In my element: Thr ough the P ough the P iodic Table with pen and computer ith Mikhail Katsnelson
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1 In my element: Through the Periodic Table with pen and computer Mikhail Katsnelson
2 A philosophical statement Knowledge begins, so to speak, in the middle, and leads into the unknown - both when moving upward, and when there is a downward movement. Our goal is to gradually dissipate the darkness in both directions, and the absolute foundation - this huge elephant carrying on his mighty back the tower of truth - it exists only in a fairy tales (Hermann Weyl)
3 What does it mean for condensed matter physics and materials science? Everything follows from quantum mechanics plus electrodynamics; QED is enough to explain all properties of matter around us That is all. Please tell me why iridium is brittle and platinum is ductile, copper is red and silver is white, iron is ferromagnetic and vanadium is not... Not talking on biochemistry and biophysics!
4 Does it help? Navier-Stocks equations: Turbulence is here! Can you explain this?
5 Is fundamental physics fundamental? Classical thermodynamics is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts (A. Einstein). The laws describing our level of reality are essentially independent on the background laws. I wish our colleagues from true theory (strings, quantum gravity, etc...) all kind of success but either they will modify electrodynamics and quantum mechanics at atomic scale (and then they will be wrong) or they will not (and then I do not care). Our way is down. How to pass from known basic laws of nature to understanding all richness and diversity of the world around us? Pure chemical elements are already complicated enough to think very seriously
6 The aim of science: Understanding Duality of understanding and knowledge Newton laws... Rotation... Air resistance... I know this stuff but the result will be... well... He does not know (?!) Newton Mechanics but it works! He feels (=understands) what to do I think I can safely say that nobody understands quantum mechanics (R. P. Feynman)
7 Scylla and Charybdis Understanding in general Everything is from water/fire/earth/gauge fields/quantum space-time foam/strings... and the rest is your problem. But why silver is white, copper is red an gold is yellow? Density functional calculations Cu Ag Au Taken from C. Ortiz, O. Eriksson and M. Klintenberg Comput. Mater. Sci. 44, 1042 (2009).
8 Scylla and Charybdis II (Nobel lecture)
9 Periodic Table Can we understand something elementary? D. I. Mendeleev
10 An example: Alkali metals Ambient conditions: all body-centered cubic Li, Na at low temperatures: 9R Why? Well... Total energies are very, very close (difference 10-4 ) Just numbers... Calculate! Why opposite behavior with pressure?
11 Understanding?! Van Hove singularities: topological property of any energy spectrum in crystals bcc Na: away from E F bcc Li: towards E F Different role of p-electrons VHS near E F destabilize crystal structure (a general theory)
12 Exchange interactions and magnetism Allows to do calculations for specific materials and explain general tendencies (e.g., AFM near half-filled d-band) Basic theory to find a way to improve properties of magnetic materials Spin-wave spectrum of iron
13 Orbital Kondo resonance Waves from defects sp «Orbital Kondo resonance» XZ Cr(001) YZ New many-body phenomenon in pure element
14 From atoms to nano and mesoscale
15 Elements are interesting Li, Na, K, Rb, Cs Ca, Sr, Ba Ti, Zr, Hf Cr, Mn, Fe, Co, Ni Ir, Rh Sc, Y, La, Yb Pu... Carbon!!!
16 Allotropes of Carbon Diamond, Graphite Graphene: prototype truly 2D crystal Nanotubes Fullerenes
17 Why graphene is interesting? 1. Applications (modern electronics is 2D, bulk is ballast) 2. Prototype membrane (new drosophila for 2D statistical mechanics) 3. CERN on the desk (mimic high energy physics) Ripples Fasolino, Los & MIK, Nature Mater. 6, 858 (2007) Klein tunneling MIK, Novoselov, Geim, Nature Phys. 2, 620 (2006)
18 Correct theories from wrong assumptions Electromagnetic fields as deformations in ether; gears and wheels Also: Dirac equation... Landau theory of superfluidity of helium...
19 Theoretical physics as a variety of mistique experience Beloved, believe not every spirit, but try the spirits whether they are of God (1 John 4:1) Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? (Matthew 7:16) Fruits: to predict something correctly (like Maxwell electromagnetic waves, and then applications) Top pleasure and top dream for a theoretician Graphene 1. Klein tunneling 2. Pseudomagnetic fields due to deformations 3. Relativistic collapse at a supercritical charge
20 Predicted and confirmed
21 Plans To combine studies of particular systems (graphene, iron...) with general concepts - Many-body theory of graphene - Statistical mechanics of membranes - Pattern formation and the origin of physical and chemical complexity - Magnetism out of equilibrium
22 Many thanks!!! To NWO for this sign of recognition and opportunity to do further really interesting science (which will be useful) To my friends, colleagues, collaborators, coauthors, teachers and pupils To Radboud University, Faculty of Science, Institute for Molecules and Materials for wonderful environment and support To FOM for support And thank you for your attention
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