexagonal boron nitride, used either as a monolayer or bilayer and placed over the graphene. Spin transport experiments were performed using ferromagnetic contacts deposited onto the barrier. We find that spin injection is still greatly suppressed in devices with a monolayer tunneling barrier due to resistance mismatch. This is, however, not the case for devices with bilayer barriers. For those devices, a spin relaxation time of ~260 ps intrinsic to the CVD graphene material is deduced. This time scale is comparable to those reported for exfoliated graphene, suggesting that this CVD approach is promising for spintronic applications which require scalable materials.

• Fabrication of ballistic suspended graphene with local-gating
R. Maurand, P. Rickhaus, P. Makk, S. Hess, E. Tovari, C. Handschin, M. Weiss, and C. Schönenberger.
Carbon, 79:486-492, aug 2014. arXiv:1409.4751
[Abstract]

Herein we discuss the fabrication of ballistic suspended graphene nanostructures supplemented with local gating. Using in situ current annealing, we show that exceptional high mobilities can be obtained in these devices. A detailed description is given of the fabrication of bottom and different top-gate structures, which enable the realization of complex graphene structures. We have studied the basic building block, the p-n junction in detail, where a striking oscillating pattern was observed, which can be traced back to Fabry–Perot oscillations that are localized in the electronic cavities formed by the local gates. Finally we show some examples how the method can be extended to incorporate multi-terminal junctions or shaped graphene. The structures discussed here enable the access to electron-optics experiments in ballistic graphene.

• CVD graphene for electrical quantum metrology
K. Thodkar, C. Nef, W. Fu, C. Schönenberger, M. Calame, F. Lüönd, F. Overney, B. Jeckelmann, and B. Jeanneret.
IEEE Proceedings of the Conference on Precision Electromagnetic Measurements (CPEM 2014), pages 540-541, aug 2014.
[Abstract]

Graphene, a two dimensional material with sp2 hybridized carbon atoms arranged in honey comb lattice, is known for its unique electronic and mechanical properties. Soon after the isolation of 2D graphene crystals Quantum Hall effect (QHE) has been observed in this material at room temperature. The Quantum Hall plateaus in graphene have large spacing between the Landau levels in comparison to other 2DEGs, which makes it an ideal material for a quantum resistance standard defined by the electron charge and Planck s constant. We will present results for graphene by Chemical Vapor Deposition (CVD) and transferred to SiO2/Si using different techniques. The transferred graphene films were patterned into millimeter scale Hall bar geometry and characterized using confocal Raman spectroscopy. First electrical transport measurements will be presented.

• High-yield fabrication of nm-size gaps in monolayer CVD graphene
C. Nef, L. Pósa, P. Makk, W. Fu, A. Halbritter, C. Schönenberger, and M. Calame.
Nanoscale, 6:7249-7254, may 2014.
[Abstract]

Herein we demonstrate the controlled and reproducible fabrication of sub-5 nm wide gaps in single-layer graphene electrodes. The process is implemented for graphene grown via chemical vapor deposition using an electroburning process at room temperature and in vacuum. A yield of over 95 percent for the gap formation is obtained. This approach allows producing single-layer graphene electrodes for molecular electronics at a large scale. Additionally, from Raman spectroscopy and electroburning carried out simultaneously, we can follow the heating process and infer the temperature at which the gap formation happens.

• Rendering graphene supports hydrophilic with non-covalent aromatic functionalization for transmission electron microscopy
R. S. Pantelic, W. Fu, C. Schönenberger, and H. Stahlberg.
Appl. Phys. Lett., 104:134103, apr 2014.
[Abstract]

Amorphous carbon films have been routinely used to enhance the preparation of frozen-hydrated transmission electron microscopy (TEM) samples, either in retaining protein concentration, providing mechanical stability or dissipating sample charge. However, strong background signal from the amorphous carbon support obstructs that of the sample, and the insulating properties of amorphous carbon films preclude any efficiency in dispersing charge. Graphene addresses the limitations of amorphous carbon. Graphene is a crystalline material with virtually no phase or amplitude contrast and unparalleled, high electrical carrier mobility. However, the hydrophobic properties of graphene have prevented its routine application in Cryo-TEM. This letter reports a method for rendering graphene TEM supports hydrophilic – a convenient approach maintaining graphene’s structural and electrical properties based on non-covalent, aromatic functionalization.

