In papers studying or searching for topological order (intrinsic or symmetry-protected) in various condensed matter systems (e.g. Field-tuned and zero-field fractional Chern insulators in magic angle graphene), a common refrain of motivation goes as follows:

  • Topological physics began with the experimental discovery of the integer and fractional quantum Hall effect, for very clean two-dimensional electron gases in a large magnetic field.
  • The large magnetic field is unfortunate, and it would be nice to get rid of it.
  • In fact the large field is not necessary, and equally interesting physics can arise in our system due to strong interactions, time-reversal breaking, etc.

But I realized I never really understood the second point: why is a large B such a problem? What applications or lines of scientific inquiry does it challenge? To what degree are these challenges insurmountable?

  • $\begingroup$ From page 1: „On a practical level, the FQHE has been proposed as a platform for fault-tolerant topological quantum computers. However, this possibility is hindered by the relatively large external magnetic field required …“ $\endgroup$ Commented Jun 19, 2023 at 3:54

1 Answer 1


One answer is that large magnetic fields are hard to make, and give you many additional experimental limitations (including just amount of physical space for the experiment). For the purposes of fundamental physics research, this is not really a barrier and large magnetic fields (up to ~100T) are routinely used to probe solid states systems. However, if you want to make nanoscale devices leveraging topological physics, and especially manipulating the topological properties of different parts of the system at the same time (for example qubits in quantum computers where everything has to happen at extremely low temperature within a dilution refrigerator), the technological challenge is enhanced greatly if external magnetic field is required.

Another aspect is that some very powerful experimental probes are not possible to do in magnetic field, such as angle resolved photoemission spectroscopy (ARPES).


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