Person:

Bhandari, Sagar

Scanning probe techniques can be used to probe electronic properties at the nanoscale, to shed light on the physics of nanoscale devices: Graphene is of great interest for its promise in both applied (e.g. spintronics and valleytronics) and fundamental research (e.g. quantum Hall and Dirac fermions). We successfully used a cooled scanning gate microscope to image the motion of electrons along cyclotron orbits for magnetic focusing in graphene. Part of my time at Harvard was also spent incorporating a low temperature scanning capacitance setup into the existing microscope as well as building a low temperature coarse positioning system.

To image magnetic focusing of electrons in graphene, a conducting tip of a scanned probe microscope is held just above the sample surface, and an applied tip-to-sample voltage creates an image charge that is moved while the transresistance between two leads is measured. The sample is a high mobility hBN-graphene-hBN sandwich etched into hall bar geometry with two point contacts along each side. By tuning the transverse magnetic field B and electron density n in the graphene layer, we observe the first few magnetic focusing peaks. For values of B and n that correspond to the first magnetic focusing peak, we observe an image of the cyclotron orbit that extends from one point contact to the other. We also study the effects of B and n on the spatial distribution of electron trajectories as we move away from the magnetic focusing peak.

We also present the design and implementation of a cooled scanning capacitance probe that operates at liquid He temperatures to image electrons in nanodevices. In this setup, an applied sample-to-tip voltage creates an image charge that is measured by a cooled charge amplifier adjacent to the tip. The circuit is based on a low-capacitance, high-electron-mobility transistor(HEMT) (Fujitsu FHX35X). The input is a capacitance bridge formed by a low capacitance pinched-off HEMT transistor and the tip-sample capacitance. We have achieved a low noise level (0.13 e/ Hz^0.5) and high spatial resolution (100 nm) for this technique, which promises to be a useful tool to study electronic behavior in nanoscale devices.

Among newly discovered two-dimensional (2D) materials, semiconducting ultrathin sheets of MoS2 show potential for nanoelectronics. However, the carrier mobility in MoS2 is limited by scattering from surface impurities and the substrate. To probe the sources of scattering, we use a cooled scanning probe microscope (SPM) to image the flow of electrons in a MoS2 Hall bar sample at 4.2 K. Capacitive coupling to the SPM tip changes the electron density below and scatters electrons flowing nearby; an image of flow can be obtained by measuring the change in resistance between two contacts as the tip is raster scanned across the sample. We present images of current flow through a large contact that decay exponentially away from the sample edge. In addition, the images show the characteristic "bullseye" pattern of Coulomb blockade conductance rings around a quantum dot as the density is depleted with a back gate. We estimate the size and position of these quantum dots using a capacitive model.

We have used cooled scanning probe microscopy (SPM) to study electron motion in nanoscale devices. The charged tip of the microscope was raster-scanned at constant height above the surface as the conductance of the device was measured. The image charge scatters electrons away, changing the path of electrons through the sample. Using this technique, we imaged cyclotron orbits that flow between two narrow contacts in the magnetic focusing regime for ballistic hBN–graphene–hBN devices. We present herein an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge density dip on the motion of ballistic electrons. The density dip locally reduces the Fermi energy, creating a force that pushes electrons away from the tip. When the tip is above the cyclotron orbit, electrons are deflected away from the receiving contact, creating an image by reducing the transmission between contacts. The data and our analysis suggest that the graphene edge is rather rough, and electrons scattering off the edge bounce in random directions. However, when the tip is close to the edge, it can enhance transmission by bouncing electrons away from the edge, toward the receiving contact. Our results demonstrate that cooled SPM is a promising tool to investigate the motion of electrons in ballistic graphene devices.

Ultrathin sheets of MoS2 are a newly discovered 2D semiconductor that holds great promise for nanoelectronics. Understanding the pattern of current flow will be crucial for developing devices. In this talk, we present images of current flow in MoS2 obtained with a Scanned Probe Microscope (SPM) cooled to 4 K. We previously used this technique to image electron trajectories in GaAs/AlGaAs heterostructures and graphene. The charged SPM tip is held just above the sample surface, creating an image charge inside the device that scatters electrons. By measuring the change in resistance ΔR while the tip is raster scanned above the sample, an image of electron flow is obtained. We present images of electron flow in an MoS2 device patterned into a hall bar geometry. A three-layer MoS2 sheet is encased by two hBN layers, top and bottom, and patterned into a hall-bar with multilayer graphene contacts. An SPM image shows the current flow pattern from the wide contact at the end of the device for a Hall density n = 1.3×1012 cm-2. The SPM tip tends to block flow, increasing the resistance R. The pattern of flow was also imaged for a narrow side contact on the sample. At density n = 5.4×1011 cm-2; the pattern seen in the SPM image is similar to the wide contact. The ability to image electron flow promises to be very useful for the development of ultrathin devices from new 2D materials.