• Electrolyte gate dependent high-frequency measurement of graphene field-effect transistor for sensing applications
W. Fu, El M. Abbassi, T. Hasler, M. Jung, M. Steinacher, M. Calame, C. Schönenberger, G. Puebla-Hellmann, S. Hellmüller, T. Ihn, and A. Wallraff.
Appl. Phys. Lett., 104:13102, jan 2014. arXiv:1401.0381
[Abstract]

We performed radiofrequency (RF) reflectometry measurements at 2�4 GHz on electrolyte-gated graphene field-effect transistors, utilizing a tunable stub-matching circuit for impedance matching. We demonstrate that the gate voltage dependent RF resistivity of graphene can be deduced, even in the presence of the electrolyte which is in direct contact with the graphene layer. The RF resistivity is found to be consistent with its DC counterpart in the full gate voltage range. Furthermore, in order to access the potential of high-frequency sensing for applications, we demonstrate time-dependent gating in solution with nanosecond time resolution.

### 2013

• Ballistic interferences in suspended graphene
P. Rickhaus, R. Maurand, M. Weiss, C. Schönenberger, Ming-Hao Liu, and K. Richter.
Nature Communications, 4(2342):1-6, aug 2013. arXiv:1304.6590
[Abstract]

Graphene is the 2-dimensional (2D) carbon allotrope with the atoms arranged in a honeycomb lattice [1]. The low-energy electronic excitations in this 2D crystal are described by massless Dirac fermions that have a linear dispersion relation similar to photons [2, 3]. Taking advantage of this optics-like electron dynamics, generic optical elements like lenses, beam splitters and wave guides have been proposed for electrons in engineered and ballistic graphene [4, 5]. Tuning of these elements rely on the ability to adjust the carrier concentration in defined areas, including the possibility to create bipolar regions of opposite charge (p-n regions). However, the combination of ballistic transport and complex electrostatic gating remain challenging. Here, we report on the fabrication and characterization of fully suspended graphene p-n junctions. By local electrostatic gating, resonant cavities can be defined, leading to complex Fabry-Perot interference patterns in the unipolar and the bipolar regime. The amplitude of the observed conductance oscillations account for quantum interference of electrons that propagate ballistically over long distances exceeding 1 micrometer. We also demonstrate that the visibility of the interference pattern is enhanced by Klein collimation at the p-n interface [6, 7]. This finding paves the way to more complex gate controlled ballistic graphene devices and brings electron optics in graphene closer to reality.

• Low-bias active control of TeraHertz-waves by coupling large-area CVD-graphene to a TeraHertz-Metamaterial
F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, Hyung Gyu, M. Beck, and J. Faist.
Nano Lett., 13(7):3193-3198, jul 2013.
[Abstract]

We propose an hybrid graphene/metamaterial device based on terahertz electronic split-ring resonators directly evaporated on top of a large-area single-layer CVD graphene. Room temperature time-domain spectroscopy measurements in the frequency range from 250 GHz to 2.75 THz show that the presence of the graphene strongly changes the THz metamaterial transmittance on the whole frequency range. The graphene gating allows active control of such interaction, showing a modulation depth of 11.5% with an applied bias of 10.6 V. Analytical modeling of the device provides a very good qualitative and quantitative agreement with the measured device behavior. The presented system shows potential as a THz modulator and can be relevant for strong light–matter coupling experiments.

• Spin symmetry of the bilayer graphene ground state
F. Freitag, M. Weiss, R. Maurand, J. Trbovic, and C. Schönenberger.
Phys. Rev. B, 87(16):161402, apr 2013.
[Abstract]

We show nonlinear transport experiments on clean, suspended bilayer graphene that reveal a gap in the density of states. Looking at the evolution of the gap in magnetic fields of different orientation, we find that the groundstate is a spin-ordered phase. Of the three possible gapped groundstates that are predicted by theory for equal charge distribution between the layers, we can therefore exclude the quantum anomalous Hall phase, leaving the layer antiferromagnet and the quantum spin Hall phase as the only possible gapped groundstates for bilayer graphene

