condensed matter physics where do we go? e. tosatti …
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CONDENSED MATTER PHYSICS WHERE DO WE GO?
E. Tosatti SISSA, ICTP, CNR-IOM Democritos Trieste, Italy
PAVIA 07/04/2011
GIUSEPPE FRANCO BASSANI (1929-2008)
CONDENSED MATTER PHYSICS
LIFE SCIENCES
ECONO- PHYSICS
NANO MESOSCOPICS
SEMI- CONDUCTORS
MATERIALS SCIENCE
QUANTUM MAGNETISM
STRONG CORRELATIONS
COMPLE- XITY GLASSES
SOFT MATTER
CHEMICAL PHYSICS
MECHANICS RHEOLOGY FRICTION
ENERGY MATERIALS
FERROICS DEVICES
COLD ATOMS PHOTONICS
GRAPHENE
TOPOLOGICAL INSULATORS
SUPERCON DUCTORS
LIQUIDS
HIGH PRESSURE
QUANTUM INFO
WHAT DRIVES CONDENSED MATTER RESEARCH
• CURIOSITY, BEAUTY -- “HARD” SYSTEMS, NON EQUILIBRIUM,..
• INDUSTRY – MATERIALS; INFORMATION; NANO
• ENERGY, SUSTAINABILITY -- SOLAR; CATALYSIS; FRICTION
• LIFE SCIENCE -- BIO; COMPLEXITY; FINANCE; ……
METHODS: ALL VERY IMPORTANT
EXPERIMENT THEORY SIMULATION
SUPERCONDUCTIVITY
KAMERLINGH ONNES 1911 BCS 1956 BCS SUPERCONDUCTOR: FREE ELECTRON METAL WITH PHONON-INDUCED ELECTRON- ELECTRON ATTRACTION
MULLER-BEDNORZ 1986: LaBaCuO3 ; THE HIGH Tc REVOLUTION-- SUPERCONDUCTIVITY THROUGH DOPING OF MOTT INSULATORS?!
1.CURIOSITY: UNDERSTANDING “HARD” SYSTEMS
NEVILL MOTT 1949
Z>0: itinerant electrons -- METAL
Z=0: localized electrons-- INSULATOR
DOS
GEORGES, KOTLYAR et al (96)
MOTT INSULATORS
WHY SUPERCONDUCTIVITY? ANDERSON’S RVB THEORY: NEAR MOTT, SINGLE ELECTRONS CANNOT PROPAGATE, BUT PAIRS CAN, SC LOWERS THE KINETIC ENERGY!
NARROW-BAND METAL WITH EL-EL REPULSION MOTT INSULATOR
P. W. ANDERSON.
SUPERCONDUCTIVITY NEAR STRONGLY CORRELATED ANTIFERRO, “RIGID” PHASES
Uemura, N&V, Nature Mater. 8, 253 (2009)
A15 STRUCTURE Cs3C60 UNDER PRESSURE TAKABAYASHI et al, Science (2009)
S=1/2 AF MOTT INSULATOR
S-WAVE SUPERCONDUCTOR
ALKALI FULLERIDES: K3C60, Rb3C60, Cs3C60 : BCS SUPERCONDUCTORS? or perhaps special
RVB SUPERCONDUCTORS?
MULTIPLET STATES FOR 3 ELECTRONS IN t1u ORBITAL, (d=3) S=3/2 S=1/2
J = JH - (3/4) EJT< ~ - 0.020 eV
5|J|
C60(3-) ISOLATED MOLECULAR ION
~ 0.1 eV
DYNAMIC JAHN TELLER DISTORTED
UNDISTORTED
HUND’s RULE
DYNAMIC JAHN TELLER MANINI ET AL 1994
DYNAMICAL MEAN FIELD THEORY (M. CAPONE, M. FABRIZIO)
U/t RATIO INCREASES FOR INCREASING VOLUME “KONDO” SCREENING CHANGES AT CRITICAL U=UcWHERE PAIRING SETS IN, ,
IMPURITY SPECTRAL DENSITY:" A SPECIAL KONDO PROBLEM"
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
U<<Uc 3
U > Uc 1
U<<Uc U > Uc
BATH
ΔSC
MET SC AFI
METAL_SUPERCONDUCTOR-INSULATOR TRANSITIONS PREDICTED
S=1/2
VOLUME
CELL VOLUME
<n> =4
BCS
SCS
MIT
FROM BCS TO SCS.
λ∼|Jeff|N(EF)
“overdoped”
“underdoped”
CAPONE et al (2004)
ΔSC
MET SC AFI
METAL-SUPERCONDUCTOR-INSULATOR TRANSITIONS PREDICTED
S=1/2
SUPERCONDUCTING “DOME” BEFORE MOTT AF INSULATOR
AF MOTT INSUL. (S=1/2)
SUPERCONDUCTING “DOME” BEFORE MOTT AF INSULATOR
Cs3C60 (A15 or FCC)
CUBIC, NO DISORDER , NO STRUCTURAL CHANGE WITH PRESS.
