Tip-induced Potential Research Articles

Scanning gate microscopy of localized states in a gate-defined bilayer graphene channel

We use Scanning Gate Microscopy to demonstrate the presence of localized states arising from potential inhomogeneities in a 50nm-wide, gate-defined conducting channel in encapsulated bilayer graphene. When imaging the channel conductance under the influence of a local tip-induced potential, we observe ellipses of enhanced conductance as a function of the tip position. These ellipses allow us to infer the location of the localized states and to study their dependence on the displacement field. For large displacement fields, we observe that localized states tend to occur halfway into the channel. All our observations can be well explained within the framework of stochastic Coulomb blockade.

Accurate characterization of tip-induced potential using electron interferometry

Using the tip of a scanning probe microscope as a local electrostatic gate gives access to real-space information on electrostatics as well as charge transport at the nanoscale, provided that the tip-induced electrostatic potential is well known. Here, we focus on the accurate characterization of the tip potential, in a regime where the tip locally depletes a two-dimensional electron gas (2DEG) hosted in a semiconductor heterostructure. Scanning the tip in the vicinity of a quantum point contact defined in the 2DEG, we observe Fabry–Pérot interference fringes at low temperature in maps of the device conductance. We exploit the evolution of these fringes with the tip voltage to measure the change in the depletion radius by electron interferometry. We find that a semi-classical finite-element self-consistent model taking into account the conical shape of the tip reaches a faithful correspondence with the experimental data.

Scanning-gate-induced effects and spatial mapping of a cavity

Tailored electrostatic potentials are at the heart of semiconductor nanostructures. We present measurements of size and screening effects of the tip-induced potential in scanning gate microscopy on a two-dimensional electron gas. First, we show methods on how to estimate the size of the tip-induced potential. Second, a ballistic cavity is studied as a function of the bias-voltage of the metallic top gates and probed with the tip-induced potential. It is shown how the potential of the cavity changes by tuning the system to a regime where conductance quantization in the constrictions formed by the tip and the top gates occurs. This conductance quantization leads to a unprecedented rich fringe pattern over the entire structure. Third, the effect of electrostatic screening of the metallic top gates is discussed.

Locally induced quantum interference in scanning gate experiments

We present conductance measurements of a ballistic circular cavity influenced by a scanning gate. In contrast to previous studies, we demonstrate the use of scanning gate microscopy as a tool for tailoring the potential landscape of nanostructures with a high degree of control. When the tip depletes the electron gas below, we observe very pronounced and regular fringes covering the entire cavity. The fringes correspond to transmitted modes in constrictions formed between the tip-induced potential and the boundaries of the cavity. Moving the tip and counting the fringes gives us exquisite control over the transmission of these constrictions. We use this control to form a quantum ring with a specific number of modes in each arm showing the Aharonov–Bohm effect in low-field magnetoconductance measurements.

Imaging magnetoelectric subbands in ballistic constrictions

We perform scanning gate experiments on ballistic constrictions in the presence of small perpendicular magnetic fields. The constrictions form the entrance and exit of a circular gate-defined ballistic stadium. Close to constrictions we observe sets of regular fringes creating a checker board pattern. Inside the stadium conductance fluctuations governed by chaotic dynamics of electrons are visible. The checker board pattern allows us to determine the number of transmitted modes in the constrictions forming between the tip-induced potential and gate-defined geometry. Spatial investigation of the fringe pattern in a perpendicular magnetic field shows a transition from electrostatic to magnetic depopulation of magnetoelectric subbands. Classical and quantum simulations agree well with different aspects of our observations.

Tilted potential induced coupling of localized states in a graphene nanoconstriction

We use the charged tip of a low temperature scanning probe microscope to perturb the transport through a graphene nanoconstriction. Maps of the conductance as a function of tip position display concentric halos, and by following the expansion of the halos with back-gate voltage we are able to identify an elongated domain over the nanoconstriction where they originate. Amplitude modulations of the transmission resonances are correlated with the gradient of the tip-induced potential and we analyze this in terms of modified coupling between localized states.

