Visualization is a Powerful Tool
The greatest advantage of the spectroscopic imaging scanning tunneling microscopy (SI-STM) is the capability to visualize various facets of the systems under study. The visualization goes beyond simply determining the geometric structure of the crystal and most importantly includes acquiring spatial information about how the electronic structure arranges itself. Modern synthetic electronic materials give rise to new phases where the patterns of electronic densities are the key to understanding their underlying symmetries and microscopic ingredients relevant to their formation. On the Research page, the d-form factor density wave, an example from my own research, demonstrates this case vividly.
Scanning Tunneling Microscope (STM)
The primary observable in scanning tunneling microscopy (STM) is the spatially and bias dependent tunneling current, I(r,V), between the STM tip and the sample under study. Owing to its exponential dependence on tip-sample separation, the tunneling current is an incredibly sensitive probe of surface corrugation as the STM tip is scanned along the sample surface. Such a measurement gives atomically resolved topographic information about the surface. The video below shows the real-time trace of the STM tip height (red trace) as it scans over atoms in a sample of BSCCO-2212. The image on the right shows the final surface topograph of the BiO termination layer
Because the tip can be within fractions of an Angstrom of the sample surface the mechanical stability and vibration free operation of the apparatus is of the utmost importance to prevent jostling the tip into the surface. While the feedback control system can also minimize the chance of tip crashes for a more mechanically noisy system, the quality of the resultant images will be greatly diminished. As such, high quality vibration isolation is one of the most important elements of proper STM design.
The tunneling process allows for the determination of the spectroscopic quantity known as the the local density of states (LDOS). It can be shown that in the weak coupling limit of tip to sample that the energy resolved differential conductance, dI/dV, is proportional to the local density of states (LDOS). The figure below shows such a curve on a sample of URu2Si2 taken at a particular position on the sample surface. In the small energy window of -5mV to 10mV, sampled every 250μV, the LDOS shows a distinct set of dips and peaks. The significance of these features was only determined by spectroscopic imaging (see next section).
Depending on the stability of an STM instrument, the acquisition time for such a spectrum can vary between several seconds and several minutes. The greater the stability, the less the averaging time and the closer that the STM tip can approach the surface thus increasing signal without the chance of crashing.
Spectroscopic Imaging Scanning Tunneling Microscope (SI-STM)
While it is not a major concern if one spectrum takes 1 minute instead of 5 seconds if one were to measure only a few spectra at a set of distinct locations, there is a substantial time difference when trying to acquire over 100 000 spectra. A highly stable instrument that can take a high quality spectrum in 5 seconds can then acquire 100 000 spectra in just under 6 days. For an STM that needs 1 minute per spectrum this time balloons to an impractical 2.5 months.
So, why would one want 100 000 spectra? This is the basis for spectroscopic imaging, where the LDOS is acquired on finely spaced spatial grid over a region of the sample surface. In this way the spatial variations of the energy resolved LDOS are imaged which can yield an almost infinite amount of information (see next section).
Below is shown a few energy layers of the LDOS map on a sample of URu2Si2. Each layer represents the density of states at a given energy spatially resolved over a 50x50nm field of view on grid of 300×300 pixels. The curve in the top right corner is a representative spectrum showing energy on the x-axis and the conductance on the y-axis. The complete map is comprised of 5.5 million data points acquired in 5 days.
Under Heavy Fermion Research is described how such a map was used to observe for the first time the formation of heavy fermion bands in momentum space. Furthermore, the amplitude of the periodic modulations in each layer of the LDOS map which provides the momentum space information is sufficiently small that the STM tip must be extremely close to the surface to achieve a high enough signal/noise ratio. The success of the experiment crucially relied on the mechanical stability of instrument. The section below on STM Infrastructure sketches some of the requirements to achieve such high performance.
What does SI-STM Visualize?
