Electron wave and quantum optics in graphene.

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

Stabilizing the Inverted Phase of a WSe2/BLG/WSe2 Heterostructure via Hydrostatic Pressure.

Bilayer graphene (BLG) was recently shown to host a band-inverted phase with unconventional topology emerging from the Ising-type spin-orbit interaction (SOI) induced by the proximity of transition metal dichalcogenides with large intrinsic SOI. Here, we report the stabilization of this band-inverted phase in BLG symmetrically encapsulated in tungsten diselenide (WSe2) via hydrostatic pressure. Our observations from low temperature transport measurements are consistent with a single particle model with induced Ising SOI of opposite sign on the two graphene layers. To confirm the strengthening of the inverted phase, we present thermal activation measurements and show that the SOI-induced band gap increases by more than 100% due to the applied pressure. Finally, the investigation of Landau level spectra reveals the dependence of the level-crossings on the applied magnetic field, which further confirms the enhancement of SOI with pressure.

Signatures of Gate-Driven Out-of-Equilibrium Superconductivity in Ta/InAs Nanowires.

Understanding the microscopic origin of the gate-controlled supercurrent (GCS) in superconducting nanobridges is crucial for engineering superconducting switches suitable for a variety of electronic applications. The origin of GCS is controversial, and various mechanisms have been proposed to explain it. In this work, we have investigated the GCS in a Ta layer deposited on the surface of InAs nanowires. Comparison between switching current distributions at opposite gate polarities and between the gate dependence of two opposite side gates with different nanowire-gate spacings shows that the GCS is determined by the power dissipated by the gate leakage. We also found a substantial difference between the influence of the gate and elevated bath temperature on the magnetic field dependence of the supercurrent. Detailed analysis of the switching dynamics at high gate voltages shows that the device is driven into the multiple phase slips regime by high-energy fluctuations arising from the leakage current.

Gate-Controlled Supercurrent in Epitaxial Al/InAs Nanowires.

Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.

Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure.

Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.

Andreev Molecule in Parallel InAs Nanowires.

Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.

Compact SQUID Realized in a Double-Layer Graphene Heterostructure.

2D systems that host 1D helical states are advantageous from the perspective of scalable topological quantum computation when coupled to a superconductor. Graphene is particularly promising for its high electronic quality, its versatility in van der Waals heterostructures, and its electron- and hole-like degenerate 0th Landau level. Here we study a compact double-layer graphene SQUID (superconducting quantum interference device), where the superconducting loop is reduced to the superconducting contacts connecting two parallel graphene Josephson junctions. Despite the small size of the SQUID, it is fully tunable by the independent gate control of the chemical potentials in both layers. Furthermore, both Josephson junctions show a skewed current-phase relationship, indicating the presence of superconducting modes with high transparency. In the quantum Hall regime, we measure a well-defined conductance plateau of 2e2/h indicative of counter-propagating edge channels in the two layers.

Electrically Controlled Spin Injection from Giant Rashba Spin-Orbit Conductor BiTeBr.

Ferromagnetic materials are the widely used source of spin-polarized electrons in spintronic devices, which are controlled by external magnetic fields or spin-transfer torque methods. However, with increasing demand for smaller and faster spintronic components utilization of spin-orbit phenomena provides promising alternatives. New materials with unique spin textures are highly desirable since all-electric creation and control of spin polarization is expected where the strength, as well as an arbitrary orientation of the polarization, can be defined without the use of a magnetic field. In this work, we use a novel spin-orbit crystal BiTeBr for this purpose. Because of its giant Rashba spin splitting, bulk spin polarization is created at room temperature by an electric current. Integrating BiTeBr crystal into graphene-based spin valve devices, we demonstrate for the first time that it acts as a current-controlled spin injector, opening new avenues for future spintronic applications in integrated circuits.

Mobility Enhancement in Graphene by in situ Reduction of Random Strain Fluctuations.

