Engineering topics

Ying, Xuzhe

Publications and source records attributed to Ying, Xuzhe.

3 records

DOE OSTI2023

Topological order in interacting semimetals

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. Here, this may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED 3 to 3+1 dimensions. In addition we discuss a (3+1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Dynamical effects from anomalies: Modified electrodynamics in Weyl semimetals

Here, we discuss the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a U⁡(1) gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say $\hat{z}$, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in $\hat{z}$ is logarithmically reduced under renormalization group flow, together with the fine-structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely, the Cherenkov radiation. At low-energy E, the inverse of the fermion lifetime scales as τ -1 ~E/PolyLog⁡(E). Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Emergent anomalies and generalized Luttinger theorems in metals and semimetals

Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this paper, we present a unified framework which allows one to discuss Luttinger theorems for ordinary metals as well as closely analogous exact statements for topological (semi)metals, whose low-energy description contains either discrete points or continuous line nodes. This framework is based on the 't Hooft anomaly of the emergent charge conservation symmetry at each point on the Fermi surface, a concept recently proposed by Else et al. Here we find that the Fermi surface codimension p plays a crucial role for the emergent anomaly. For odd p, such as ordinary metals (p = 1) and magnetic Weyl semimetals (p = 3), the emergent symmetry has a generalized chiral anomaly. For even p, such as graphene and nodal line semimetals (both with p = 2), the emergent symmetry has a generalized parity anomaly. When restricted to microscopic symmetries, such as U(1) and lattice symmetries, the emergent anomalies imply (generalized) Luttinger theorems, relating Fermi surface volume to various topological responses. The corresponding topological responses are the charge density for p = 1, Hall conductivity for p = 3, and polarization for p = 2. As a by-product of our results, we clarify exactly what is anomalous about the surface states of nodal line semimetals.

36 MATERIALS SCIENCE↗