Condensed concepts

At the conference in Bangalore last week, Jeremy Levy (U. Pittsburgh) gave a fascinating talk about a significant new discovery that allows one to fabricate nanoscale electronic circuits at the interface between two transition metal oxide materials. (as described in this Science paper ) There were several things that were circumstantial about this discovery. * Jeremy had tickets to the 2006 World Cup Final in Germany. This led to a visit to Augsburg that stimulated the original ideas. * As a kid, Jeremy had played with Etch A Sketch and understanding how it works inspired the basic idea on how to "write" the circuit onto the interface. * The original fabrication was not done under vacuum but in air. It turned out that the water vapour present was essential to inducing charge carriers into the interface. When I started writing this post I thought the discovery involved serendipity , but that involves more when one is looking for something different.

This follows an earlier post about how spinons and gauge fields emerge in quantum antiferromagnets. It closely follows a review article by Subir Sachdev. Red font highlights important comments. The magnetic moment for a system with ordering wavevector K [which is incommensurate with the reciprocal lattice] can be written as One introduces a spinor w , which parameterizes N 1,2 by w to The Z 2 gauge transformation where ( r , )= 1. This Z 2 gauge invariance plays an important role in stabilising a spin liquid. [Compare this to a commensurate antiferromagnetic where there is a U(1) symmetry associated with the Schwinger bosons]. The idea is to use the Higgs mechanism to reduce the unbroken gauge invariance from U(1) to a discrete gauge group, Z 2 , and so reduce the strength of the gauge-flux fluctuations. [ This is key because U(1) gauge theories are confining in 2+1 dimensions, whereas Z2 can have a deconfined phase ]. To break U(1) down to Z 2 , we need a Higgs scalar, , that ca