Scanning gate microscopy measurements on a superconducting single-electron transistor

We present measurements on a superconducting single-electron transistor (SET) in which the metallic tip of a low-temperature scanning force microscope is used as a movable gate. We characterize the SET through charge stability diagram measurements and compare them to scanning gate measurements taken in the normal conducting and the superconducting states. The tip-induced potential is found to have a rather complex shape. It consists of a gate voltage-dependent part and a part which is independent of gate voltage. Further scanning gate measurements reveal a dependence of the charging energy and the superconducting gap on the tip position and the voltage applied to it. We observe an unexpected correlation between the magnitude of the superconducting gap and the charging energy. The change in EC can be understood to be due to screening, however the origin of the observed variation in Δ remains to be understood. Simulations of the electrostatic problem are in reasonable agreement with the measured capacitances.

Measurement of the tip-induced potential in scanning gate experiments

We present a detailed experimental study on the electrostatic interaction between a quantum dot and the metallic tip of a scanning force microscope. Our method allowed us to quantitatively map the tip-induced potential and to determine the spatial dependence of the tip's lever arm with high resolution. We find that two parts of the tip-induced potential can be distinguished, one that depends on the voltage applied to the tip and one that is independent of this voltage. The first part is due to the metallic tip while we interpret the second part as the effect of a charged dielectric particle on the tip. In the measurements of the lever arm we find fine structure that depends on which quantum state we study. The results are discussed in view of scanning gate experiments where the tip is used as a movable gate to study nanostructures.

In situ treatment of a scanning gate microscopy tip

In scanning gate microscopy, where the tip of a scanning force microscope is used as a movable gate to study electronic transport in nanostructures, the shape and magnitude of the tip-induced potential are important for the resolution and interpretation of the measurements. Contaminations picked up during topography scans may significantly alter this potential. We present an in situ high-field treatment of the tip that improves the tip-induced potential. A quantum dot was used to measure the tip-induced potential.

Role of the electric field in surface electron dynamics above the vacuum level

Scanning tunneling spectroscopy (STS) is used to study the dynamics of hot electrons trapped on a Cu(100) surface in field emission resonances (FER) above the vacuum level. Differential conductance maps show isotropic electron interference wave patterns around defects whenever their energy lies within a surface projected band gap. Their Fourier analysis reveals a broad wave vector distribution, interpreted as due to the lateral acceleration of hot electrons in the inhomogeneous tip-induced potential. A line-shape analysis of the characteristic constant-current conductance spectra permits to establish the relation between apparent width of peaks and intrinsic line-width of FERs, as well as the identification of the different broadening mechanisms.

Imaging of quantum interference patterns within a quantum point contact

Visualization of quantum interference patterns has been obtained within a quantum point contact using scanning gate microscopy. The area distribution of the interference pattern is shown to be consistent with the interference area obtained from the magnetoconductance fluctuations of a quantum point contact. Both distributions follow the Gaussian unitary ensemble, corresponding to chaotic behavior. The interference is caused by the random potential fluctuations within the channel, which is modified by the tip-induced potential.

Domain nucleation and hysteresis loop shape in piezoresponse force spectroscopy

Electromechanical hysteresis loop measurements in piezoresponse force microscopy (PFM) [piezoresponse force spectroscopy (PFS)] have emerged as a powerful technique for probing ferroelectric switching behavior on the nanoscale. Interpretation of PFS data requires the relationship between the domain parameters and PFM signal to be established. Here, the authors analyze the switching process using modified point charge model. The charge parameters are selected to reproduce tip-induced surface potential and tip radius of curvature. The relationship between geometric parameters of semiellipsoidal domain and PFM signal is derived using linear Green’s function theory. The role of domain nucleation on hysteresis loop is established.

Scanning a metallic tip close to a quantum point contact

Low-temperature transport experiments on a quantum point contact under the influence of a scanning gate are reported. The scanning gate is the metallic tip of a scanning force microscope operating at a temperature of 300 mK. In particular, the influence of the scanning tip on conductance resonances observed in the gate-characteristics of the point contact is studied. The strongest conductance resonances appear to be related to the local potential within the channel of the point contact. As a consequence, the point contact with its conductance resonances can be used as a sensor for the local tip-induced potential.