Microscopic corrugations are ubiquitous in graphene even when placed on atomically flat substrates. These result in random local strain fluctuations limiting the carrier mobility of high quality hBN-supported graphene devices. We present transport measurements in hBN-encapsulated devices where such strain fluctuations can be in situ reduced by increasing the average uniaxial strain. When ∼0.2% of uniaxial strain is applied to the graphene, an enhancement of the carrier mobility by ∼35% is observed while the residual doping reduces by ∼39%. We demonstrate a strong correlation between the mobility and the residual doping, from which we conclude that random local strain fluctuations are the dominant source of disorder limiting the mobility in these devices. Our findings are also supported by Raman spectroscopy measurements.

Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field.

Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field.

Breaking the Quantum PIN Code of Atomic Synapses.

Atomic synapses represent a special class of memristors whose operation relies on the formation of metallic nanofilaments bridging two electrodes across an insulator. Due to the magnifying effect of this narrowest cross section on the device conductance, a nanometer-scale displacement of a few atoms grants access to various resistive states at ultimately low energy costs, satisfying the fundamental requirements of neuromorphic computing hardware. However, device engineering lacks the complete quantum characterization of such filamentary conductance. Here we analyze multiple Andreev reflection processes emerging at the filament terminals when superconducting electrodes are utilized. Thereby, the quantum PIN code, i.e., the transmission probabilities of each individual conduction channel contributing to the conductance of the nanojunctions, is revealed. Our measurements on Nb2O5 resistive switching junctions provide profound experimental evidence that the onset of the high conductance ON state is manifested via the formation of truly atomic-sized metallic filaments.

A non-oxidizing fabrication method for lithographic break junctions of sensitive metals.

Electrochemically active metals offer advanced functionalities with respect to the well-established gold electrode arrangements in various electronic transport experiments on atomic scale objects. Such functionalities can arise from stronger interactions with the leads which provide better coupling to specific molecules and may also facilitate metallic filament formation in atomic switches. However, the higher reactivity of the electrode metal also imposes challenges in the fabrication and reliability of nanometer scale platforms, limiting the number of reported applications. Here we present a high-yield lithographic fabrication procedure suitable to extend the experimental toolkit with mechanically controllable break junctions of oxygen sensitive metallic electrodes. We fabricate and characterize silver break junctions exhibiting single-atomic conductance and superior mechanical and electrical stability at room temperature. As a proof-of-principle application, we demonstrate resistive switching between metastable few-atom configurations at finite voltage bias.

In Situ Strain Tuning in hBN-Encapsulated Graphene Electronic Devices.

Using a simple setup to bend a flexible substrate, we demonstrate deterministic and reproducible in situ strain tuning of graphene electronic devices. Central to this method is the full hBN encapsulation of graphene, which preserves the exceptional quality of pristine graphene for transport experiments. In addition, the on-substrate approach allows one to exploit strain effects in the full range of possible sample geometries and at the same time guarantees that changes in the gate capacitance remain negligible during the deformation process. We use Raman spectroscopy to spatially map the strain magnitude in devices with two different geometries and demonstrate the possibility to engineer a strain gradient, which is relevant for accessing the valley degree of freedom with pseudomagnetic fields. Comparing the transport characteristics of a suspended device with those of an on-substrate device, we demonstrate that our new approach does not suffer from the ambiguities encountered in suspended devices.

Spin-polarized electrons in monolayer MoS2.

