Anomalous Dimensions and Unparticles in the Cuprate Superconductors

Condensed Matter Seminars

Speaker: Philip Phillips
Date & Time: March 10, 2016, 2:00 - 3:00
Location: Hennings 318
Local Contact: George Sawatzky
Intended Audience: Graduate

High-temperature superconductivity in the cuprates remains an unsolved problem because no knock-down experiment has revealed unambiguously the nature of the charge carriers in the normal state. I will show here that what is strange about the normal state is that the current for the underlying charge carriers possess an anomalous dimension. To show this, I will focus on the optical conductivity. Two features are problematic: 1) violation of the f-sum rule and 2) power-law scaling in the mid-infrared. So befuddling is the latter that even high-energy theorists have written papers on the puzzling ω-2/3 scaling law in the cuprates. The key claim here is that the observed power law is a universal consequence of gravity in the presence of translational symmetry breaking. I will explain this claim and report on a calculation that tests it. I will show that the general claim is not true. As an alternative, I will show how unparticles or a scale invariant sector in the mid-infrared can account for the experimentally observed power law and a violation of the f-sum rule. A feature of the unparticle construction is that they admit an anomalous dimension for the current. I will show how an anomalous dimension can be constructed from massive gravity. I will also show how anomalous dimensions can be experimentally probed by the fractional Aharonov- Bohm effect in the normal state of the cuprates.