Contrasting lattice geometry dependent versus independent quantities: Ramifications for Berry curvature, energy gaps, and dynamics
Physical Review B: Condensed Matter and Materials Physics American Physical Society 102 (2020) 165148
Abstract:
In the tight-binding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in three-dimensional space, are independent pieces of information. In this paper we identify a notion of geometry-independence: any physical quantity or observable that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be “geometry-independent.” The band structure itself, and for example the Chern numbers of the bands in a two-dimensional system, are geometryindependent, while the Bloch-band Berry curvature is geometry-dependent. Careful identification of geometry-dependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometry-independence to certain classes of interacting systems, where the many-body energy gap is evidently geometry-independent, we shed new light on a hypothesized relation between many-body energy gaps of fractional Chern insulators and the uniformity of Bloch band Berry curvature in the Brillouin zone. We furthermore explore the geometry-dependence of semiclassical wave packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometry-dependent, while the other is geometry-independent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.From anyons to Majoranas
Nature Reviews Physics Springer Nature 2:12 (2020) 667-668
Abstract:
Anyons, particles that are neither bosons nor fermions, were predicted in the 1980s, but strong experimental evidence for the existence of the simplest type of anyons has only emerged this year. Further theoretical and experimental advances promise to nail the existence of more exotic types of anyons, such as Majorana fermions, which would make topological quantum computation possible.From anyons to Majoranas
Nature Review Physics Nature 2:12 (2020) 667-668
Abstract:
Anyons, particles that are neither bosons nor fermions, were predicted in the 1980s, but strong experimental evidence for the existence of the simplest type of anyons has only emerged this year. Further theoretical and experimental advances promise to nail the existence of more exotic types of anyons, such as Majorana fermions, which would make topological quantum computation possible.Transport properties of multilayer graphene
Physical Review B American Physical Society 101 (2020) 245438
Abstract:
We apply the semi-classical Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked multilayers with an even number of layers. We show that the window for hydrodynamic transport in multilayer graphene is similar to the case of bilayer graphene. We introduce a simple hydrodynamic model which we dub the multi-fluid model and which can be used to reproduce the results for the electrical conductivity and thermopower from the semi-classical Boltzmann equation.Partial equilibration of the anti-Pfaffian edge due to Majorana Disorder
Physical Review Letters American Physical Society 124 (2020) 126801