Electrons in graphene can travel for several microns without scattering at low temperatures, and their motion becomes ballistic, following classical trajectories. When a magnetic field B is applied perpendicular to the plane, electrons follow cyclotron orbits. Magnetic focusing occurs when electrons injected from one narrow contact focus onto a second contact located an integer number of cyclotron diameters away. By tuning the magnetic field B and electron density n in the graphene layer, we observe magnetic focusing peaks. We use a cooled scanning gate microscope to image cyclotron trajectories in graphene at 4.2 K. The tip creates a local change in density that casts a shadow by deflecting electrons flowing nearby; an image of flow can be obtained by measuring the transmission between contacts as the tip is raster scanned across the sample. On the first magnetic focusing peak, we image a cyclotron orbit that extends from one contact to the other. In addition, we study the geometry of orbits deflected into the second point contact by the tip.

A cooled scanning probe microscope (SPM) is an ideal tool to image electronic motion in graphene: the SPM tip acts as a scanning gate, which interacts with the electron gas below. We introduce the technique using our group's previous work on imaging electron flow from a quantum point contact in a GaAs 2DEG and tuning an InAs quantum dot in an InAs/InP nanowire. Carriers in graphene have very different characteristics: electrons and holes travel at a constant speed with no bandgap, and they pass through potential barriers via Klein tunneling. In this paper, we review the extension of SPM imaging techniques to graphene. We image the cyclotron orbits passing between two narrow contacts in a single-atomic-layer graphene device in a perpendicular magnetic field. Magnetic focusing produces a peak in transmission between the contacts when the cyclotron diameter is equal to the contact spacing. The charged SPM tip deflects electrons passing from one contact to the other, changing the transmission when it interrupts the flow. By displaying the change in transmission as the tip is raster scanned above the sample, an image of flow is obtained. In addition, we have developed a complementary technique to image electronic charge using a cooled scanning capacitance microscope (SCM) that uses a sensitive charge preamplifier near the SPM tip to achieve a charge noise level 0.13 e Hz−1/2 with high spatial resolution 100 nm. The cooled SPM and SCM can be used to probe the motion of electrons on the nanoscale in graphene devices.

Graphene has been touted as the prototypical two-dimensional solid of extraordinary stability and strength. However, its very existence relies on out-of-plane ripples as predicted by theory and confirmed by experiments. Evidence of the intrinsic ripples has been reported in the form of broadened diffraction spots in reciprocal space, in which all spatial information is lost. Here we show direct real-space images of the ripples in a few-layer graphene (FLG) membrane resolved at the atomic scale using monochromated aberration-corrected transmission electron microscopy (TEM). The thickness of FLG amplifies the weak local effects of the ripples, resulting in spatially varying TEM contrast that is unique up to inversion symmetry. We compare the characteristic TEM contrast with simulated images based on accurate first-principles calculations of the scattering potential. Our results characterize the ripples in real space and suggest that such features are likely common in ultrathin materials, even in the nanometer-thickness range.

A cooled scanning probe microscope (SPM) has been used to image cyclotron orbits of electrons through high-mobility graphene in a magnetic field.1-5 In a hBN-graphene-hBN device patterned into a hall bar geometry, the magnetic field focuses a current Ii injected from one narrow contact into another narrow contact located an integer number of cyclotron diameters away, creating a voltage Vc. The degree of focusing is measured by the transresistance Rm = Vc/Ii. In SPM, the tip can either enhance or decrease conductance in the sample by deflecting electrons into or away from the second contact, respectively.3,4 Our SPM images of magnetic focusing feature a region in which the tip transitions from enhancing to decreasing the conductance in the sample where the change in transresistance caused by the tip is equal to zero. In this paper, we investigate how the location of this region in the graphene sample changes as we modulate the electron density n and magnetic field B. By plotting line-cuts of the change in trans-resistance for different electron densities and magnetic fields, we identify trends in the inflection point where the tip changes from enhancing to decreasing the conductance in the sample. From the location of each transition region, we show that the cyclotron diameter of the electron trajectories can be obtained, and explain the trends in inflection point location for different electron densities and magnetic fields.