## Tuesday, December 20, 2016

### Mapping current at the nanoscale - part 2 - magnetic fields!

A few weeks ago I posted about one approach to mapping out where current flows at the nanoscale, scanning gate microscopy.   I had made an analogy between current flow in some system and traffic flow in a complicated city map.  Scanning gate microscopy would be analogous recording the flow of traffic in/out of a city as a function of where you chose to put construction barrels and lane closures.  If sampled finely enough, this would give you a sense of where in the city most of the traffic tends to flow.

Of course, that's not how utilities like Google Maps figure out traffic flow maps or road closures.  Instead, applications like that track the GPS signals of cell phones carried in the vehicles.  Is there a current-mapping analogy here as well?  Yes.  There is some "signal" produced by the flow of current, if only you can have a sufficiently sensitive detector to find it.  That is the magnetic field.  Flowing current density $\mathbf{J}$ produces a local magnetic field $\mathbf{B}$, thanks to Ampere's law, $\nabla \times \mathbf{B} = \mu_{0} \mathbf{J}$.
 Scanning SQUID microscope image of x-current density  in a GaSb/InAs structure, showing that the current is  carried by the edges.  Scale bar is 20 microns.  Image

Fortunately, there now exist several different technologies for performing very local mapping of magnetic fields, and therefore the underlying pattern of flowing current in some material or device.  One older, established approach is scanning Hall microscopy, where a small piece of semiconductor is placed on a scanning tip, and the Hall effect in that semiconductor is used to sense local $B$ field.

 Scanning NV center microscopy to see magnetic fields, Scale bars are 400 nm.
Considerably more sensitive is the scanning SQUID microscope, where a tiny superconducting loop is placed on the end of a scanning tip, and used to detect incredibly small magnetic fields.  Shown in the figure, it is possible to see when current is carried by the edges of a structure rather than by the bulk of the material, for example.

A very recently developed method is to use the exquisite magnetic field sensitive optical properties of particular defects in diamond, NV centers.  The second figure (from here) shows examples of the kinds of images that are possible with this approach, looking at the magnetic pattern of data on a hard drive, or magnetic flux trapped in a superconductor.  While I have not seen this technique applied directly to current mapping at the nanoscale, it certainly has the needed magnetic field sensitivity.  Bottom line:  It is possible to "look" at the current distribution in small structures at very small scales by measuring magnetic fields.