## Department of Physics

### Department News

### Colloquium Announcement for Friday, September 29, 2017 (Speaker: Prof. Carlos Wexler)

**Sep 25, 2017**

Numbers in Condensed Matter Systems- a talk dedicated to the 2016 Nobel Prize in Physics

Speaker: Prof. Carlos Wexler

Date: Friday, September 29, 2017

Time: 4pm

Room: 205 Currens Hall

Abstract: In 1980 Klaus von Klitzing discovered [1] a remarkable quantization of the Hall conductance [2] of a quasi two-dimensional electron gas in a strong magnetic field at low temperatures: the conductance jumps in exact multiples of a fundamental conductance unit (depending only on Planck's constant and the change of the electron) and is independent on the type of semiconductor used, detailed experimental geometry and the presence of impurities or defects. In fact, this quantization is precise to less than a part per billion (and is currently the standard by which the unit of resistance, the Ohm, is defined!). How is it possible that such high-precision and highly reproducible measurements result from "dirty", and somewhat poorly controlled experimental conditions? The answer came in part from the realization of Thouless and colleagues about the topological nature of the Quantum Hall Effect, the Hall conductance is demonstrated to depend on the topology (a global property), and is thus robust against small defects or imperfections [3]. Another "application" of topology in condensed matter systems came earlier. In early 1970s there was considerable controversy on whether any long-range order could exist in 2D systems due to large-scale fluctuations. Experiments, however, showed clear evidence of low-temperature superfluidity and superconductivity. In 1972 Kosterlitz and Thouless [4] proposed a new type of phase transition based on the emergence, at the critical temperature, of free quantized vortices and anti-vortices. Vortices are a kind of topological defect where the fluid circulates around a singularity or core; they are topological as they correspond to the behavior of the fluid all the way around them! We call these vortices "quantized" because their "strength" can only come in integer multiples of a quantum of circulation (superfluids) or a quantum of flux (superconductors), which depend only on fundamental constants. This makes these objects remarkably robust, as they cannot easily dissipate by smoothly loosing strength. The Kosterlitz-Thouless vortex unbinding transition is able to explain in detail the emergence of two-dimensional superfluidity and superconductivity [5].

Notes:

Von Klitzing was awarded the Nobel in 1985; a second Nobel was awarded in 1998 to H. Stormer, D. Tsui and R. Laughlin for the discovery and explanation of the fractional QHE.

Ratio of longitudinal current to transverse induced voltage.

Thouless and Haldane shared 50% of the the 2016 Nobel Prize for their discoveries (I am not discussing Haldane´s work in this talk). It is remarkable that the QHE has resulted in 3 Nobel Prizes in Physics (1985, 1998, 2016)!

The transition was discovered independently by the late Vadim L. Berezinskii and is often referred to as the Berezinskii-Kosterlitz-Thouless transition. 5. Thouless and Kosterlitz shared 50% of the 2016 Nobel Prize for this achievement. Berezinskii died in 1980; Nobel Prizes are not given posthumously

About the speaker: Professor Carlos Wexler is a Professor of physics and the President of the Graduate Faculty Senate at the University of Missouri, Columbia. His research interests are in theoretical modeling and computer simulations of "nano-sponges"--materials with pores in the nanometer scale--that are capable of storing hydrogen and natural gas, phases and phase transitions observed in numerous quasi-two dimensional systems such as two-dimensional electron systems (Quantum Hall Effects), spins and spin chains ("Extended Universality"), and organic films deposited on a substrate.