1144 Fe based superconductors: natural example of orbital selective self-doping and chemical pressure induced Lifshitz transition

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Abstract

A systematic density functional theory based first principles electronic structure studies on AeAFe4As4 known as, 1144 iron based superconductors (IBSC) for various Ae = Ca, Sr, Eu and different alkali metals A = K, Rb, Cs are presented. Our study reveals multi-orbital derived multi-band nature of the electronic structure as well as Fermi surfaces for all the compounds. In contrast to the electronic structure of most of the Fe-based superconductors, significant contribution from As-4pz and its mixing with Fe-3d is found at the Fermi level. A unique feature of the electronic structure of these compounds reveal orbital selective electron/hole self-doping. This is due to natural chemical pressure of larger/smaller atomic (Ae/A) sizes of various members of 1144 family. The different chemical potential (self-doping) of different orbital derived electron/hole bands causes crossing of the Fermi level for some bands, leading to orbital selective chemical pressure induced topological Lifshitz transition. This natural pressure induced orbital selective Lifshitz transition of hole bands is a unique characteristic of this family of iron based superconductors. Our conclusions remain robust even in presence of moderate electron correlation and spin-orbit coupling. Different combinations of Ae and A in different 1144 materials causes different bandwidths to different orbital selective bands; bandwidths of different bands that crosses Fermi level around Γ-point are evaluated. A large value of bandwidths for most of the compounds including EuAFe4As4 indicates weak correlation effect in these compounds.

Introduction

The discovery of superconductivity in LaFeAsO(F) [1] in 2008 stimulated research on iron based superconductors and a large number of other iron pnictides and chalcogenides were discovered in subsequent years [2], [3], [4], [5]. Among the above mentioned IBSCs, AEFe2As2 (AE = Ca, Sr, Ba, Eu), popularly known as 122-family, is most studied due to availability of high quality single crystals with a variety of chemical substitutions. This 122-family comprise many exotic phases like spin density wave (SDW) [6], [7], [8], orbital order [9], [10], [11], [12], structural transition [13], [14] etc. in their phase diagram. Recently, a new family of IBSCs CaAFe4As4 (A = K, Rb, Cs), SrAFe4As4 (A = Rb, Cs) [15] and EuAFe4As4 (A = Rb, Cs) [16] [1144] was discovered which has gained a significant attention among the scientific community due to its interesting properties. This 1144 family are the sandwich of two different kinds of 122 compounds where alkaline earth element and alkali element occupy different atomic positions in its crystal structure. There is alternate alkali metal (K, Rb, Cs) and alkaline earth metal (Ca, Sr) or Eu spacer layer in between FeAs-layers. Unlike 122 compounds which crystallize in body-centered tetragonal structure with space group I4/mmm, 1144 compounds crystallize in primitive tetragonal structure having space group P4/mmm [15]. There are two inequivalent atomic sites for As-atoms in FeAs-layer. The AeAFe4As4 (=AeA44) iron pnictides show quite similar superconducting transition temperatures 33.1 K, 35 K, 31.6 K, 35.1 K, 36.8 K, 36 K, 35 K for CaK44, CaRb44, CaCs44, SrRb44, SrCs44, EuRb44, EuCs44 compounds respectively. Recent experimental studies also revealed difference in vortex dynamics indicating distinct origins of vortex pinning in 122 and 1144 superconductors [17]. The iron based superconductors in general show diverse types of magnetic orders. Although striped spin density wave (SSDW) type magnetic order is observed in majority of the IBSCs, some hole doped 122 compounds show a transition from SSDW to spin charge density wave (SCDW) magnetic states [18], [19]. The magnetic ground state of 1144 compounds is also very interesting in this regard. Although the parent compounds AeAFe4As4 (Ae = Ca, Sr) do not show any magnetic order [20], Hedgehog spin vortex crystal (SVC) type magnetic state was observed to be stabilized in hole compensated (Ni or Co doping at Fe site) 1144 compounds [21], [22]. Thus, all the three types of magnetic order i.e., SSDW, SCDW and SVC are possible for IBSCs. The SVC magnetic phase is stabilized by the reduced symmetry of the AeAFe4As4 crystal. The existence of large configuration space for magnetic fluctuations is believed to promote high temperature superconductivity [22]. In 122 compounds a collapsed tetragonal (cT) phase transition is observed due to variation of chemical or mechanical pressure leading to a modification of the whole structure and suppression of superconductivity [23]. Unlike 122 family, 1144 family show half cT (hcT) transition with external pressure and the transition is layer selective. The first collapsed tetragonal transition is observed at an external pressure 4GPa where the transition is induced due to As-As pz bonding across Ca layer with suppression of superconductivity. The second cT transition appeared at the pressure of 12GPa across the K-layer [24]. This hcT phase transition was predicted by Density Functional Theory (DFT) based ab initio calculations only by invoking the Hedgehog type long range spin order which is observed to be absent in the superconducting state of the undoped 1144 superconductors [24]. This magnetic order has only been realized experimentally in hole compensated CaK44 superconductors. Recently, layer selective two consecutive hcT transitions at different pressures was predicted in all the 1144 compounds [25]. On the other hand, The EuA44 (A = Rb, Cs) superconductors got much attention due to its peculiar magnetic properties in superconducting phase [26]. Experimentally it was found that EuRbFe4As4 shows superconductivity with transition temperature (Tc) 36.5 K and Eu spin ferromagnetism with Curie temperature (TCurie) 15 K [27]. Thus, EuRb44 is a ferromagnetic superconductor (FMSC). In EuCs44 compound ferromagnetic superconductivity was observed with Tc = 35.2 K and TCurie = 15.5 K [28]. Experimental phase diagram with respect to Ni doping at Fe site of EuRb44 reveals that from FMSC EuRb44 gradually transform into superconducting ferromagnet (SCFM) with Tc = 11.2 K and TCurie = 15.1 K at around 7% Ni doping. The superconductivity is completely suppressed when Ni doping is greater than 8% due to compensation of self hole doping with the addition of extra itinerant electrons of Ni. The hole depletion also seems to recover SDW order at Ni doping greater than 5%. This might improve our understanding about the interplay between superconductivity and magnetism. Therefore, the overall dynamics of magnetism of 1144 compounds seems very different compared to that of other iron based superconductors; most of the undoped compounds other than EuA44 do not show any long range magnetic order. Also in EuA44 compounds no magnetic order of Fe is observed. Furthermore, irrespective of the underlying magnetic structure or structural details superconducting transition temperature is nearly uniform in all the 1144 family members suggesting magnetic structure do not influence superconductivity in these compounds. Thus a thorough and systematic electronic structure studies on 1144 families are presented with non-magnetic ground state in this work. These materials being multi-orbital derived multi-band type, intra-inter-orbital nesting effects are expected to play significant role in superconductivity of these Fe based compounds and has been emphasized.

