Physical meaning of terms in the Qi, Wu, Zhang model

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SUMMARY

The Hamiltonian of the Qi, Wu, Zhang model is defined in momentum space as H(\vec{k})=(\sin k_x) \sigma_{x}+(\sin k_y) \sigma_{y}+ (m+\cos k_x+\cos k_y)\sigma_{z}. Each term in this Hamiltonian represents distinct physical phenomena: the sine terms correspond to the coupling of spin with momentum, while the cosine terms relate to the mass and spatial configuration of the system. Understanding these components is crucial for analyzing the model's implications in condensed matter physics.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of Hamiltonian mechanics
  • Familiarity with spin operators in quantum physics
  • Basic knowledge of momentum space representation
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  • Study the derivation of the Hamiltonian in the Qi, Wu, Zhang model
  • Explore the physical implications of spin-momentum coupling
  • Learn about the significance of mass terms in quantum systems
  • Investigate real space Hamiltonians and their analysis techniques
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Physicists, particularly those specializing in condensed matter physics, quantum mechanics students, and researchers interested in spintronics and topological phases of matter.

Joker93
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The Hamiltonian of the Qi, Wu, Zhang model is given by(in momentum space):
## H(\vec{k})=(sink_x) \sigma_{x}+(sink_y) \sigma_{y}+(m+cosk_x+cosk_y)\sigma_{z} ## .
What is the physical meaning of each component of this Hamiltonian?

Note: for the real space Hamiltonian(where maybe the analysis of the physical content each of the term is easier), see attached.
 

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  • Qi, Qu, Zhang real space Hamiltonian.png
    Qi, Qu, Zhang real space Hamiltonian.png
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Could someone help with the math formatting? I can't get it right!
 
Joker93 said:
Could someone help with the math formatting? I can't get it right!
Don't use a bold letter H within ##'s. Use {\bf H} instead.
 
better even \mathbf{H}
 

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