Recently it has been discovered that in Weyl semimetals the surface state Berry curvature can diverge in certain regions of momentum. This occurs in a continuum description of tilted Weyl cones, ...which for a slab geometry results in the Berry curvature dipole associated to the surface Fermi arcs growing linearly with slab thickness. Here we investigate analytically incarnations of lattice Weyl semimetals and demonstrate this diverging surface Berry curvature by solving for their surface states and connect these to their continuum descriptions. We show how the shape of the Fermi arc and the Berry curvature hot-line is determined and confirm the 1/k^{2} divergence of the Berry curvature at the end of the Fermi arc as well as the finite-size effects for the Berry curvature and its dipole, using finite-slab calculations and surface Green's function methods. We further establish that apart from affecting the second-order, nonlinear Hall effect, the divergent Berry curvature has a strong impact on other transport phenomena as the Magnus-Hall effect and the nonlinear chiral anomaly.
We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as 1 / k2, where k is the distance to a hot line in the surface Brillouin zone that ...connects the projection of Weyl nodes with opposite chirality, but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally and, in particular, leads to a surface Berry curvature dipole that grows linearly with the thickness of a slab of a Weyl semimetal material in the limit of the long lifetime of surface states. This implies the emergence of a gigantic contribution to the nonlinear Hall effect in such devices.
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter ...in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combination of time-reversal and inversion symmetries and are accompanied by topologically protected “drumhead” surface states. In the bulk, these nodal line systems exhibit Landau level quantization and flat bands upon applying a magnetic field. In the presence of spin-orbit coupling, these topological semimetals are found to generically form (strong) topological insulators. This comprehensive classification of the electronic band structures of three-dimensional honeycomb systems might serve as guidance for future material synthesis.
Recently it has been discovered that in Weyl semimetals the surface state Berry curvature can diverge in certain regions of momentum. This occurs in a continuum description of tilted Weyl cones, ...which for a slab geometry results in the Berry curvature dipole associated to the surface Fermi arcs growing linearly with slab thickness. Here we investigate analytically incarnations of lattice Weyl semimetals and demonstrate this diverging surface Berry curvature by solving for their surface states and connect these to their continuum descriptions. We show how the shape of the Fermi arc and the Berry curvature hot-line is determined and confirm the 1/k^2 divergence of the Berry curvature at the end of the Fermi arc as well as the finite size effects for the Berry curvature and its dipole, using finite slab calculations and surface Green's function methods. We further establish that apart from affecting the second order, non-linear Hall effect, the divergent Berry curvature has a strong impact on other transport phenomena as the Magnus-Hall effect and the non-linear chiral anomaly.
In recent years it has become clear that electronic Berry curvature (BC) is a key concept to understand and predict physical properties of crystalline materials. A wealth of interesting Hall-type ...responses in charge, spin and heat transport are caused by the BC associated to electronic bands inside a solid: anomalous Hall effects in magnetic materials, and various nonlinear Hall and Nernst effects in non-magnetic systems that lack inversion symmetry. However, for the largest class of known materials -- non-magnetic ones with inversion symmetry -- electronic BC is strictly zero. Here we show that precisely for these bulk BC-free materials, a finite BC can emerge at their surfaces and interfaces. This immediately activates certain surfaces in producing Hall-type transport responses. We demonstrate this by first principles calculations of the BC at bismuth, mercury-telluride (HgTe) and rhodium surfaces of various symmetries, revealing the presence of a surface Berry curvature dipole and associated quantum nonlinear Hall effects at a number of these. This opens up a plethora of materials to explore and harness the physical effects emerging from the electronic Berry curvature associated exclusively to their boundaries.
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter ...in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combination of time-reversal and inversion symmetries and are accompanied by topologically protected "drumhead" surface states. In the bulk, these nodal line systems exhibit Landau level quantization and flat bands upon applying a magnetic field. In the presence of spin-orbit coupling, these topological semimetals are found to generically form (strong) topological insulators. This comprehensive classification of the electronic band structures of three-dimensional honeycomb systems might serve as guidance for future material synthesis.
We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as \(1/k^2\), where \(k\) is the distance to a hot-line in the surface Brillouin zone ...that connects the projection of Weyl nodes with opposite chirality but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally, and in particular leads to a surface Berry curvature dipole that grows linearly with the thickness of a slab of a Weyl semimetal material in the limit of long lifetime of surface states. This implies the emergence of a gigantic contribution to the non-linear Hall effect in such devices.
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