One of the very important fact about IBSCs is the occurrence of Lifshitz like topological transition in almost all the families due to doping [29], pressure [30], magnetic field [31] etc. Be it Ba1-xKxFe2As2 at x 0.8 [32] where electron band at the M point is shifted above the Fermi level (Fl) or LiFe1-xCoxAs for x0.1 [33], Ba(Fe1-xCox)2As2 for x 0.11 [34] where three hole bands at the Γ-point sinks below the Fl and Lifshitz transition occurs. Further, in many iron based superconductors a direct correlation between highest Tc and Lifshitz transition is found. For example, in Ba1-xNaxFe2As2 the highest Tc is 34 K for x 0.5 where Lifshitz transition like topological transition is induced due to hole doping [35], [38]. Also, in BaFe2-xCoxAs2 for electon doping x 0.11 and BaFe2(As1-xPx)2 for isovalent doping x 0.37 the highest Tc and Lifshitz transition is found to coincide [35], [38]. This transition has also been noted in K-dosed FeSe thin films [36], [37] also. Recently, in 112 compounds Ca1-xLaxFe2As2 a possible interconnection between critical temperature and Lifshitz like topological transition has been probed theoretically [35], [38], [39]. All these findings obviously indicate a direct interrelationship between these two phenomena: superconductivity and Lifshitz transition in IBSCs. Our calculated electronic structure of newly discovered undoped 1144 Fe based compounds reveal Lifshitz transition in these compounds also. We show in this work that these materials are self-doped where doping is orbital selective and undergo orbital selective Lifshitz transition.

