Combining Scanning Gate Microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of electron probability density |Ψ| 2 (x, y) in embedded mesoscopic quantum rings (QRs). The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wavefunction interferences. Simulations of both |Ψ| 2 (x, y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Ψ| 2 (x, y). Thanks to the scanning tunnelling microscope (STM), remarkable precision has been achieved in the local scale imaging of surface electron systems. Only a few years after the STM invention, electron interferences could be visualized in real space inside artificially confined surface structures, the "quantum corrals" [1]. However, since they rely on the measurement of a current between a tip and the sample, STM techniques are useless when the system of interest is buried under an insulating layer, as in two-dimensional electron gases (2DEGs) confined in semiconductor heterostructures. To circumvent the obstacle, a new method was developed: the Scanning Gate Microscopy (SGM). SGM consists in mapping the conductance of the system as the polarized tip, acting as a flying nano-gate, scans at a constant distance above the 2DEG. SGM gave many valuable insights into the physics of quantum point contacts (QPCs) [7].[In some cases, the mechanism of SGM image formation is readily understandable. For example, in the vicinity of a QPC [2], coherent electron flow is imaged due to multiple reflections and interferences of electrons bouncing between the QPC and the tip-induced depleted region. In comparison, the situation seems more complex when the tip scans directly over an open mesoscopic billiard [6]: the tip perturbation extends over the whole system of interest, so that all semi-classical trajectories are modified. The mechanisms that link conductance maps to the properties of unperturbed electrons still need to be clarified. Recently, we showed that SGM images in the vicinity of a QR allow direct observation of iso-phase lines for electrons in an electrostatic Aharonov-Bohm (AB) experiment [8].In this Letter, we discuss SGM images obtained as the tip scans directly over coherent quantum rings (QRs). Experimentally, we find that the amplitude of conductance modulations shares a common temperature dependence with the Aharonov-Bohm effect, a direct evidence that SGM probes the quantum nature of electrons. On the other hand, we perform quantum mechanical simulations of SGM experiments. First, the amplitude of conductance fringes is found to evolve linearly at low perturbation amplitude, both in experiments and simulations. Second, we observe a direct correspondence between simulated SGM data and simulations of the electron probability density |Ψ| 2 (x, y, E F ). We deduce that, in this linear regime, SGM reliably maps |Ψ| 2 (x, y, E F ) in coherent QRs.We fabricated two QRs, samples R1 and R2, from an InGa...

T raditionally, the understanding of quantum transport, coherent and ballistic 1 , relies on the measurement of macroscopic properties such as the conductance. Although powerful when coupled to statistical theories, this approach cannot provide a detailed image of 'how electrons behave down there'. Ideally, understanding transport at the nanoscale would require tracking each electron inside the nanodevice. Significant progress towards this goal was obtained by combining scanning probe microscopy with transport measurements 2-7 . Some studies even showed signatures of quantum transport in the surroundings of nanostructures 4-6 . Here, scanning probe microscopy is used to probe electron propagation inside an open quantum ring exhibiting the archetype of electronwave interference phenomena: the Aharonov-Bohm effect 8 . Conductance maps recorded while scanning the biased tip of a cryogenic atomic force microscope above the quantum ring show that the propagation of electrons, both coherent and ballistic, can be investigated in situ, and can even be controlled by tuning the potential felt by electrons at the nanoscale.An open quantum ring (QR) in the coherent regime of transport is a good example of an interferometer: its conductance peaks when electron waves interfere constructively at the output contact and decreases to a minimum for destructive interferences. Varying either the magnetic flux encircled by the QR or the electrostatic potential in one arm allows the interference to be tuned. This gives rise to the well-known magnetic 9 and electrostatic 10,11 Aharonov-Bohm (AB) oscillations. Although these effects have been studied extensively through transport measurements, those techniques lack the spatial resolution necessary to probe interferences in the interior of QRs. In this work, we perturb the propagation of electrons through a QR with an atomic force microscope (AFM) tip. We therefore take advantage of both the imaging capabilities of the AFM and the high sensitivity of the conductance measurement to electron phase changes.A three-dimensional image of the QR used here, as measured by our AFM in the conventional topographical mode, is shown in Fig. 1a. The QR is fabricated from an InGaAs/InAlAs heterostructure hosting a two-dimensional electron system (2DES) with a sheet density of 2 × 10 16 m −2 , buried 25 nm below the sample surface 12 . Electron-beam lithography and wet etching were used to pattern the QR and interconnections. At the experimental temperature (4.2 K), the QR is smaller than the intrinsic electron mean free path measured in the 2DES (l μ = 2.3 μm). Transport is thus in the ballistic regime, with electrons travelling along 'billiardball'-like trajectories. Moreover, the observation of periodic AB oscillations (Fig. 1b, inset) in the magnetoconductance of our QR attests that transport is also in the coherent regime 13 . The periodicity of these oscillations is found to be 26 mT, consistent with the average radius of circular electron trajectories in the QR: r = 220 nm.The metallized tip of t...

