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