Mott insulators
Mott insulators
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