Benoît Hackens

Imaging electron wave functions inside open quantum rings

Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).

Imaging and controlling electron transport inside a quantum ring

Traditionally, the understanding of quantum transport, coherent and ballistic1, 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 measurements2,3,4,5,6,7. Some studies even showed signatures of quantum transport in the surroundings of nanostructures4,5,6. Here, scanning probe microscopy is used to probe electron propagation inside an open quantum ring exhibiting the archetype of electron-wave interference phenomena: the Aharonov–Bohm effect8. 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.

On the imaging of electron transport in semiconductor quantum structures by scanning-gate microscopy: successes and limitations

This paper presents a brief review of scanning-gate microscopy applied to the imaging of electron transport in buried semiconductor quantum structures. After an introduction to the technique and to some of its practical issues, we summarize a selection of its successful achievements found in the literature, including our own research. The latter focuses on the imaging of GaInAs-based quantum rings both in the low-magnetic-field Aharonov-Bohm regime and in the high-field quantum Hall regime. Based on our own experience, we then discuss in detail some of the limitations of scanning-gate microscopy. These include possible tip-induced artefacts, effects of a large bias applied to the scanning tip, as well as consequences of unwanted charge traps on the conductance maps. We emphasize how special care must be paid in interpreting these scanning-gate images.

Transport Inefficiency in Branched-Out Mesoscopic Networks: An Analog of the Braess Paradox

We present evidence for a counterintuitive behavior of semiconductor mesoscopic networks that is the analog of the Braess paradox encountered in classical networks. A numerical simulation of quantum transport in a two-branch mesoscopic network reveals that adding a third branch can paradoxically induce transport inefficiency that manifests itself in a sizable conductance drop of the network. A scanning-probe experiment using a biased tip to modulate the transmission of one branch in the network reveals the occurrence of this paradox by mapping the conductance variation as a function of the tip voltage and position.

Imaging Coulomb islands in a quantum Hall interferometer

In the quantum Hall regime, near integer filling factors, electrons should only be transmitted through spatially separated edge states. However, in mesoscopic systems, electronic transmission turns out to be more complex, giving rise to a large spectrum of magnetoresistance oscillations. To explain these observations, recent models put forward the theory that, as edge states come close to each other, electrons can hop between counterpropagating edge channels, or tunnel through Coulomb islands. Here, we use scanning gate microscopy to demonstrate the presence of QH Coulomb islands, and reveal the spatial structure of transport inside a QH interferometer. Locations of electron islands are found by modulating the tunnelling between edge states and confined electron orbits. Tuning the magnetic field, we unveil a continuous evolution of active electron islands. This allows to decrypt the complexity of high-magnetic-field magnetoresistance oscillations, and opens the way to further local-scale manipulations of QH localized states.

Current crowding effects in superconducting corner-shaped Al microstrips

The superconducting critical current of corner-shaped Al superconducting microstrips has been investigated. We demonstrate that the sharp turns lead to asymmetric vortex dynamics, allowing for easier penetration from the inner concave angle than from the outer convex angle. This effect is evidenced by a rectification of the voltage signal otherwise absent in straight superconducting strips. At low magnetic fields, an enhancement of the critical current with increasing magnetic field is observed for a particular combination of field and current polarity, confirming a theoretically predicted competing interplay of superconducting screening currents and applied currents at the inner side of the turn.

Local density of states in mesoscopic samples from scanning gate microscopy

We study the relationship between the local density of states (LDOS) and the conductance variation Delta 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 Delta G is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and Delta 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-Delta G correspondence by means of exact numerical simulations, when localized states or semiclassical orbits characterize the wave function of the system.

Wigner and Kondo physics in quantum point contacts revealed by scanning gate microscopy.

Quantum point contacts exhibit mysterious conductance anomalies in addition to well-known conductance plateaus at multiples of 2e(2)/h. These 0.7 and zero-bias anomalies have been intensively studied, but their microscopic origin in terms of many-body effects is still highly debated. Here we use the charged tip of a scanning gate microscope to tune in situ the electrostatic potential of the point contact. While sweeping the tip distance, we observe repetitive splittings of the zero-bias anomaly, correlated with simultaneous appearances of the 0.7 anomaly. We interpret this behaviour in terms of alternating equilibrium and non-equilibrium Kondo screenings of different spin states localized in the channel. These alternating Kondo effects point towards the presence of a Wigner crystal containing several charges with different parities. Indeed, simulations show that the electron density in the channel is low enough to reach one-dimensional Wigner crystallization over a size controlled by the tip position.

Direct growth of graphitic carbon on Si(111)

Appropriate conditions for direct growth of graphitic films on Si(111) 7 × 7 are investigated. The structural and electronic properties of the samples are studied by Auger electron spectroscopy, X-ray photoemission spectroscopy, low energy electron diffraction (LEED), Raman spectroscopy, and scanning tunneling microscopy (STM). In particular, we present STM images of a carbon honeycomb lattice grown directly on Si(111). Our results demonstrate that the quality of graphene films formed depends not only on the substrate temperature but also on the carbon buffer layer at the interface. This method might be very promising for graphene-based electronics and its integration into the silicon technology.

Sign reversal and tunable rectification in a ballistic nanojunction

Low-temperature measurements show that an asymmetric mesoscopic junction patterned in a two-dimensional electron gas can exhibit tunable rectification, including sign reversal. Strikingly, we observe that the amplitude and sign of the effect are governed by the conductances of the channels and that rectification is reversed without reversing the asymmetry of the device. Based on the temperature dependence of the rectified voltage, we show that the effect is ballistic and exhibits unexpected features with respect to predictions of available models.