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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
Published on: October 12, 2019
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Knots and Non-Hermitian Bloch Bands.
Haiping Hu1,2, Erhai Zhao1
1Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA.
Physical Review Letters
|January 22, 2021
Summary
Knots in quantum physics classify non-Hermitian Hamiltonians using eigenenergy strings. A global biorthogonal Berry phase (Q) acts as a knot invariant, revealing phase transitions via exceptional points.
Area of Science:
- Quantum Physics
- Topological Quantum Field Theory
- Condensed Matter Physics
Background:
- Knots were historically disregarded in quantum physics as atomic models.
- A link between knot invariants and Wilson loops in topological quantum field theory was later established.
Purpose of the Study:
- To establish knots tied by eigenenergy strings as a complete topological classification for 1D non-Hermitian Hamiltonians.
- To explore the role of knot invariants in characterizing topological phases and transitions.
Main Methods:
- Utilizing eigenenergy strings to define knots for classifying non-Hermitian Hamiltonians.
- Proving the global biorthogonal Berry phase (Q) as a Z_{2} knot invariant equal to permutation parity.
- Analyzing phase transitions through exceptional points.
Main Results:
- Demonstrated a complete topological classification of 1D non-Hermitian Hamiltonians using knot theory.
- Identified the global biorthogonal Berry phase (Q) as a key knot invariant.
- Characterized phase transitions occurring at exceptional points, with two distinct types.
Conclusions:
- Knot theory provides a powerful framework for understanding non-Hermitian systems.
- The developed algorithm enables the construction of Hamiltonians for desired knots.
- Quantum quench schemes can probe the topological knot structure.
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