Dirac and Weyl superconductors in three dimensions

Chirality-Dependent Hall Effect in Weyl Semimetals

We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and they can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and circularly polarized lights to generate and probe such a chirality-dependent Hall effect.

Dirac Semimetals in Two Dimensions

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin Hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are not gapped by spin-orbit interactions and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of nonsymmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.

Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN

Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2, both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

Weyl spin liquids

The fractionalization of quantum numbers in interacting quantum many-body systems is a central motif in condensed-matter physics with prominent examples including the fractionalization of the electron in quantum Hall liquids or the emergence of magnetic monopoles in spin-ice materials. Here, we discuss the fractionalization of magnetic moments in three-dimensional Kitaev models into Majorana fermions (and a Z_{2} gauge field) and their emergent collective behavior. We analytically demonstrate that the Majorana fermions form a Weyl superconductor for the Kitaev model on the recently synthesized hyperhoneycomb structure of β-Li_{2}IrO_{3} when applying a magnetic field. We characterize the topologically protected bulk and surface features of this state, which we dub a Weyl spin liquid, including thermodynamic and transport signatures.

Weyl superfluidity in a three-dimensional dipolar Fermi gas

Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a direction-dependent two-body effective attraction generated by a rotating external field. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition temperature of the Weyl superfluidity is found to be within the experimental scope for atomic dipolar Fermi gases.

Observation of Fermi arc surface states in a topological metal

The topology of the electronic structure of a crystal is manifested in its surface states. Recently, a distinct topological state has been proposed in metals or semimetals whose spin-orbit band structure features three-dimensional Dirac quasiparticles. We used angle-resolved photoemission spectroscopy to experimentally observe a pair of spin-polarized Fermi arc surface states on the surface of the Dirac semimetal Na3Bi at its native chemical potential. Our systematic results collectively identify a topological phase in a gapless material. The observed Fermi arc surface states open research frontiers in fundamental physics and possibly in spintronics.