Coulomb interactions are crucial in determining the ground state of an ideal two-dimensional electron gas (2DEG) in the limit of low electron densities1. In this regime, Coulomb interactions dominate over single-particle phase-space filling. In silicon and gallium arsenide, electrons are typically localized at these low densities. In contrast, in transition-metal dichalcogenides (TMDs), Coulomb correlations in a 2DEG can be anticipated at experimentally relevant electron densities. Here, we investigate a 2DEG in a gated monolayer of the TMD molybdenum disulfide2. We measure the optical susceptibility, a probe of the 2DEG which is local, minimally invasive and spin selective3. In a magnetic field of 9.0 T and at electron concentrations up to n ≃ 5 × 1012 cm-2, we present evidence that the ground state is spin-polarized. Out of the four available conduction bands4,5, only two are occupied. These two bands have the same spin but different valley quantum numbers. Our results suggest that only two bands are occupied even in the absence of a magnetic field. The spin polarization increases with decreasing 2DEG density, suggesting that Coulomb interactions are a key aspect of the symmetry breaking. We propose that exchange couplings align the spins6. The Bohr radius is so small7 that even electrons located far apart in phase-space interact with each other6.

GHz nanomechanical resonator in an ultraclean suspended graphene p-n junction.

We demonstrate high-frequency mechanical resonators in ballistic graphene p-n junctions. Fully suspended graphene devices with two bottom gates exhibit ballistic bipolar behavior after current annealing. We determine the graphene mass density and built-in tension for different current annealing steps by comparing the measured mechanical resonant response to a simplified membrane model. In a graphene membrane with high built-in tension, but still of macroscopic size with dimensions 3 × 1 µm2, a record resonance frequency of 1.17 GHz is observed after the final current annealing step. We further compare the resonance response measured in the unipolar with the one in the bipolar regime. Remarkably, the resonant signals are strongly enhanced in the bipolar regime.

New Generation of Moiré Superlattices in Doubly Aligned hBN/Graphene/hBN Heterostructures.

The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superlattices can result in a third superlattice with a period larger than the maximum period (14 nm) in the graphene/hBN system, which we explain in a simple model. This new type of band structure engineering allows one to artificially create an even wider spectrum of electronic properties in two-dimensional materials.

Quantum-Confined Stark Effect in a MoS2 Monolayer van der Waals Heterostructure.

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 (∼1012 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.

From electroburning to sublimation: substrate and environmental effects in the electrical breakdown process of monolayer graphene.

We report on the characterization of the electrical breakdown (EB) process for the formation of tunneling nanogaps in single-layer graphene. In particular, we investigated the role of oxygen in the breakdown process by varying the environmental conditions (vacuum and ambient conditions). We show that the density of oxygen molecules in the chamber is a crucial parameter that defines the physical breakdown process: at low density, the graphene lattice is sublimating, whereas at high density, the process involved is oxidation, independent of the substrate material. To estimate the activation energies of the two processes, we use a scheme which consists of applying voltage pulses across the junction during the breakdown. By systematically varying the voltage pulse length, and estimating the junction temperature from a 1D thermal model, we extract activation energies which are consistent with the sublimation of graphene under high vacuum and the electroburning process under air. Our study demonstrates that, in our system, a better control of the gap formation is achieved in the sublimation regime.

Multiple Physical Time Scales and Dead Time Rule in Few-Nanometers Sized Graphene-SiOx-Graphene Memristors.

The resistive switching behavior in SiOx-based phase change memory devices confined by few nanometer wide graphene nanogaps is investigated. Our experiments and analysis reveal that the switching dynamics is not only determined by the commonly observed bias voltage dependent set and reset times. We demonstrate that an internal time scale, the dead time, plays a fundamental role in the system's response to various driving signals. We associate the switching behavior with the formation of microscopically distinct SiOx amorphous and crystalline phases between the graphene electrodes. The reset transition is attributed to an amorphization process due to a voltage driven self-heating; it can be triggered at any time by appropriate voltage levels. In contrast, the formation of the crystalline ON state is conditional and only occurs after the completion of a thermally assisted structural rearrangement of the as-quenched OFF state which takes place within the dead time after a reset operation. Our results demonstrate the technological relevance of the dead time rule which enables a zero bias access of both the low and high resistance states of a phase change memory device by unipolar voltage pulses.

Giant Valley-Isospin Conductance Oscillations in Ballistic Graphene.

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 Tworzidlo 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.