Slater vs Anderson Construction of modern condensed matter

Slater vs. Anderson: Construction of modern condensed matter physics Ki-Seok Kim (POSTECH)

https: //en. wikipedia. org/wiki/John_C. _Slater https: //en. wikipedia. org/wiki/Philip_Warren_Anderson

Slater joined the Harvard faculty on his return from Europe in 1925, then moved to MIT in 1930. His research papers covered many topics. A year by year selection, up to his switch to work relating to radar includes: • 1924: theoretical part of his Ph. D. work, [20] the Bohr-Kramers-Slater (BKS) theory, [21] • 1925: widths of spectral lines; [22] ideas that came very close to the electron spins principle, [23] • 1926 and 1927: explicit attention to electron spin, [24] and to the Schrödinger equation; [25] • 1928: the Hartree self-consistent field, [26] the Rydberg formula, [27] https: //en. wikipedia. org/wiki/John_C. _Slater • 1929: the determinantal expression for an antisymmetric wave function, [28] [29] • 1930: Slater type orbitals (STOs) and atomic shielding constants, • 1931: linear combination of atomic orbitals, [30] van der Waals forces[31] (with Jack Kirkwood, as a Chemistry Research Associate). • 1932 to 1935: atomic orbitals, [32] metallic conduction, [33][34] application of the Thomas–Fermi method to metals, [35] • 1936: ferromagnetism, [36] (with Erik Rudberg, later Chairman of the Nobel Prize committee for Physics) inelastic scattering, [37] and (with his Ph. D. student William Shockley and close to his own Ph. D. topic), optical properties of alkali halides[38] • 1937 and 1938: augmented plane waves, [39] superconductivity, [40] ferromagnetism, [41] electrodynamics, [42] • 1939 he published "only" a book: the definitive Introduction to Chemical Physics, • 1940 the Grüneisen constant, [43] and the Curie point, [44] • 1941 phase transition analogous to ferromagnetism in potassium dihydrogen phosphate. [45] In his memoir, [1] Morse wrote "In addition to other notable papers. . . on. . . Hartree's self-consistent field, [26] the quantum mechanical derivation of the Rydberg constant, [27] and the best values of atomic shielding constants, [29] he wrote a seminal paper on directing valency[30] " (what became known, later, as linear combination of atomic orbitals). In further comments, [18] John Van Vleck pays particular attention to (1) the 1925 study of the spectra of hydrogen and ionized helium, [23] that J. V. V. considers one sentence short of proposing electron spin (which would have led to sharing a Nobel prize), and (2) what J. V. V. regards as Slater's greatest paper, that introduced the mathematical object now called the Slater determinant. [28] "These were some of the achievements (that led to his) election to the National Academy. . . at. . . thirty-one. He played a key role in lifting American theoretical physics to high international standing. "[18] Slater's doctoral students, during this time, included Nathan Rosen Ph. D. in 1932 for a theoretical study of the hydrogen molecule, and William Shockley Ph. D. 1936 for an energy band structure of sodium chloride, who later received a Nobel Prize for the discovery of the transistor.

https: //www. aip. org/history-programs/niels-bohr-library/oral-histories/30429 Anderson: Yes, with Kubo and I had two things in common. One was we both did antiferromagnetic spin waves. My anti. Perromagnetic spin wave paper was before that. Both of us talked about our early anti-Perromagnetic spin waves at a meeting that was reported in REVIEWS OF MODERN PHYSICS that took place in Washington in 1952. A notorious meeting, because John Slater’s delightful personality was particularly evident at this point. We had a panel discussion in the evening, and just about the time that everyone else got interested, Slater got bored and said, “I think we have to go to bed, ” and stamped off the stage. Hoddeson: Oh no. Anderson: Just before van Vleck was going to talk about his stuff. Hoddeson: He never did anything beyond what he did in the thirties, did he? Anderson: That’s right. Slater? Oh no, he tried to develop, and maybe even did develop a band theory of anti-ferromagnetism, in the late forties. He didn’t like Mott insulators. He didn’t like the Peierl’s idea of the strong interaction. And somehow, although he invented the Slater integrals, he wiped the integral FO out of his consciousness, as not being what we now call U, a phase of magnetism physics? It didn’t fit band theory, so he scrubbed this out. And therefore he couldn’t possibly produce an explanation for manganese oxide being an insulator, unless it was anti-ferromagnetic. And he had this theory that it was antiferromagnetic and therefore it was an insulator, and got a band splitting on that. Slater would not have it that there was band splitting for any other reason than periodicity. And he just, although he’d invented much of many body theory, he just insisted on ignoring everything he’d done before the war. He just changed.

