Reconstructing the wavefunction of magnetic topological insulators MnBi2Te4 and MnBi4Te7 using spin-resolved photoemission

TL;DR

This work tackles the unresolved surface-band structure of magnetic topological insulators MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$ by performing spin- and orbitally resolved ARPES and constructing a wavefunction-based k·p model that includes a γ-term to account for out-of-plane spin components. The authors demonstrate that the prominent surface states are well described by a single-band, p-orbital wavefunction with J_z = ±1/2, and they quantify how the orbital composition governs the surface-state gap, reconciling discrepancies between theory and experiment. They further analyze a hybridized, Rashba-like regime in SL MnBi$_4$Te$_7$ using an extended Hamiltonian within the same wavefunction framework. The approach enables direct access to quantum geometry (Berry curvature, quantum metric) from experimental parameters and offers intrinsic insights for tuning magnetic gaps in topological insulators.

Abstract

Despite their importance for exotic quantum effects, the surface electronic structure of magnetic topological insulators MnBi2Te4 and MnBi4Te7 remains poorly understood. Using high-efficiency spin- and angle-resolved photoemission spectroscopy, we directly image the spin-polarization and orbital character of the surface states in both compounds and map our observations onto a model wavefunction to describe the complex spin-orbital texture, which solidifies our understanding of the surface band structure by establishing the single-band nature of the most prominent states. Most importantly, our analysis reveals a new mechanism for reducing the magnetic gap of the topological surface states based on the orbital composition of the wavefunction.

Figures (9)

• Figure 1: (a) A schematic of the experimental geometry for spin-resolved ARPES measurements. Momentum space is mapped along $k_x$ ($\Gamma-K$) by rotating the sample about the $\theta$-axis. Data in this figure is taken with $p$-polarized light. (b) A simplified illustration of the surface state spin texture in materials with $C_{3v}$ symmetry. Near $\Gamma$ the surface state hosts in-plane helical spin texture, which becomes out-of-plane approaching lower binding energy. In the following, spin-resolved ARPES data are plotted with the 2D colorscale shown, where red-blue denotes the spin-polarization and white-black denotes the photoemission intensity. (c) In-plane $S_y$ and (d) out-of-plane $S_z$ measurement for MnBi$_2$Te$_4$, which consists of septuple layers (SL) stackings. (e,f) Same for quintuple layer (QL) terminated MnBi$_4$Te$_7$, which consists of alternative stacking of QL and SL.
• Figure 2: (a) Measurement schematic with $p$-polarized light, which mainly couples to $p_x$ and $p_z$ orbitals. (b) Similarly, $s$-polarized light mainly couples to $p_y$ orbitals. (c,d) $S_y$ of MnBi$_2$Te$_4$ measured with $p$- and $s$-pol, respectively. (e,f) Same but for QL MnBi$_4$Te$_7$. (g,h) $S_z$ of MnBi$_2$Te$_4$ measured with $p$- and $s$-pol, respectively. (i,j) Same but for QL MnBi$_4$Te$_7$. (k) $S_y$ extracted from the MnBi$_2$Te$_4$ surface state measured with both light polarizations (markers) overlapped with the model (lines). (l) Same but for QL MnBi$_4$Te$_7$. (m) $S_z$ extracted from the MnBi$_2$Te$_4$ surface state measured with both light polarizations, overlapped with the model. (n) Same but for QL MnBi$_4$Te$_7$. We note that asymmetries in the $p$-pol data with respect to $k=0$ are attributed to the measurement geometry, which is included in the modeling [See Appendix \ref{['sec:spintexture_formalism']}].
• Figure 3: Spin-resolved ARPES measurements of SL MnBi$_4$Te$_7$. (a,b) $S_y$ data with $p$- and $s$-pol light. (c) The corresponding momentum distribution curves (MDCs) of spin-up $I_\uparrow$ ($+y$-direction) and spin-down $I_\downarrow$ ($-y$-direction) intensities. Each MDC is integrated within an energy window of 33 meV. Each MDC pair is normalized by the maximum intensity for that pair to facilitate a comparison between MDCs at different energies. The markers denote peak positions of both bands, with blue-red coloring indicating the overall polarization of each peak. (d) Cartoon model of a pair of Rashba-split states and Dirac TSS without band hybridization, where color denotes $S_y$. (e) The same, with hybridization. (f,g) $S_z$ images with $p$- and $s$- pol. (h) $S_y$ extracted along the black dashed line in (a), with $43$ meV integration window for both light polarizations (markers) overlapped with the model (lines). The data within $k=\pm0.05\hbox{\normalfont\AA}^{-1}$ is excluded from the comparison due to the number of overlapping bands in this region. (i) Same but for $S_z$.
• Figure 4: Measurement geometry for circular dichroism (CD)-ARPES of QL MnBi$_4$Te$_7$. Circularly-polarized light is incident at $50^{\circ}$ with respect to the surface normal. $\Gamma-K$ is along the $x$-axis. The yellow plane indicates the plane from which the electrons are collected. (a) and (b) show the CD-ARPES data before and after $180^{\circ}$ rotation of the sample, plotted in the 2D colorscale as shown. (c,d) CD of the surface state before and after sample rotation. (e,f) CD yielded from our model with wavefunction parameters derived from the spin-resolved measurements.
• Figure 5: Data for Bi$_2$Te$_3$ taken at room temperature along $\Gamma-K$. Specific measurements are $S_z$ with (a) $p$-pol and (b) $s$-pol, and $S_y$ with (c) $p$- pol and (d) $s$-pol. (e) $S_z$ with both $p$ and $s$- pol from spin image (dots), overlapped with result yielded from model(lines). (f) Same but for $S_y$.