Beyond visualizing the surface topography and defect locations SI-STM maps out the LDOS as a function of position r=(x,y), and energy E = eV, g(r,E). Within this multidimensional data set is contained an almost infinite amount of information. One can liken it to the data from the region of collision inside a particle accelerator where layers and layers of physics is buried waiting to be discovered through novel data analysis and theoretical interpretation. Similarly, because of the fundamental nature of the density of states, within g(r,E) is contained a wealth of information about the active physics and electronic organization:
- intra-unit-cell and energy resolved density of states
- momentum space band structure through quasiparticle interference imaging
- self-energy alterations due to mode coupling
- real space electronic density disorder
- short length scale order
- energy scale maps
- identification of bosonic modes
- global and local broken symmetries
- localization effects
- spatial inhomogeneity of microscopic coupling parameters
- superconducting gap symmetries
- mechanism for pair mediation in novel superconductors
- phase and domain boundaries
- local images of bound statesvortex core structure
The gallery gives a few examples of the various images generated by SI-STM data that are used to identify the various physical observables listed above.
The range of observables can be expanded even further by extending the capabilities of the apparatus. For example, by using a spin polarized or superconducting tip, increasing the measurement bandwidth, biasing the sample for non-equilibrium measurements, or mechanically straining the sample for broken symmetry studies.
Advantages of SI-STM for Material Exploration
Modern synthetic materials are host to a rich interplay between localized and itinerant physics making the simultaneous knowledge of real and momentum space information critically important. As we engineer materials to finely tune between these two extremes we require more in depth and detailed knowledge about the electronic structure modifications. In these terms SI-STM provides the following advantages
- simultaneous access to energy resolved real space and momentum space electronic structure
- temperature range: 150K → 10mK to span multiple thermodynamic phases including access quantum critical regimes
- Magnetic field: Up to 20T (currently limited by magnet technology)
- Sub-100 μV energy resolution to detect fine alterations to electronic structure including low temperature superconductivity
- Sub-Angstrom spatial resolution for intra-unit cell research
The most important design consideration for developing a SI-STM system is mechanical stability. Without it the time required to obtain spectroscopic images as discussed in the previous sections inflates to impractical periods rendering the whole practice unfeasible. Furthermore, weak spectroscopic signatures require positioning the tip very close to the surface to increase the signal. Without high stability the tactic would be disastrous. The main principles of mechanical stability to consider are
- Quiet Surroundings: Choose a location in a building that is removed from external noise sources such as foot traffic, roads, windows, air ventilation work. Typically this means constructing an STM in the basement within a separate experimental room not generally accessible during operation.
- High Inertia: Regardless of location there will always be external sources of mechanical excitation such as the vibrations in the floor or the flow of air the experimental room. By making a massive support structure for the STM, external forces will only generate minimal motion that can be transferred to the STM head.
- Resonance frequency mismatch: If one views the STM infrastructure like a set of Russian dolls, in which there are successive levels vibration isolation, then the most effective way to minimize the transfer of kinetic energy to the next stage is to offset their resonant frequencies. Making the outer layer of vibrations isolation have a very low resonance frequency and then shifting to higher values on the inner layers is a passive method to quiet the STM stage. In fact the the STM head itself also follows this layering scheme making the head design and materials one of the most important elements. In the schematic diagram below, the massive 30 ton concrete slab, atop which sits the STM experimental room, is made to float by the use of 6 high load air springs. When the springs are pressurized the natural resonance frequency of the room is 1-2Hz. Inside the room 3 lead filled pillars support a massive table assembly which suspends the liquid helium (LHe) dewar housing the cryogenic STM probe. The table’s natural resonance frequency when floating is 10-15Hz. The cryogenic probe (not shown) terminates near the bottom of the LHe dewar at the STM stage. The probe is made to be extremely rigid so that its mechanical modes are in the kHz range. Finally, the STM head itself, pictured below to the right, is designed and constructed from materials that push its mechanical mode resonances to the tens of kilohertz.
- Acoustic Isolation: Acoustic noise that is not directly transferred through the foundations of the STM room and table assembly are not blocked by the isolation system described above. Furthermore, any room can have acoustic modes that when excited can generate large amplitude motion at the STM head. Layers of high quality acoustic isolation in the successive layers of the STM infrastructure are necessary for the quiet and successful operation of the STM.
- Low Temperatures: Removing jitter due to thermal motion provides a final but important element to quiet the STM head. At 4K, taking into account all of the above vibration isolation tactics, the vibrational amplitude of the STM tip reaches as astonishingly low 10-15m Hz-1.
Finally, the image below is a view from outside the RF-shielded floating acoustic room peering in to see the naked STM probe with the LHe dewar lowered into the pit below. While the scale of the instrument is large, the visual access it grants to the quantum world is well worth it.