Theory of scanning gate microscopy

The conductance of graphene nanoribbons and nanoconstrictions under the effect of a scanning gate microscopy tip is systematically studied. Using a scattering approach for noninvasive probes, the first- and second-order conductance corrections caused by the tip potential disturbance are expressed explicitly in terms of the scattering states of the unperturbed structure. Numerical calculations confirm the perturbative results, showing that the second-order term prevails in the conductance plateaus, exhibiting a universal scaling law for armchair graphene strips. For stronger tips, at specific probe potential widths and strengths beyond the perturbative regime, the conductance corrections reveal the appearance of resonances originated from states trapped below the tip. The zero-transverse-energy mode of an armchair metallic strip is shown to be insensitive to the long-range electrostatic potential of the probe. For nanoconstrictions defined on a strip, scanning gate microscopy allows to get insight into the breakdown of conductance quantization. The first-order correction generically dominates at low tip strength, while for Fermi energies associated with faint conductance plateaus, the second-order correction becomes dominant for relatively small potential tip strengths. In accordance with the spatial dependence of the partial local density of states, the largest tip effect occurs in the central part of the constriction, close to the edges. Nanoribbons and nanoconstrictions with zigzag edges exhibit a similar response as in the case of armchair nanostructures, except when the intervalley coupling induced by the tip potential destroys the chiral edge states.

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.

Scanning gate microscopy is used to locally investigate electron transport in a high-mobility two-dimensional electron gas formed in a GaAs/AlGaAs heterostructure. Using quantum point contacts, we observe branches caused by electron backscattering decorated with interference fringes similar to previous observations by Topinka et al (2000 Science289 2323). We investigate the branches at different points of a conductance plateau as well as between plateaus, and demonstrate that the most dramatic changes in branch pattern occur at the low-energy side of the conductance plateaus. The branches disappear at magnetic fields as low as 50 mT, demonstrating the importance of backscattering for the observation of the branching effect. The spacing between the interference fringes varies by more than 50% for different branches across scales of microns. Several scenarios are discussed to explain this observation.

We have developed a new high-frequency scanning gate microscopy (HF-SGM), in which high-frequency electrical signals can be applied on the conductive tip of an atomic force microscope (AFM). The high-frequency characteristics are investigated by correlation measurement on a semiconductor quantum point contact (QPC). The time-dependent potential of the tunneling barrier is induced from the AFM tip and probed with another voltage pulse applied on the source electrode. The measurement indicates that an electrical pulse as short as 5 ns can be applied without significant distortion. The demonstrated HF-SGM would allow us to investigate the dynamic response from various nanostructures.

In a nanomechanical resonator coupled to a quantum point contact, the back action of the electronic state on mechanical motion is studied. The quantum point contact conductance changing with subband index and the eigenfrequency of the resonator are found to correlate. A model is constructed explaining the frequency deviations by the variable ability of the quantum point contact to screen the piezoelectric charge induced by mechanical oscillations. The observed effects can be used to develop electromechanical methods for studying the density of states in quasi-one-dimensional systems.

Reprint of : Scattering approach to scanning gate microscopy

An investigation of the background potential in quantum constrictions using scanning gate microscopy and a swarming algorithm

Scanning gate microscopy on a graphene quantum point contact

The authors present scanning gate microscopy (SGM) measurements of an in-plane gated open quantum dot and relate structures within the measurement to a theoretical calculation of the change in conductance in a similar dot. The dot was fabricated in GaAs/AlGaAs. Electron beam lithography and wet etching were used to isolate the two dimensional electron gas and form the device geometry. The SGM image was then high-pass filtered to show both classical and quantum behavior and similarities to a calculated structure are suggested.

Probing single charge dynamics in solids can give insights into various quantum transport phenomena, most of which are fragile and short-time-scaled. Detection of these events in real-time requires a mesoscopic electrical amplifier with unprecedented sensitivity and operational bandwidth. In this work, we explore a hybrid electrical amplifier consisting of a semiconducting quantum point contact galvanically coupled to a superconducting λ/2 transmission-line resonator for ultra-fast and ultra-sensitive charge amplification. The resonator, made of aluminium with a coplanar waveguide geometry, is designed to operate at its first harmonic resonant mode ∼3.4 GHz, where the reflected power from the resonator is amplitude-modulated by the conductance changes in the quantum point contact channel. From the sidebands of the amplitude modulated reflected signal we extract a conductance sensitivity of 2.85×10−7e2/h/Hz 11.05pSHz−1/2 ). This sensitivity translates to a unit signal-to-noise measurement time ∼1.62 ns for a variation of 0.01 ( e2/h in the conductance. From the analysis of the noise characteristics of the device, we find that up to a few MHz of signal frequency the sensitivity is limited by the photon assisted shot-noise associated with the electron tunnelling in the QPC channel. The optimization of various operational parameters of the device reveals a bandwidth of ∼155 MHz which corresponds to a rise-time ∼2.2 ns. Both the sensitivity and bandwidth that we obtain are greater by an order compared to the existing reports. In addition, the device also exhibits very good sensitivities ∼3.58×10−4e2/h/Hz up to a measurable frequency of 240 MHz. The extremely high sensitivity, shot-noise limited detection, ultra-fast operation reaching the nanosecond time-scales, and the circuit QED architecture makes this scheme an attractive choice for single charge detection and counting experiments for spin-qubit readout and quantum electrical metrology.

Coherent charge transport along ballistic paths can be introduced into graphene by Andreev reflection, for which an electron reflects from a superconducting contact as a hole, while a Cooper pair is transmitted. We use liquid-helium cooled scanning gate microscopy (SGM) to image Andreev reflection in graphene in the magnetic focusing regime, where carriers move along cyclotron orbits between contacts. Images of flow are obtained by deflecting carrier paths and displaying the resulting change in conductance. When electrons enter the superconductor, Andreev-reflected holes leave for the collecting contact. To test the results, we destroy Andreev reflection with a large current and by heating above the critical temperature. In both cases, the reflected carriers change from holes to electrons.

Imaging of Condensed Quantum States in the Quantum Hall Effect Regime

We examine the properties of an infinite-$U$ Anderson impurity coupled to both normal and superconducting metals. Both the cases of a quantum dot and a quantum point contact containing an impurity are considered; for the latter, we study both one and two-channel impurities. Using a generalization of the noncrossing approximation which incorporates multiple Andreev reflection, we compute the impurity spectral function and the linear-response conductance of these devices. We find generically that the Kondo resonance develops structure at energies corresponding to the superconducting gap, and that the magnitude of the resonance at the Fermi energy is altered. This leads to observable changes in the zero-bias conductance as compared to the case with no superconductivity.

Selective control of edge-channel trajectories by scanning gate microscopy

The use of lithium metal in secondary batteries has been impeded by its tendency to form dendrites: branching conductive structures of metal that can lead to capacity loss and, ultimately, internal shorts in the battery. Patterned electrodes, in addition to artificially increasing the current density of cells by increasing the surface area available for reaction, also generate a nonuniform electric field in the vicinity of the electrode surface. This nonuniform electric field, though rapidly screened by the electrolyte, can promote inhomogeneous deposition and Solid Electrolyte Interphase formation. As the consequence of these effects is not theoretically apparent since Solid Electrolyte Interphase volume and conductivity changes can, in principle, offset variations in local current density, we have performed experiments to examine the deposition of Li on nonuniform electrode surfaces using Atomic Force Microscopy. We measure the local variations in topography, SEI thickness, and composition, and discuss their implications for the formation of dendrites in Li metal.