Research Overview

(1) Phonon helicity in Dirac materials

In this work, we introduce the concept of phonon helicity as a novel phonon dynamics in Dirac materials. We find that a non-vanishing phonon angular momentum (PAM) can be induced by the Berry curvature of electrons through electron-phonon interactions, in materials whose low energy effective theory is described by a 2+1D Dirac equation. We take the Dirac material BaMnSb2 as a prototypical example and demonstrate that the electronic Berry curvature can give rise to a new term in the phonon self-energy, which subsequently induces an elliptical polarization of phonons and endows them with a nonzero PAM. Remarkably, the direction of PAM is locked to the direction of the phonon momentum; we refer to this PAM texture as "phonon helicity'', in analogy to the helical spin texture of spin-orbit-coupled bands for electronic systems.

Reference: Phys. Rev. Lett. 127, 125901 (2021).

(2) Quasi-symmetry in topological materials

In this work, we introduce the concept of quasi-symmetry in topological materials. We find that this quasi-symmetry does not protect a gapless crossing, but rather enforces band anti-crossings with perturbatively small gaps. This is of remarkable and direct consequences to the material: quasi-symmetries are not linked to crystalline symmetries and hence stabilize such near-degeneracies at low symmetry points, leading to a new kind of Wigner/von-Neumann theorem. Moreover, we demonstrate experimentally the importance of these ideas for the spectrum of the topological semi-metal CoSi. The parametrically small gap, enforced by the quasi-symmetry, is immediately broken down by miniscule magnetic fields, hence for the quantum orbit this near-degeneracy is indistinguishable from a true degeneracy. This allows complex orbit patterns to self-intersect without admixture, and thereby stabilizes a tantalizingly simple angle-spectrum in face of the complex Fermi surface geometry in this material. The frequencies are observed to be almost perfectly angle independent, thus significantly less dispersive than predicted by current DFT calculations – a puzzle in the community.

Reference: arXiv preprint arXiv:2108.00279 (2021).

(3) Competing vortex topologies in iron-based superconductors

In this work, we establish a unified theory for vortex topologies in iron-based superconductors (FeSCs). We challenge the common belief that Fu-Kane theory can faithfully describe the vortex Majorana physics in FeSCs and further proposes a new theoretical paradigm of understanding vortex topological physics in FeSCs. Our paradigm implies that the Fu-Kane theory could fail to faithfully describe FeSCs as it ignores the existence of 3D bulk Dirac nodes near the Fermi level, a general topological band features shared by all known FeSCs. We find that its vortex topological phase diagram is qualitatively different from that of a simple Fu-Kane theory, owing to the additional bulk Dirac nodes near the topological insulating gap. Remarkably, our new phase diagram contains an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion simultaneously. In the presence of lattice symmetry breaking, the hybrid vortex gets topologically trivialized and becomes Majorana-free, which naturally explains the puzzle of ubiquitous trivial vortices observed in LiFeAs.

Reference: Phys. Rev. Lett. 123, 027003 (2019), arXiv preprint arXiv:2110.11357 (2021).

(4) Spin selective Andreev reflection due to Majorana zero modes

In this work, we detect Majorana zero modes (MZMs) by using the spin selective Andreev reflection. The existence of MZMs has been predicted by Fu and Kane, in a vortex core of a topological insulator-superconductor heterostructure. The self-conjugate property of MZMs results in an unique tunneling signal: spin selective Andreev reflection (SSAR). The incoming electrons with certain spin polarization in the lead or scanning tunneling microscope (STM) tip are reflected as counter propagating holes with the same spin. Our recent spin-polarized STM experiment shows a spin-polarization dependence of the zero-bias differential tunneling conductance at the center of a vortex core. Theoretically, we consider a 2D Rashba-type Hamiltonian on a spherical surface with an s-wave superconducting pairing due to the proximity effect, to examine the localized in-gap excitations of a pair of vortices. Generally, the MZM is not a spin eigenstate, while the spin polarization of the MZM's wave function at the vortex core center is parallel to the external magnetic field. Hence the SSAR takes place, namely, the non-vanishing Andreev reflection occurs only when the STM tip has the spin polarization parallel to the magnetic field. Our theoretical results turn out to be in good agreement with the experiment. 

Reference: Phys. Rev. Lett. 116, 257003 (2016), Phys. Rev. B 94, 224501 (2016).