GANIN et al, Nature (2008) TAKABAYASHI et al, Science (2009)
VOLUME PER C60
Tc CUPRATES
WHY STRONGLY CORRELATED SUPERCONDUCTIVITY FALLS NEAR LOW-SPIN MOTT INSULATORS
1. NEAR MOTT QUASIPARTICLE BANDWIDTH ZW DROPS TO ZERO
2. NEAR MOTT, QUASIPARTICLES ALSO CEASE TO REPEL ONE ANOTHER (CHARGE FREEZING)
3. NEAR MOTT, PAIRING “ATTRACTION” (OR REPULSION) J BETWEEN Q-P.'s IN SPIN CHANNEL STANDS UNALTERED.
4. ON-SITE CORRELATIONS INCREASE ELECTRON KINETIC ENERGY (NFL); SUPERCONDUCTIVITY CURES THAT
5. SUPERCONDUCTING MAXIMUM WHEN | J |= ZW, AS IN “U<0”
6. AS IN U<0, MAX kBTc ~ 0.07 | J | (ROBASZKIEWICZ 1981)
7. FULLERIDES ACT AS “PHONON- INDUCED ON-SITE RVBs”
c M. CAPONE, M. FABRIZIO, C. CASTELLANI, E. TOSATTI SCIENCE 296, 2364 (2002); REV. MOD. PHYS. 81, 943 (2009)
DYNAMIC JAHN TELLER DISTORTED
PROPERTIES OF SCS STATE
--! non Fermi liquid normal state, susceptibility large and increasing with T (spin gap)
--? better kinetic energy, larger Drude weight, in SC state than in normal state (unlike BCS, like cuprates)
--! despite large mass near Mott, Cv jump is “normal”
--? pseudogap features if enough close to Mott (similar, but not identical, to underdoped cuprates)
-- ! two separate energy scales, visible in ARPES
STRONGLY CORRELATED MATERIALS: WHERE DO WE GO?
• IMPROVE UNDERSTANDING OF STRONG CORRELATIONS
• NOVEL SUPERCONDUCTORS, NOVEL THERMOELECTRICS, …
• ORGANICS, HEAVY FERMION SYSTEMS, QUANTUM MAGNETS, …
CONDUCTANCE METAL CONTACTS-- 250 YEARS AFTER VOLTA
2. NANO – PROPERTIES OF NANOSIZE MATTER ARE NOT THE SAME
Rodrigues et al. (2000)
(Au)
METAL NANOCONTACTS
CO
HEAT HEAT HEAT
(Figure from B. Altshuler) A TYPICAL “NANO” EFFECT
G < GMAX = (e2/h) (NUP + NDOWN)
ROLF LANDAUER
E-E F
(eV
)
k (2ππ/a) k (2ππ/a)
nonmagnetic T=0 ferromagnetic
CONDUCTANCE MUST DEPEND ON MAGNETISM
a = 2.17 Å a = 2.17 Å
dxz ,yz
s d3 z2 r2
s d3 z2 r2
dxy , x2 y2
spin up spin down
( m = 1.13 mB )
N = 1
N = 6
Ni
N=4x2=8
“FIRST PRINCIPLES” CALCULATIONS OF BALLISTIC CONDUCTANCE
BULK BULK
1. “DENSITY FUNCTIONAL THEORY” (DFT) ELECTRONIC STRUCTURE CALCULATION OF BULK METAL & CONTACT REGION (ABOVE) , ALLOWING FOR NONUNIFORM MAGNETISM
WALTER KOHN
2. IDENTIFY BULK BANDS THAT CROSS THE FERMI LEVEL AND CAN CONDUCT (“CHANNELS”)
3. MATCH BULK AND CONTACT, OBTAIN TRANSMISSION AND REFLECTION MATRICES Tij, Rij
4. BALLISTIC CONDUCTANCE FROM LANDAUER FORMULA
G/G0= 1.6 Ni 3-atom contact
A. Smogunov et al (2004) V~0
(2004)
T= 4.2 K
transport
s electrons d electrons
(Picture by A. Delin)
A. Delin, E.T., PRL (2003) P. Gava et al Eur.J. Phys. B (2010)
SIMILAR RESULTS FOR PLATINUM
CAUTION, SUPERPARAMAGNETISM
SPONTANEOUS MAGNETISM IN A METAL JUNCTION
THEORY (DFT)
Pd
PARKS el al Science (2010)
KONDO “ZERO BIAS ANOMALY” ACROSS MAGNETIC IMPURITIES
VITALI et al (2008)
M
Cu STM TIP
Cu
Co
Picture from Neel et al
KONDO EFFECT
Jun Kondo SCREENING
s S
EXERCISE: MAGNETIC IMPURITY IN A NONMAGNETIC METAL NANOCONTACT
S Au
Ni
STANDARD LANDAUER CONDUCTANCE CALCULATION: STILL OK?
