## Wednesday, November 18, 2020

### Hard condensed matter can be soft, too.

In the previous post, I mentioned that one categorization of "soft" condensed matter is for systems where quantum mechanics is (beyond holding atoms together, etc.) unimportant.  In that framing, "hard" condensed matter looks at systems where $\hbar$ figures prominently, in the form of quantum many-body physics.  By that labeling, strongly interacting quantum materials are the "hardest" systems out there, with entanglement, tunneling, and quantum fluctuations leading to rich phenomena.

 Orientation textures in a liquid crystal, from wikipedia
Interestingly, in recent years it has become clear that these hard CM systems can end up having properties that are associated with some soft condensed matter systems.  For instance, liquid crystals are canonical soft matter systems.  As I'd explained long ago here, liquid crystals are fluids made up of objects with some internal directionality (e.g., a collection of rod-like molecules, where one can worry about how the rods are oriented in addition to their positions).  Liquid crystals can have a variety of phases, including ones where the system spontaneously picks out a direction and becomes anisotropic.  It turns out that sometimes the electronic fluid in certain conductors can spontaneously do this as well, acting in some ways like a nematic liquid crystal.  A big review of this is here.  One example of this occurs in 2D electronic systems in high magnetic fields in the quantum Hall regime; see here for theory and here for a representative experiment.  Alternately, see here for an example in a correlated oxide at the cusp of a quantum phase transition.

Another example:  hydrodynamics is definitely part of the conventional purview of soft condensed matter.   In recent years, however, it has become clear that there are times when the electronic fluid can also be very well-described by math that is historically the realm of classical fluids.   This can happen in graphene, or in more exotic Weyl semimetals, or perhaps in the exotic "strange metal" phase.  In the last of those, this is supposed to happen when the electrons are in such a giant, entangled, many-body situation that the quasiparticle picture doesn't work anymore.

Interesting that the hardest of hard condensed matter systems can end up having emergent properties that look like those of soft matter.