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π π π π π π π π π
π π π π π π π π π
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Berry-phase Approach to Electric Polarization<br />
and Charge Fractionalization<br />
Dennis P. Clougherty<br />
Department of Physics University of Vermont<br />
(Dated: August 4, 2010)
Outline<br />
• Quick Review<br />
Berry phase in quantum systems<br />
adiabatic theorem, spin-1/2 in B, analogies<br />
• Semiclassical dynamics<br />
Berry connection, curvature, LDOS<br />
• 1D dimer model: fractionally charged kinks<br />
Rice-Mele, Su-Schrieffer-Heeger<br />
• Fractionally charged vortices in 2D dimer model
Berry<br />
phase<br />
Berry<br />
curvature<br />
Chern<br />
numbers<br />
Applications<br />
• Interference<br />
• Energy spectrum<br />
• Polarization in crystals<br />
• spin dynamics<br />
• electron dynamics in crystals<br />
• fermion fractionalization<br />
• quantum Hall<br />
• quantum charge pumps<br />
• topological insulators
Ashcroft+Mermin<br />
INCOMPLETE--missing terms due to Berry curvature
Kink soliton in SSH<br />
A<br />
t1<br />
domain wall between phases<br />
+<br />
topological solitons<br />
B<br />
x
2 Kinks on a ring<br />
t1<br />
+
Conclusions<br />
• New way to calculate inhomogeneous<br />
polarization with Berry curvature<br />
• Fermion fractionalization can be understood as a<br />
Berry curvature effect
Di Xiao, ORNL<br />
Acknowledgments<br />
Qian Niu, UT Austin<br />
Junren Shi, ICQS Beijing
Outline<br />
• Quick Review<br />
Berry phase in quantum systems<br />
adiabatic theorem, spin-1/2 in B, analogies<br />
• Semiclassical dynamics<br />
Berry connection, curvature, LDOS<br />
• 1D dimer model: fractionally charged kinks<br />
Rice-Mele, Su-Schrieffer-Heeger<br />
• Fractionally charged vortices in 2D dimer model
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