### 2012

• Homogeneity of bilayer graphene
F. Freitag, M. Weiss, R. Maurand, J. Trbovic, and C. Schönenberger.
Solid State Communications, 152(22):2053-2057, nov 2012. arXiv:1207.4424v2
[Abstract]

We present non-linear transport measurements on suspended, current annealed bilayer graphene devices. Using a multi-terminal geometry we demonstrate that devices tend to be inhomogeneous and host two different electronic phases next to each other. Both of these phases show gap-like features of different magnitude in non-linear transport at low charge carrier densities, as already observed in previous studies. Here, we investigate the magnetic field dependence and find that both features grow with increasing field, the smaller one with 0.6meV/T, the larger one with a 5�10 times higher field dependence. We attribute the larger of the two gaps to an interaction induced broken symmetry state and the smaller one to localization in the more disordered parts of the device.

• Quantum Hall Effect in Graphene with Superconducting Electrodes
P. Rickhaus, M. Weiss, L. Marot, and C. Schönenberger.
Nano Letters, 12(4):1942-1945, apr 2012. arXiv:1303.3394v1
[Abstract]

We have realized an integer quantum Hall system with superconducting contacts by connecting graphene to niobium electrodes. Below their upper critical field of 4 T, an integer quantum Hall effect coexists with superconductivity in the leads but with a plateau conductance that is larger than in the normal state. We ascribe this enhanced quantum Hall plateau conductance to Andreev processes at the graphene–superconductor interface leading to the formation of so-called Andreev edge-states. The enhancement depends strongly on the filling-factor and is less pronounced on the first plateau due to the special nature of the zero energy Landau level in monolayer graphene.

• Spontaneously Gapped Ground State in Suspended Bilayer Graphene
F. Freitag, J. Trbovic, M. Weiss, and C. Schönenberger.
Phys. Rev. Lett., 108(7):76602, feb 2012. arXiv:1104.3816
[Abstract]

Bilayer graphene bears an eight-fold degeneracy due to spin, valley and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kind of devices. In bilayers of type B1 the eight-fold zero-energy Landau level (LL) is partially lifted above a threshold field revealing an insulating nu=0 quantum Hall state at the charge neutrality point (CNP). In bilayers of type B2 the LL lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G < e^2/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.

### 2011

• Conductance fluctuations in graphene devices with superconducting contacts in different charge density regimes
F. Freitag, J. Trbovic, and C. Schönenberger.
Phys. Status Solidi B (arXiv:1108.4599), 248(11):2649-2652, oct 2011. arXiv:1108.4599
[Abstract]

Conductions fluctuations (CF) are studied in single layer graphene devices with superconducting source and drain contacts made from aluminium. The CF are found to be enhanced by superconductivity by a factor of 1.4–2. This (near) doubling of the CF indicates that the phase coherence length is equation image ≳ equation image. As compared to previous work, we find a relatively weak dependence of the CF on the gate voltage, and hence on the carrier density. We also demonstrate that whether the CF are larger or smaller at the charge neutrality point (CNP) can be strongly dependent on the series resistance RC, which needs to be subtracted.

### 2010

• Superconductivity-enhanced conductance fluctuations in few layer graphene
J. Trbovic, N. Minder, F. Freitag, and C. Schönenberger.
Nanotechnology, 21:274005, jun 2010. arXiv:0912.0389
[Abstract]

We investigate the mesoscopic disorder induced rms conductance variance δG in short few-layer graphene (FLG) flakes contacted by two superconducting (S) Ti/Al contacts. By sweeping the back-gate voltage, we observe pronounced conductance fluctuations superimposed on a linear background of the two-terminal conductance G. The linear gate voltage induced response can be modelled by a set of interlayer and intralayer capacitances. δG depends on temperature T and source–drain voltage Vsd. δG increases with decreasing T and |Vsd|. When lowering |Vsd|, a pronounced cross-over at a voltage corresponding to the superconducting energy gap Δ is observed. For |V_{\mathrm {sd}}|\lesssim \Delta the fluctuations are markedly enhanced. Expressed in the conductance variance GGS of one graphene–superconductor (G–S) interface, values of 0.58e2/h are obtained at the base temperature of 230 mK. The conductance variance in the sub-gap region is larger by up to a factor of 1.4–1.8 compared to the normal state. The observed strong enhancement is due to phase coherent charge transfer caused by Andreev reflection at the G–S interface.