Spatially-resolved electronic structure of stripe domains in IrTe$_2$ through electronic structure microscopy

Phase separation in the nanometer- to micrometer-scale is characteristic for correlated materials, for example, high temperature superconductors, colossal magnetoresistance manganites, Mott insulators, etc. Resolving the electronic structure with spatially-resolved information is critical for revealing the fundamental physics of such inhomogeneous systems yet this is challenging experimentally. Here by using nanometer- and micrometer-spot angle-resolved photoemission spectroscopies (NanoARPES and MicroARPES), we reveal the spatially-resolved electronic structure in the stripe phase of IrTe$_2$. Each separated domain shows two-fold symmetric electronic structure with the mirror axis aligned along 3 equivalent directions, and 6$\times$1 replicas are clearly identified. Moreover, such electronic structure inhomogeneity disappears across the stripe phase transition, suggesting that electronic phase with broken symmetry induced by the 6$\times$1 modulation is directly related to the stripe phase transition of IrTe$_2$. Our work demonstrates the capability of NanoARPES and MicroARPES in elucidating the fundamental physics of phase-separated materials.


Introduction
By focusing the beam size down to a few µm or even 100 nm scale by a Fresnel zone plate [1][2][3] (for synchrotron light source) or a lens 4 (for laser source), nanometer-and micrometer-spot angleresolved photoemission spectroscopies (NanoARPES 1-3 and MicroARPES 4 , Fig. 1a) provide two important advantages over conventional ARPES which has a typical beam size of 50-100 µm.
Firstly, it allows to measure the electronic structure of small samples, which has been demonstrated in atomically thin flakes [5][6][7] or samples with mixed crystal orientations 8,9 . Secondly and more importantly, for phase-separated materials which consist of multiple domains with distinct electronic structures [10][11][12][13][14] , the newly added spatial-resolving capability provides new opportunities to reveal the intrinsic electronic structure of individual domain and the evolution of the phase separation across the phase transition. Such information cannot be obtained by conventional ARPES, which is, however, indispensable for understanding the fundamental physics of phase-separated materials. Recently, NanoARPES and MicroARPES have been applied to probe the electronic structure of individual domain in CeSb 15 and Fe-based superconductors [16][17][18][19] by utilizing the spectroscopic capability of ARPES. Combining the advantages of both microscopic and spectroscopic capabilities of NanoARPES and MicroARPES will allow for direct visualization of separated domains with spatially-resolved information and the evolution of domains across the phase transition, thereby further elucidating the complex physics of phase-separated materials.