Soft-mode paradigm Slater: Long wave-length fluctuations Anderson: Local excitations

Transport measurements to be discussed

Two types of universalities at quantum criticality, governed by UV vs. IR physics • Anderson: Role of emergent localized moment fluctuations in universal physics of quantum criticality, regardless of IR physics • Slater: Role of emergent long wave-length excitations in universal physics of quantum criticality, regardless of UV physics

Slater vs. Anderson in Si: P & Si-MOSFET 2018년도 2학기 고급통계역학 (PHYS 513 -01) Anderson metal-insulator transitions

Metal-insulator transition in Si-MOSFET metal-oxide-semiconductor field-effect transistor

Reaction of referees (1993): Referee A: “The paper should not be published in PRL. Everyone knows there is no zero-temperature conductivity in 2 -d. ” Referee B: “The reported results are most intriguing, but they must be wrong. If there indeed were a metal-insulator transition in these systems, it would have been discovered years ago. ” Referee C: “I cannot explain the reported behavior offhand. Therefore, it must be an experimental error. ”

Anderson localization

Ø always insulating behavior

Timeline: 1993: Metal-insulator transition in 2 D is discovered. Paper submitted to Phys. Rev. Lett. and rejected. Proposal submitted to NSF and declined. 1994: Proposal submitted to NSF and declined. 1995: Proposal submitted to NSF and declined. 1996: Proposal submitted to NSF and declined. 1997: Proposal submitted to NSF and declined. However, also in 1997….

…a similar transition has been confirmed in Si MOSFETs from another source and observed in other 2 D structures: • Si-MOSFETS from IBM (Popovic, Washburn, and Fowler) • p-Si: Ge (Coleridge’s group; Ensslin’s group) • p-Ga. As/Al. Ga. As (Tsui’s group, Boebinger’s group) • n-Ga. As/Al. Ga. As (Tsui’s group, Stormer’s group, Eisenstein’s group) • n-Si: Ge (Okamoto’s group) (Hanein, Shahar, Tsui et al. , PRL 1998) • p-Al. As (Shayegan’s group)

Slater’s perspective: Finkelstein’s theory • One parameter scaling theory for the conductance: Anderson localization in two dimensional normal metals (Orthogonal class: TRS without PHS & SOC) • Weak localization corrections (described by Cooperon dynamics): upturn of the electrical resistivity with respect to temperature as lowered Spin triplet interactions: weakening the Anderson localization and resulting in downturn of the resistivity as further lowered • Two parameter scaling theory for the conductance and the triplet interaction coefficient

Landau’s Fermi-liquid theory + Anderson localization: Finkelstein’s theory

Coulomb energy rs = Fermi energy Wigner crystal Strongly correlated liquid Gas ~35 ~1 rs strength of interactions increases Long range order Short range order Random electrons

Emergence of localized magnetic moments in the vicinity of metal-insulator transitions • Anderson model: host (metallic) electrons, impurity electrons, effective interactions between impurity electrons, and effective hybridization between itinerant and impurity electrons • Various impurity states: empty, valence fluctuation (fractional filling), and doubly degenerate (single occupancy) • Emergence of a localized magnetic moment + itinerant electrons The Kondo effect • Kondo vs. RKKY: An effective two-fluid model for interaction-driven Mott-type metal-insulator transitions

Anderson’s perspective for Si-MOSFET (clean): Emergence of localized magnetic moments (Role of the self-consistent Kondo effect) • View point I: Pure Mott transition from a Wigner crystalline phase (low density and clean limit) Heavy fermion physics • Role of emergent localized spin excitations: strong inelastic scattering between partially itinerant electrons and strongly fluctuating local moments upturn of the electrical resistivity with respect to temperature as lowered & unitary scattering between quasiparticles and completely screened impurities, given by the Kondo effect downturn of the resistivity as further lowered

Anderson’s perspective for Si: P & Si-MOSFET: Emergence of localized magnetic moments (From a random singlet (RKKY) phase to the Kondo effect) • View point II: Disordered Kondo lattice model picture (effective two-fluid model) randomly arising localized magnetic moments in the vicinity of the metal-insulator transition (even in the metallic state) and partially itinerant electrons • Competition between the Kondo effect and RKKY interactions in the presence of strong disorder (random positions of emergent localized magnetic impurities) Nature of metal-insulator transitions ?

Proximity to Mott quantum criticality, governed by UV vs. IR physics

Kappa-class organic salts

Slater vs. Anderson: Everywhere in the physics of strongly correlated electrons • High Tc cuprates: Fermi-liquid based (spin fluctuation) theory vs. Mott insulating proximate theory (E&C-DMFT, Stripe, Spin liquids, …) • Quantum criticality in heavy fermion physics: Hertz-Moriya. Millis (spin fluctuation) theory vs. Kondo breakdown theory (E&C-DMFT, Spin-liquids, …) 2013, 2014, 2016 물성물리학특론 II 양자상전이 현상의 이해를 위한 양자장론 접근 방법 (PHYS 702 -01)

• Anderson’s perspective UV (DMFT & Kondo dominant) or IR (Spin liquid & RKKY dominant) insulating fixed point described by emergent localized magnetic fluctuations Towards a nonperturbative theoretical framework: From Slater to Anderson • Slater’s perspective IR metallic fixed point described by long wavelength collective excitations: Diffusion & Copperon in Si: P & Si. MOSFET and collective spin fluctuations in high Tc superconductivity