Download Weyl Semimetals

Weyl Semimetals
Journal Club, 09/08/2013
Semimetals: basic questions
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Is it possible for a gapless system to have a defining
topological feature?
How can one distinguish phases of a system with gapless
degrees of freedom?
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Weyl semimetal, as an example
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Brief review: Dirac equation
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Dirac equation for a spin-1/2 particle with mass
Dirac algebra
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Weyl representation:
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is diagonal (Dirac representation:
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is diagonal)
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Brief review: Dirac equation
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In momentum space, with
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Using the Weyl representation
are eigenstates of
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: helicity is a good quantum
number
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Weyl semimetals
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Valence and conduction bands touch
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Non-degenerate band: time-reversal symmetry is broken
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One possible Hamiltonian
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Expanding around
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where
Weyl equation
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How robust are the Weyl nodes?
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The system is 3D! Expanding around a node
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Solve for
3 equations; 3 unknowns
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Magnetic Monopoles (review)
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What is the magnetic charge of a Dirac node?
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Consider the eingestates of
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The Berry flux is
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Topological Response: Chiral
Anomaly
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Breaks down the conservation of particles at a given Weyl
point
Independent equations for R/L ?
QFT: Cut-off violates conservation (Adler-Bell-Jackiw
anomaly)
Another derivation: Starting with B in the z-direction
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Landau Levels
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Topological Response: Chiral
Anomaly
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Solving the Dirac equation with an applied magnetic field,
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Topological Response: Chiral
Anomaly
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Effect of the electric field
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Rate of increase/decrease of electrons
force density of states density of modes
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Change of momentum per unit volume
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Topological Response: Anomalous
Hall Effect
Using the Lorentz force
and the basic equations for the QHE
and
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Is Graphene a Topological
Semimetal?
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If just nearest-neighbor hopping is taken into account,
Sublattice symmetry: changing the sign of
amplitudes on one sublattice reverses the sign
1D: Class AIII, edge states with zero-energy
zigzag model
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Experimental Proposal
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Goal: distinguish anomalyrelated physics from
conventional metallic behavior
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