The operation of 1-3 nm thick SOI MOSFETs, in double-gate (DG) mode and single-gate (SG) mode (for either front or back channel), is systematically analyzed. Strong interface coupling and threshold voltage variation, large influence of substrate depletion underneath the buried oxide, absence of drain current transients, degradation in electron mobility are typical effects in these ultra-thin MOSFETs. The comparison of SG and DG configurations demonstrates the superiority of DG-MOSFETs: ideal subthreshold swing and remarkably improved transconductance (consistently higher than twice the value in SG-MOSFETs). The experimental data and the difference between SG and DG modes is explained by combining classical models with quantum calculations. The key effect in ultimately thin DG-MOSFETs is volume inversion, which primarily leads to an improvement in mobility, whereas the total inversion charge is only marginally modified.

In the present work, the electronic and vibrational properties of both pristine V 2 C and fullyterminated V 2 CT 2 (where T = F, O, OH) 2D monolayers are investigated using density functional theory. Firstly, the atomic structures of V 2 C-based MXene phases are optimized and their respective dynamical stabilities are discussed. Secondly, electronic band structures are computed indicating that V 2 C is metallic as well as all the corresponding functionalized systems. Thirdly, the vibrational properties (phonon frequencies and spectra) of V 2 C-based MXenes are computed thanks to density functional perturbation theory and reported for the first time. Both Raman (E g , A 1g ) and infrared active (E u , A 2u ) vibrational modes are predicted ab initio with the aim to correlate the experimental Raman peaks with the calculated vibrational modes and to assign them with specific atomic motions. The effect of the terminal groups on the vibrational properties is emphasized as well as on the presence and position of the corresponding Raman peaks. Our results provide new insights for the identification and characterization of V 2 C-based samples using Raman spectroscopy.

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The magnetotransport of freestanding, vacuum filtered, thin films of Mo 2 CT z , Mo 1.33 CT z , Mo 2 TiC 2 T z , and Mo 2 Ti 2 C 3 T z was measured in the 10-300-K temperature (T) range. Some of the films were annealed before measuring their transport properties. Analysis of the results suggest that-with the exception of the heavily defective Mo 1.33 CT z composition-in the 10-to 200-K temperature regime, variable range hopping between individual MXene sheets is the operative conduction mechanism. For Mo 1.33 CT z it is more likely that variable range hopping within individual flakes is rate limiting. At higher temperatures, a thermally activated process emerges in all cases. It follows that improved fabrication processes should lead to considerable improvements in the electrical transport of Mo-based MXenes.

We study the relationship between the local density of states (LDOS) and the conductance variation ∆G in scanning-gate-microscopy experiments on mesoscopic structures as a charged tip scans above the sample surface. We present an analytical model showing that in the linear-response regime the conductance shift ∆G is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and ∆G. We analyze the physical conditions for the validity of this relationship both for one-dimensional and two-dimensional systems when several channels contribute to the transport. We focus on realistic Aharonov-Bohm rings including a random distribution of impurities and analyze the LDOS-∆G correspondence by means of exact numerical simulations, when localized states or semi-classical orbits characterize the wavefunction of the system.

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