Historical research guide · 0981 · 2019
Quantum atmospherics for materials diagnosis
Qing-Dong Jiang · Frank Wilczek
In one minute
Qing-Dong Jiang and Frank Wilczek point out that a material does not stop at its surface. If the matter inside breaks a symmetry — if it treats left and right, or forward and backward in time, differently — the quantum fluctuations of the electromagnetic field just outside inherit that lopsidedness. They call the result a quantum atmosphere, and they propose using it as an instrument: park an atom or a nitrogen-vacancy centre a few nanometres above a sample and read the material’s hidden order off the shift in the atom’s spectral lines, without touching the sample. One case is worked out in full. The surface of a topological insulator carries the extra term of axion electrodynamics, a piece of theory Wilczek wrote in 1987 for fundamental physics and now realised in a solid, and the atmosphere above it pulls on an electron’s spin like a magnetic field of about ten gauss at ten nanometres — far above what diamond magnetometers detect. They give the same treatment to time-reversal-breaking superconductors, then classify every operator such an atmosphere can be built from.
Connection
Chapter 2 holds that the vacuum is a structured medium rather than an absence, and this is that structure being turned into an instrument — the material’s own broken symmetry printed into the empty space above it and read back through an atom’s spectrum. Chapter 5 gets the analogue case, a field theory written for fundamental physics turning up inside a solid, and chapter 11 gets a way to identify a superconductor that does not depend on the Meissner effect and so survives in small samples and in the presence of magnetism.
From the source
Symmetry-breaking states of matter transmit their broken symmetry, through quantum fluctuations, to atoms and molecular complexes sitting near them, perturbing those spectra — so the vacuum immediately outside a sample becomes a readable diagnostic of the order inside it, and the authors judge spectroscopy an easier route to these effects than the long-range Casimir-type forces they also produce.Abstract; Introduction, first and second paragraphs; Summary
A topological insulator’s boundary carries the axion-electrodynamics term, the product of the electric and magnetic fields with a coefficient that is an odd integer times the fine-structure constant; because that product is a total derivative it changes nothing in the bulk, but at a boundary it leaves a Chern-Simons surface action and a two-photon vertex that violates parity and time reversal locally while preserving their product.Equations 1 and 2; Figure 1
Evaluating the corresponding Feynman diagram gives a spin-dependent potential falling as the inverse square of the distance from the surface, which written as an equivalent Zeeman field is of order ten gauss at ten nanometres — many orders of magnitude above the sensitivity of nitrogen-vacancy-centre magnetometry — although it is not true magnetic flux, so a SQUID detector registers nothing.Equations 3, 4 and 5; the paragraph following Equation 4
Applying an external electric field introduces no time-reversal violation of its own, but on such a surface it induces either a Hall-like current sheet or a surface magnetic charge, and either one produces a real magnetic field aligned or antialigned with the applied field of order ten gauss for a field of ten thousand volts per centimetre.Equation 6 and the paragraph introducing it
Chiral superconductors break time-reversal symmetry through the finite orbital angular momentum of their Cooper pairs, and their atmosphere produces a state-dependent magnetic energy shift that splits states of opposite angular momentum — mimicking a Zeeman interaction with an emergent magnetic field, and offering a discovery signature that does not rely on the Meissner effect, which is poorly suited to small regions and is itself disrupted by magnetism.Section ‘Atmosphere of superconductors’; Equation 7
Classifying every local electromagnetic operator that is quadratic in the fields and lowest order in gradients by its parity and time-reversal character yields eight candidates beyond the two Maxwell terms, and that inventory tells an experimenter what to look for: exclude a normal-times-spin interaction in a planar geometry first, then look for the two-direction operator in a more complex geometry, and watch for an atmospheric magnetic field whose direction depends on whether the applied electric field is rising or falling.Section ‘Operator analysis of polarizabilities’; Equations 9 to 14
The way in
https://doi.org/10.1103/physrevb.99.201104How to cite it
Qing-Dong Jiang, Frank Wilczek (2019) Quantum atmospherics for materials diagnosis doi:10.1103/physrevb.99.201104