Crystalline-electromagnetic responses of higher order topological semimetals

Abstract

Previous work has shown that time-reversal symmetric Weyl semimetals with a quadrupolar arrangement of first-order Weyl nodes exhibit a mixed crystalline-electromagnetic response. For systems with higher order Weyl nodes, which are attached to both surface and hinge Fermi arcs, additional phenomena appear on surfaces of codimension $n>1$, such as electromagnetic responses of the hinges. Here we construct a model possessing a quadrupole of higher order Weyl nodes to study the interplay between higher order topology and mixed crystalline-electromagnetic responses. We show that the higher order nature of the Weyl nodes yields a dipole of Dirac nodes on certain surfaces, leading to a mixed crystalline-electromagnetic \emph{surface} response that binds charge to dislocations and momentum-density to magnetic fields. In addition, we show that the model possesses a bulk quadrupole moment of crystal-momentum that provides a link between the bulk and surface responses of the system.

References in corpus (72)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Weyl Semimetal in a Topological Insulator Multilayer
• Quantized Electric Multipole Insulators
• Topological Materials: Weyl Semimetals
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Experimental observation of Weyl points
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Topological response in Weyl semimetals and the chiral anomaly
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Quantum Oscillations from Surface Fermi-Arcs in Weyl and Dirac Semi-Metals
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Weyl Metals
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Electronic Transport and quantum oscillation of Topological Semimetals
• Topological Semimetals from first-principles
• Higher Order Topological Phases: A General Principle of Construction
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Higher-Order Weyl Semimetals
• Topological Quadrupolar Semimetals
• Gauging spatial symmetries and the classification of topological crystalline phases
• Higher-order Weyl Semimetals
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Boundary Green functions of topological insulators and superconductors
• Boundary-obstructed topological phases
• Torsional Response and Dissipationless Viscosity in Topological Insulators
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Torsional chiral magnetic effect in Weyl semimetal with topological defect
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Torsion, Parity-odd Response and Anomalies in Topological States
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Square-root higher-order Weyl semimetals
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Patterns of Electro-magnetic Response in Topological Semi-metals
• Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings
• Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Classification of Dirac points with higher-order Fermi arcs
• Dislocation defect as a bulk probe of monopole charge of multi-Weyl semimetals
• Floquet higher-order Weyl and nexus semimetals
• Emergent anomalies and generalized Luttinger theorems in metals and semimetals
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Torsion-induced chiral magnetic current in equilibrium
• Chiral kinetic theory of anomalous transport induced by torsion
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals

Cited by in corpus (5)

• Two-Dimensional Higher-Order Topological Metals
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Quantized crystalline-electromagnetic responses in insulators
• Disclinations, dislocations, and emanant flux at Dirac criticality