NO! KONDO = MANY BODY EFFECT
t U
SOLVE BY,e.g., NUMERICAL RENORMALIZATION GROUP (WILSON)
ANDERSON MODEL
1. DFT ELECTRONIC STRUCTURE CALCULATION: -- IDENTIFY NATURE, SYMMETRY OF CONDUCTION CHANNELS -- MAGNETIZATION, SPIN OF IMPURITY -- SYMMETRY OF FILLED + EMPTY MAGNETIC ORBITALS -- EXTRACT SCATTERING PHASE SHIFTS OF CONDUCTION ELECTRONS FOR EACH SYMMETRY& BOTH SPINS
2. BUILD GENERALIZED ANDERSON MODEL, INCLUDING ALL SCATTERING SYMMETRY CHANNELS -- ADJUST PARAMETERS OF ANDERSON MODEL TO REPRODUCE DFT PHASE SHIFTS WITHIN HARTEE-FOCK APPROX.
3. SOLVE ANDERSON MODEL WITH e.g.,WILSON NUMERICAL RENORMALIZATION GROUP (NRG) TO OBTAIN SPECTRAL DENSITY, CONDUCTANCE.
“DFT + NRG” STRATEGY P. LUCIGNANO et al. NATURE MAT. 8, 563 (2009).
PREDICT GEOMETRY-DEPENDENT ZERO_BIAS CONDUCTANCE ANOMALIES
subst. subst. bridge REGULAR
KONDO “FERRO”- KONDO (sketch)
Experiment? LUCIGNANO et al. NATURE MAT. 8, 563 (2009).
NANO: WHERE DO WE GO?
-- USE THE NANOSCALE TO PRODUCE NOVEL EFFECTS
-- NANO-MECHANICS, NANO-ELECTRONICS, NANO-BIO,… AN EXPANDING UNIVERSE
3. FRICTION and NANOFRICTION
(MEYER) (BRAUN)
Relevance -- FRICTION: energy conservation; materials durability & wear; seismology; …
-- NANOFRICTION: basic understanding of friction; nanotechnology; …
STICK-SLIP FRICTION
low velocity &/or soft system high velocity &/or stiff system
NANOFRICTION: THE ATOMIC FORCE MICROSCOPE
-- ATOMIC STICK-SLIP SLIDING MOTION OF TIP: VERY NONLINEAR
-- ENCLOSED AREA IN (F, x) PLANE YIELDS FRICTIONAL ENERGY
(MEYER et al)
HEINI ROHRER GERD BINNIG
FRICTION: VERY LITTLE THEORY. NEED MODELS, AND SIMULATION
ATOMIC STICK-SLIP SIMULATIONS
A. BENASSI et al. PRB (RC) 82, 081401 (2010)
SLIDER FORCE
SIMULATION: HIGH SPEED NANOFRICTION?
CLUSTER “KICKING”
Au NANOCLUSTERS ON GRAPHITE: CROSSOVER FROM DRIFT TO BALLISTIC SLIDING
R. GUERRA, A. VANOSSI, U. TARTAGLINO, E.T., Nature Mat. 9, 634 (2010)
THERMALLY DIFFUSING Au CLUSTER (ALSO DRIFTING UNDER WEAK QCM FORCE)
SAME CLUSTER, NOW KICKED AT 100 m/s
BALLISTIC CROSSOVER DRIFT
SPIN EFFECTIVELY “TRAPPED” IN UP OR DOWN STATE BY SPIN- PHONON COUPLING (AS IN CALDEIRA-LEGGETT BARRIER ESCAPE)
MAGNETIC NANOFRICTION: SPIN-BOSON MODEL
“SINGLE SPIN HYSTERESIS” , WITH MAGNETIC DISSIPATION , FOR UP SPIN ONLY. F.PELLEGRINI et a. PRL 105, 146103 (2010)
CORRUGATION DISSIPATION Fe NiO
?
E
FRICTION: WHERE DO WE GO?
• FORMULATE MORE THEORY OF FRICTION?
• USE NANOFRICTION RESULTS TO UNDERSTAND FRICTION ON LARGER SCALE, INCLUDING EARTHQUAKES
• CONTROL FRICTION: LUBRICATION AND BEYOND
CONDENSED MATTER PHYSICS
LIFE SCIENCES
ECONO- PHYSICS
NANO MESOSCOPICS DISORDER
SEMI- CONDUCTORS
MATERIALS SCIENCE
QUANTUM MAGNETISM
STRONG CORRELATIONS
COMPLE- XITY GLASSES
SOFT MATTER
CHEMICAL PHYSICS
MECHANICS RHEOLOGY FLUIDS FRICTION
ENERGY MATERIALS
FERROICS DEVICES
COLD ATOMS QUANTUM OPTICS ?
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CURIOSITY, BEAUTY, LIVELINESS, RELEVANCE
ANDREA BENASSI ANDREA VANOSSI
MICHELE FABRIZIO MASSIMO CAPONE CLAUDIO CASTELLANI
ANDREA DAL CORSO PROCOLO LUCIGNANO ALEXANDER SMOGUNOV
GIUSEPPE SANTORO FRANCO PELLEGRINI ROBERTO GUERRA UGO TARTAGLINO
OLEG BRAUN
NICOLA MANINI