Patterns of Electro-magnetic Response in Topological Semi-metals

Abstract

Topological semimetals are gapless states of matter which have robust and unique electromagnetic responses and surface states. In this paper, we consider semimetals which have point like Fermi surfaces in various spatial dimensions $D=1,2,3$ which naturally occur in the transition between a weak topological insulator and a trivial insulating phase. These semimetals include those of Dirac and Weyl type. We construct these phases by layering strong topological insulator phases in one dimension lower. This perspective helps us understand their effective response field theory that is generally characterized by a 1-form $b$ which represents a source of Lorentz violation and can be read off from the location of the nodes in momentum space and the helicities/chiralities of the nodes. We derive effective response actions for the 2D and 3D Dirac semi-metals, and extensively discuss the response of the Weyl semimetal. We also show how our work can be used to describe semi-metals with Fermi-surfaces with lower co-dimension as well as to describe the topological response of 3D topological crystalline insulators.

42 pages, 19 figures

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• Z_2 and Chiral Anomalies in Topological Dirac Semimetals
• Torsion, Parity-odd Response and Anomalies in Topological States
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Absence of equilibrium chiral magnetic effect
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• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Current-induced second harmonic generation in inversion-symmetric Dirac and Weyl semimetals
• Chiral anomaly in Dirac semimetals due to dislocations
• Self-organized pseudo-graphene on grain boundaries in topological band insulators
• Chiral Separation Effect in lattice regularization
• Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions
• Trapped state at a dislocation in a weak magnetomechanical topological insulator
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Anatomy of the chiral vortical effect
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Disorder driven phase transitions in weak AIII topological insulators
• Unified Topological Response Theory for Gapped and Gapless Free Fermions
• Chiral Separation effect in non-homogeneous systems
• Connecting the dots: Time-reversal symmetric Weyl Semimetals with tunable Fermi arcs
• Unconventional electromagnetic mode in neutral Weyl Semimetals
• Anomalous Hall effect in Weyl superconductors
• Analogies between the Black Hole Interior and the Type II Weyl Semimetals
• Embedded Topological Semimetals
• Effective field theories of topological crystalline insulators and topological crystals
• Effect of interactions on the topological expression for the chiral separation effect
• Translation symmetry-enriched toric code insulator
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Equilibrium Chiral Magnetic Effect: spatial inhomogeneity, finite temperature, interactions
• Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields
• Momentum Space Topology and Non-Dissipative Currents
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Crystalline-electromagnetic responses of higher order topological semimetals
• The Quantum Skin Hall Effect
• Fermionic dualities with axial gauge fields
• Anomalous transport phenomena and momentum space topology
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• Ultrafast Carrier Relaxation and Second Harmonic Generation in a Higher-Fold Weyl Fermionic System PtAl
• Classical limit for Dirac fermions with modified action in the presence of the black hole