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Mott insulators

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<strong>Mott</strong> <strong>insulators</strong><br />

Atomic limit - view electrons in real space<br />

Virtual system:<br />

lattice of H-Atoms:<br />

a B<br />


<strong>Mott</strong> <strong>insulators</strong><br />

Atomic limit - view electrons in real space<br />

Virtual system:<br />

2a B<br />

lattice of H-Atoms:<br />

d<br />

a B<br />


<strong>Mott</strong> <strong>insulators</strong><br />

Atomic limit - view electrons in real space<br />

Virtual system:<br />

lattice of H-Atoms:<br />

a B<br />


<strong>Mott</strong> <strong>insulators</strong><br />

Metal-insulator transition from the insulating side<br />

Hubbard-model:<br />

density: n=1<br />

„ground state“<br />

n.n. hopping<br />

t = 0<br />

onsite repulsion<br />

E<br />

charge excitation<br />

U<br />

h<br />

d


<strong>Mott</strong> <strong>insulators</strong><br />

Metal-insulator transition from the insulating side<br />

Hubbard-model:<br />

density: n=1<br />

„ground state“<br />

n.n. hopping<br />

onsite repulsion<br />

t > 0<br />

W = 4d t<br />

E<br />

charge excitation<br />

U<br />

h<br />

d<br />

metal-insulator transition: U c = 4dt


<strong>Mott</strong> <strong>insulators</strong><br />

Metal side<br />

tight-binding model<br />

h<br />

d<br />

half-filled<br />

conduction<br />

band<br />

density<br />

empty sites h = 1/4<br />

doubly occupied sites d = 1/4<br />

singly occupied sites s = 1/2<br />

reducing mobility


<strong>Mott</strong> <strong>insulators</strong><br />

Metal-insulator transition from the metallic side<br />

Gutzwiller<br />

approximation<br />

Fermi liquid property<br />

renormalized<br />

momentum<br />

distribution<br />

n k<br />

Z<br />

k<br />

single particle spectral function<br />

quasiparticle weight:<br />

k F<br />

A<br />

coherent<br />

quasiparticles<br />

metallic<br />

variational<br />

at MIT<br />

A<br />

lower<br />

Hubbard band<br />

upper<br />

Hubbard band<br />

E<br />

insulating<br />

µ<br />

renormalized hopping E

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