第6回 物理工学科教室談話会 (講師:Prof. Jan Zaanen)

日 時: 2010年9月24日(金曜日) 14:00-
場 所: 工学部6号館1階 大会議室(103号室)
講 師: Prof. Jan Zaanen
Instituut Lorentz for Theoretical Physics, Leiden University
題 目: ”Mott collapse, statistical quantum criticality and high Tc superconductivity”

Shortly after the discovery of high Tc superconductivity nearly a quarter of a century ago Phil Anderson pointed out that this phenomenon might be rooted in the proximity to the Mott insulator. His ‘resonating valence bond’ idea was instrumental as a metaphor for this ‘different’ physics but due to the lack of real mathematical control this ‘Mottness’ problem turned into one of the main problems of modern fundamental physics. In some modified form similar principles might be at work in the new iron superconductors. Much more recently ZhengYu Weng of Tsinghua discovered that this Mottness actually alters the fundamental rules of quantum statistics: in doped Mott insulators neither Fermi-Dirac nor Bose-Einstein statistics is ruling, but instead a novel form of “Weng Statistics” where the exclusion principle and so forth are governed by the precise organization of the quantum matter. Based on high temperature expansions and a variety of other controlled results on the t-J model I will argue that Weng statistics is underlying the physics of the underdoped pseudogap regime, with its intrinsic tedencies towards superconductivity that are however hampered by equally intrinsic tendencies towards a variety of competing orders. I then will show that Weng statistics excludes the Fermi-liquid behavior found in overdoped cuprates, with the implication that the Mottness has to come to an end in optimally doped cuprates. Optimally doped cuprates are in the grip of a clash between Weng- and Fermi-Dirac statistics taking the form of a highly non-classical form of quantum criticality. Although we know very little about such states, I will present new results from numerical DCA calculations by Jarrel’s group showing that at such a quantum critical point one finds a ‘relevant quantum critical’ pair susceptibility that greatly enhances the BCS type superconducting instability.