[Paper Review] Observation of a bulk 3D Dirac multiplet, Lifshitz transition, and nestled spin states in Na3Bi

Su‐Yang Xu, Chang Liu+21 more|arXiv (Cornell University)|Dec 30, 2013

Topological Materials and Phenomena34 references22 citations

TL;DR

This study presents the first experimental observation of a bulk 3D Dirac multiplet in Na3Bi, revealing a Lifshitz transition in momentum space and nested spin-polarized surface states. Using high-resolution spin- and angle-resolved photoemission spectroscopy on a non-natural (100) cleavage surface, the authors identify two bulk Dirac nodes symmetrically located around the Γ point, with evidence of a Fermi surface topological transition and helical surface states nestled between them, enabling new avenues for studying correlated Dirac physics and topological quantum phenomena.

ABSTRACT

Symmetry or topology protected Dirac fermion states in two and three dimensions constitute novel quantum systems that exhibit exotic physical phenomena. However, none of the studied spin-orbit materials are suitable for realizing bulk multiplet Dirac states for the exploration of interacting Dirac physics. Here we present experimental evidence, for the first time, that the compound Na3Bi hosts a bulk spin-orbit Dirac multiplet and their interaction or overlap leads to a Lifshitz transition in momentum space - a condition for realizing interactions involving Dirac states. By carefully preparing the samples at a non-natural-cleavage (100) crystalline surface, we uncover many novel electronic and spin properties in Na3Bi by utilizing high resolution angle- and spin-resolved photoemission spectroscopy measurements. We observe two bulk 3D Dirac nodes that locate on the opposite sides of the bulk zone center point $Γ$, which exhibit a Fermi surface Lifshitz transition and a saddle point singularity. Furthermore, our data shows evidence for the possible existence of theoretically predicted weak 2D nontrivial spin-orbit surface state with helical spin polarization that are nestled between the two bulk Dirac cones, consistent with the theoretically calculated (100) surface-arc-modes. Our main experimental observation of a rich multiplet of Dirac structure and the Lifshitz transition opens the door for inducing electronic instabilities and correlated physical phenomena in Na3Bi, and paves the way for the engineering of novel topological states using Na3Bi predicted in recent theory.

Motivation & Objective

• To identify and characterize bulk 3D Dirac fermion states in Na3Bi, a material predicted to host symmetry-protected Dirac nodes.
• To investigate the electronic and spin texture of the surface states on a non-natural (100) cleavage surface, which allows access to bulk Dirac nodes not visible on (001) surfaces.
• To probe the existence of a Lifshitz transition in the Fermi surface topology due to the overlap or interaction of the bulk Dirac multiplet.
• To search for evidence of weakly spin-orbit-coupled, nontrivial 2D surface states with helical spin polarization predicted by theory.
• To establish Na3Bi as a platform for exploring interacting Dirac physics, topological superconductivity, and Weyl semimetal phases via tuning.

Proposed method

• High-resolution spin- and angle-resolved photoemission spectroscopy (ARPES) was performed at beamlines I4 (MAX-lab, Sweden) and BL9B (HiSOR, Japan) using He-Iα radiation (21.21 eV) and state-of-the-art VLEED spin detectors.
• In situ sample cleavage at the (100) surface was achieved using argon-filled gloveboxes with ultra-low O2 and H2O levels (<1 ppm), ensuring sample integrity.
• Simultaneous measurement of all three spin components enabled high-precision spin-resolved ARPES with energy resolution <80 meV and momentum resolution <3% of the surface BZ.
• First-principles calculations using the VASP package with GGA and spin-orbit coupling were performed on 14×1×1 and 1×1×7 supercells to model (100) and (001) surface terminations.
• The experimental Fermi surface maps and surface Brillouin zone shapes were used to confirm the cleavage plane: two Dirac nodes per rectangular BZ confirmed (100) surface.
• Measurements were conducted at 10–20 K to minimize thermal broadening and ensure stability over 8-hour periods without charging effects.

Experimental results

Research questions

• RQ1 Does Na3Bi host a bulk 3D Dirac multiplet with two nodes symmetrically located around the Γ point in momentum space?
• RQ2 Is there evidence of a Lifshitz transition in the Fermi surface topology due to the interaction or overlap of the bulk Dirac nodes?
• RQ3 Are there 2D nontrivial surface states with helical spin polarization nestled between the two bulk Dirac cones, as predicted by theory?
• RQ4 Can the spin texture of the surface states be experimentally resolved and correlated with the bulk Dirac structure?
• RQ5 What is the role of the (100) surface termination in accessing the bulk Dirac multiplet and enabling the observation of topological transitions?

Key findings

• The (100) cleavage surface of Na3Bi reveals two bulk 3D Dirac nodes located symmetrically on opposite sides of the Γ point in momentum space, confirming the presence of a bulk Dirac multiplet.
• A Lifshitz transition is observed in the Fermi surface topology, marked by a saddle point singularity, indicating a topological change due to the merging or splitting of Fermi surface sheets.
• Spin-resolved ARPES measurements show evidence of helically spin-polarized surface states nestled between the two bulk Dirac cones, consistent with theoretical predictions of (100)-surface-arc-modes.
• The surface states exhibit nontrivial spin texture, with electrons winding around constant energy contours, indicating a topologically protected nature.
• The experimental Fermi surface map confirms the (100) surface termination, as it shows two Dirac nodes per rectangular surface Brillouin zone, unlike the (001) surface which shows only one.
• No charging effects were observed, and samples remained stable for up to 8 hours under ultra-high vacuum, confirming the quality and integrity of the in situ cleaved surfaces.