We introduce a non-linear frequency dependent D+1 terminal conductance that characterizes a D dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a ballistic conductor we show that this conductance is quantized and probes the Eul
er characteristic of the Fermi sea. We critically address the roles of electrical contacts and of Fermi liquid interactions, and we propose experiments on 2D Dirac materials such as graphene using a triple point contact geometry.
Topological mechanics and phononics have recently emerged as an exciting field of study. Here we introduce and study generalizations of the three-dimensional pyrochlore lattice that have topologically protected edge states and Weyl lines in their bul
k phonon spectra, which lead to zero surface modes that flip from one edge to the opposite as a function of surface wavenumber.
Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific space group in
tricacies or band-tuning conditions. Restricting ourselves to cases with strong spin-orbit interaction, we develop a general framework which captures existing systems and predicts new examples of nodal materials. In many previously proposed systems, the three-dimensional nature of the space group has obscured key generalities. Therefore, we show how within our framework one can predict and characterize a diverse set of nodal phenomena even in two-dimensional systems constructed of three-dimensional sites, known as the Layer Groups. Expanding on an existing discussion by Watanabe, Po, Vishwanath, and Zaletel of the relationship between minimal insulating filling, nonsymmorphic symmetries, and compact flat manifolds, we characterize the allowed semimetallic structures in the layer groups and draw connections to related three-dimensional systems.
We propose and characterize a new $mathbb{Z}_2$ class of topological semimetals with a vanishing spin--orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac Line Nodes (DLNs) and t
wo-dimensional (2D) nearly-flat surface states, protected by inversion and time--reversal symmetries. We develop the $mathbb{Z}_2$ invariants dictating the presence of DLNs based on parity eigenvalues at the parity--invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu$_3$N near the Fermi energy by doping non-magnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This paper includes a brief discussion of the effects of spin--orbit interactions and symmetry-breaking as well as comments on experimental implications.
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dime
nsional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) ($mu_1,mu_2$) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials.
Bilayer graphene in a perpendicular electric field can host domain walls between regions of reversed field direction or interlayer stacking. The gapless modes propagating along these domain walls, while not strictly topological, nevertheless have int
eresting physical properties, including valley-momentum locking. A junction where two domain walls intersect forms the analogue of a quantum point contact. We study theoretically the critical behavior of this junction near the pinch-off transition, which is controlled by two separate classes of non-trivial quantum critical points. For strong interactions, the junction can host phases of unique charge and valley conductances. For weaker interactions, the low-temperature charge conductance can undergo one of two possible quantum phase transitions, each characterized by a specific critical exponent and a collapse to a universal scaling function, which we compute.
We study theoretically the electrical current and low-frequency noise for a linear Josephson junction structure on a topological insulator, in which the superconductor forms a closed ring and currents are injected from normal regions inside and outsi
de the ring. We find that this geometry offers a signature for the presence of gapless 1D Majorana fermion modes that are predicted in the channel when the phase difference phi, controlled by the magnetic flux through the ring, is pi. We show that for low temperature the linear conductance jumps when phi passes through pi, accompanied by non-local correlations between the currents from the inside and outside of the ring. We compute the dependence of these features on temperature, voltage and linear dimensions, and discuss the implications for experiments.
