Electronic structure reconstruction of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the collapsed tetragonal phase

We report the electronic structure reconstruction of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the low temperature collapsed tetragonal (CT) phase observed by angle-resolved photoemission spectroscopy. Different from $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Rh}}_x{)}_2{\mathrm{As}}_2$ and the annealed ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ where all hole Fermi surfaces are absent in their CT phases, the cylindrical hole Fermi surface still persists in the CT phase of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. Furthermore, we found at least three well separated electronlike bands around the zone corner in the CT phase of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$, which are more dispersive than the electronlike bands in the high temperature tetragonal phase. Based on these observations, we propose that the weakening of correlations (as indicated by the reduced effective mass), rather than the lack of Fermi surface nesting, might be responsible for the absence of magnetic ordering and superconductivity in the CT phase.

Figure 1

The crystallographic and transport properties of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. (a) The x-ray diffraction pattern for our single crystal. The inset is a photograph of a typical sample. (b) The low-energy electron diffraction pattern taken in the CT phase at 15 K, showing $1\times 2$ and $2\times 1$ surface reconstructions marked by red arrows. (c) dc susceptibility as a function of temperature under a magnetic field of 0.2 T. Data around the hysteretic drops are magnified in the insets, which correspond to the CT transition. (d) The temperature dependence of the electrical resistivity. Data at low temperatures are magnified in the insets.

Figure 2

Electronic structure of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the HT phase. (a) The photoemission intensity map integrated over [$E_F-5$ meV, $E_F+5$ meV]. Solid black lines represent the Fermi surface contours. Cut directions are indicated by blue arrows. (b), (c) The photoemission intensity plot and its second derivative with respect to energy along cut 1. (d) The selected EDCs for data in panel (b). (e) The photoemission intensity plot along cut 2. Solid lines in panels (b), (c), and (e) are a guide for the eyes for band dispersions. Data were taken with randomly polarized 21.2 eV photons at 90 K.

Figure 3

Electronic structure of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the CT phase. (a) The photoemission intensity map integrated over ($E_F-5$ meV, $E_F+5$ meV). Solid black lines represent the Fermi surface contours. Cut directions are indicated by blue arrows. (b), (c) The photoemission intensity plot and its second derivative with respect to energy along cut 1. (d) The selected EDCs for data in panel (b). (e), (f) The photoemission intensity plot and its second derivative with respect to energy along cut 2. (g) The MDC integrated over ($E_F-6$ meV, $E_F+6$ meV) fitted by eight Lorentzian peaks. (h) The corresponding MDCs near $E_F$ in panel (e). Solid lines in panels (b), (c), (e), and (f) are a guide for the eyes for band dispersions. Data were taken with randomly polarized 21.2 eV photons at 12 K.

Figure 4

Photon-energy dependence of bands of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the HT phase at 115 K. (a) Indication of cut directions in the projected two-dimensional Brillouin zone. (b), (c) The photoemission intensity plots along cut 1 taken with 34 and 22 eV photons, respectively. (d) The photon-energy dependence of the EDCs at $\Gamma$($Z$). (e) The photon-energy dependence of the MDCs at $E_F$ along cut 1. The Fermi crossings of $\alpha$ in the corresponding high-symmetry planes are shown. (f), (g) The photoemission intensity plots along cut 2 taken with 36 and 24 eV photons, respectively. (h) The photon-energy dependence of the EDCs at $M$($A$). (e) The photon-energy dependence of the MDCs at $E_F$ along cut 2. Dashed lines in panels (b), (c), (f), and (g) are a guide for the eyes for band dispersions.

Figure 5

Photon-energy dependence of bands of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the CT phase at 6 K. (a) Indication of cut directions in the projected two-dimensional Brillouin zone. (b), (c) The photoemission intensity plots along cut 1 taken with 40 and 26 eV photons, respectively. (d) The photon-energy dependence of the EDCs at $\Gamma$($Z$). (e) The photon-energy dependence of the MDCs at $E_F$ along cut 1. The Fermi crossings of ${\alpha }_{\mathrm{CT}}$ in the corresponding high-symmetry plane is shown. (f), (g) The photoemission intensity plots along cut 2 taken with 16 and 28 eV photons, respectively. (h) The photon-energy dependence of the EDCs at $M$($A$). (e) The photon-energy dependence of the MDCs at $E_F$ along cut 2. Dashed lines in in panels (b), (c), (f), and (g) are a guide for the eyes for band dispersions.

Figure 6

Polarization dependence of photoemission data of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. (a) Experimental setup for polarization-dependent ARPES. The $x$ and $y$ directions are defined to be along the nearest Fe-Fe bonds. (b) Indication of cut direction in the projected two-dimensional Brillouin zone. The $\Gamma -M$ direction is parallel to the $k_x$ ($k_y$) direction in the reciprocal space. (c) Illustration of the spatial symmetry of the $3d$ orbitals with respect to the mirror plane. (d1) The photoemission intensity plots taken with 103 eV linearly polarized photons along the $\Gamma$($Z$)-$M$($A$) direction in the HT phase at 90 K. The left one was taken under the $p$ geometry, while the right one was taken under the $s$ geometry. (e1) The corresponding MDCs for the data in panel (d1). (d2), (e2) The corresponding CT phase ($T=16$ K) data for data in panels (d1) and (e1), respectively. Data were taken with 72 eV linearly polarized photons. (f) The summary of the orbitals (even or odd) of low-energy electronic structure in these two phases. Bands that could not be clearly resolved are represented by dashed black lines.

Figure 7

Temperature dependence of photoemission data. (a), (b) Photoemission intensity plots of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ measured along cuts 1 and 2, respectively, in the HT phase. (c), (d) The same for those in the CT phase as in panels (a) and (b). Dashed lines are a guide for the eyes for band dispersions. (e), (f) The EDCs at $\Gamma$($Z$) and $M$($A$) for a cooling procedure, respectively. Peak positions are indicated by short bars. (g) The EDCs of ${\mathrm{Ca}}_{1-x}{\mathrm{Pr}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ at the zone center [$\Gamma$($Z$)] for a warming-cooling cycle. (h) The summary of band tops of $\zeta$ (${\zeta }_{\mathrm{CT}}$) obtained in panel (g), which exhibits a hysteresis. The dc susceptibility in Fig. 1 is overlaid for comparison (translucent blue lines). (i) Indication of cut directions in the projected two-dimensional Brillouin zone. All data were taken with randomly polarized 21.2 eV photons.