Results and discussion
Spatially-resolved electronic structures of different domains. Figure 1d,e shows two representative NanoARPES spectra measured along theΓ-K direction (Fig. 1c) of IrTe 2 at 80 K from two domains A and B, and they are strikingly different. While the dispersion in domain A is relatively simple with strong intensity at energies from -2.5 to -0.5 eV, the dispersion in domain B shows weak intensity starting from -1 eV to the Fermi energy (E F ) with many weaker bands near E F . In addition, compared to domain A, there is an additional band near theK point (marked by box 2 in  To further investigate the electronic structure of these separated domains, we map out the full three-dimensional electronic dispersions for each domain. Figure 2a,b shows the spatially-resolved intensity maps measured on two representative samples where separated domains are clearly observed. Figure 2c-j shows the intensity maps at E F and -0.2 eV from four different domains. All these intensity maps clearly reveal the two-fold symmetry of the electronic structure with the symmetry axis aligned along three equivalentΓ-M directions at angles of 0 • , 120 • and -120 • (indicated by red solid arrows), which is in sharp contrast to previous ARPES measurements 26,[32][33][34][35][36][37][38] where spatial averaging gives rise to apparently three-fold symmetric electronic structure. Therefore, the strikingly different dispersions in Fig. 1 originate from different orientations of the mirror symmetry axes. Here, the observation of two-fold symmetric electronic structure in a three-fold symmetric crystal confirms the broken symmetry in the stripe phase, and the space-and momentum-resolving capability allows to reveal the intrinsic electronic structure of each individual domain.
With the capability to resolve the electronic structure of each individual domain, we can now investigate the intrinsic electronic structure and the nature of the stripe phase. The two-fold symmetric Fermi surface map (Fig. 3a) shows replica oval pockets around theΓ point translated by a scattering wave vectors of 1/3 a * (Fig. 3b)  NanoARPES and MicroARPES measurements, we reveal the electronic reconstructions of 1/6 and 1/3 a * , which suggests that the two-fold symmetric electronic structure is likely associated with the 6×1 reconstruction in the stripe phase. We note that in principle 5×1 or 8×1 would also be compatible with the two-fold symmetric Fermi surface, however signatures of 5×1 or 8×1 replicas have not been resolved experimentally, suggesting that those domains do not have significant contribution to the dispersions.
Temperature evolution of the spatially-resolved intensity map. To confirm that such spatial inhomogeneity is directly related to the stripe phase transition, we perform temperaturedependent MicroARPES measurement. Figure 4a-h shows spatially-resolved intensity maps measured at temperatures from 80 K to 300 K. Separated domains on the order of tens to hundreds of micrometers with different intensity contrast are clearly observed below the stripe transition temperature. Remarkably, above the stripe phase transition temperature, the spatial intensity map becomes much more homogeneous at 300 K (Fig. 4h) similar to its optical image. After cooling back to 80 K, the spatial inhomogeneity appears again but with different distribution, suggesting that its distribution is related to history (Fig. 4j). The observation of the stripe domains and its disappearance at high temperature provides direct evidence that the inhomogeneous electronic structure is an intrinsic property of the low temperature stripe phase.  Therefore, temperature dependent MicroARPES measurements show that the spatial inhomogeneity is directly related to the different orientations of the stripe phases, and there is a coexistence of both 6×1 stripe domains with different stripe orientations ( Fig. 5d-g) and other mixed domains (gray area in Fig. 5g) as schematically shown in Fig. 5g.

Conclusion
In summary, the energy-, momentum-and space-resolving capability of NanoARPES and Mi-croARPES allows to visualize the separated domains and reveal the intrinsic and inhomogeneous electronic structure in the stripe phase of IrTe 2 . Replica bands with 1/6 a * wave vector (or 6×1 modulation) are identified in the dispersion which resembles the 6×1 reconstruction of the high temperature electronic state (see Supplementary Figure 6 and Supplementary Note 3). We note that the period of the phase is strongly related to the Ir-Ir dimer concentration, and different dimer concentration leads to complex (3n+2)×1 stripe period. At the highest dimer concentration 21,39 , this corresponds to the 6×1 electronic ground state (Fig. 5d-f). Here by directly revealing the electronic structure of each individual domain using NanoARPES and MicroARPES, we show that the 6×1 stripe phase is indeed the electronic ground state and the 6×1 modulation is directly related to the stripe phase transition of IrTe 2 . Our work resolves the puzzle in the electronic structure of the stripe phase of IrTe 2 , and we envision that the application of NanoARPES and MicroARPES to other phase-separated systems can yield important information on the intrinsic underlying physics.

Methods
Sample growth. High quality IrTe 2 single crystal was grown by self-flux method. Ir pellet (99.95%, Alfa Aesar) and Te ingot (99.99%, Alfa Aesar) in an atomic ratio of 5:95 were mixed together and sealed in an evacuated silica ampoule. The mixture was heated up to 900 • C first and kept for several hours, then to 1150 • C and kept for two days, finally cooled down to 920 • C in several hours with a low rate. Liquid Te was separated from IrTe 2 single crystal by centrifugation.
ARPES measurement. MicroARPES measurements have been performed in the home laboratory at Tsinghua University with fourth harmonic generation light source. The photon energy is set to 6.2 eV with p-polarization. The energy resolution was set to 15 meV. The beam size is 15 µm. The sample was measured in a working vacuum at greater than 7 × 10 −11 Torr. Surface sensitive NanoARPES measurements were performed at the beamline ANTARES of the synchrotron