Various physical properties like magnetism, nematicity, superconductivity are orbital selective [40], [41]. For some iron chalcogenides, orbital selective band renormalization is thought to play a crucial role in realizing different phases like SDW, orbital order, nematic order, superconductivity etc. The reduction of bandwidth (or bandwidth renormalization) usually indicate a manifestation of overall electron correlation. For example, gradual suppression of superconductivity in Rb0.8Fe2(Se1-zSz)2 for (z = 0.0, 0.5, 1.0) may be associated with a gradual reduction in bandwidth [42]. Thus a systematic study on the bandwidth of different bands might be helpful in understanding the modification of orbital selective electron correlation for different combinations of Ae (Ca, Sr or Eu) or A (K, Rb, Cs) in 1144 compounds.

Rest of the paper is organized as follows; in Section 2, we present the details of our computational method used in this work. In this paper, we have performed a systematic DFT based first principles calculation to have an insight into the electronic structure of different 1144 IBSCs. For a particular alkaline earth metal (Ca, Sr) or Eu, three different alkali metals i.e., K, Rb, Cs are considered. Our electronic structure study reveals that all the 1144 compounds show very much mixed multi-orbital character for each bands close to the Fl. The As 4pz orbital contributes significantly to the band structure and Fermi surface like 112 compounds [43]. In case of EuA44 compounds Eu 5d orbitals have a very small (nearly negligible) contribution to the density of states (DOS) at the Fermi level (Fl). This indicates to the fact that Eu atoms effect the electronic structure of these compounds in an indirect way just like Ca or Sr. The calculated orbital projected band structures (BSs), DOS and Fermi surfaces (FSs) are presented in Section 3. To the best of our knowledge detailed orbital character of FSs for this family of iron based superconductors is presented for the first time in this work. In Section 4 we describe various undoped members of 1144 iron pnictides which are actually self-doped, undergo natural chemical pressure induced orbital selective Lifshitz transition. This is a unique finding which might lead to an universal connection between Lifshitz transition and superconductivity in IBSCs. Role of electronic correlation effects in Fe based superconductors, have a mixed scenario [44], [45], [46] about it. In Section 5 we explicitly consider the effect of electron correlation on electronic structures, where a moderate value of electronic repulsion, treated within GGA + U method, in presence and absence of spin orbit coupling are presented. Occurrence of Lifshitz transition is found to be robust even in presence of electronic correlations and SOC. Furthermore, our studies on the bandwidth of different bands disclose that for a particular Ae, changing element A modifies the bandwidth of different bands effecting the overall electron correlation. Comparatively lower value of bandwidth in EuA44 compounds indicate comparatively increased correlation effect in these compounds. We have conferred our bandwidth related results in Section 6. The discussions and summary of our work are presented in Section 7.

Section snippets

Theory and computational method

We have performed calculations using plane wave pseudo potential method as implemented in Quantum Espresso [47], CASTEP [48] and VASP [49]. We have presented the results calculated with Quantum Espresso in subsequent sections. In our simulations the electronic exchange correlation is treated within the generalized gradient approximation (GGA) parametrized by Perdew-Burke-Enzerhof (PBE) functional [50]. Non-spin-polarized single point energy calculations were carried out for tetragonal phase

CaAFe4As4 (A = K, Rb, Cs)

We present the electronic structure of the undoped CaAFe4As4 (A = K, Rb, Cs) to investigate the effect of substitution of alkali metal atoms of gradually increasing atomic radius on the electronic structure of these materials. We have calculated detailed BSs and FSs projected on different Fe-3d as well as As 4pz orbitals to know the orbital nature of the bands and Fermi surfaces along major symmetric directions. We have also presented the partial density of electronic states to investigate the

Chemical pressure induced Orbital selective Lifshitz transition

The mechanism of superconductivity in Fe-based systems after 11 years of its discovery is still illusive and completely an open question. So in this work we have taken an observational route to the problem. In this section we illustrate through a number of detailed experimental and theoretical studies that a large number of systems exhibit Lifshitz transition where highest Tc is achieved i.e, Lifshitz transition somehow restricts Tc. Lifshitz transition (LT) is a common phenomena in many

Effect of electron correlation and spin orbit coupling on the electronic structure

So far we have discussed electronic structure of 1144 superconducting materials based on DFT. As mentioned in the earlier section that up to moderate values of electron correlation low energy electronic structure only undergoes quantitative modifications. Overall qualitative nature of electronic structure, specially the occurrence of Lifshitz transition remain unaltered. However, some 1144 Fe based superconductors not only contain Fe-3d but also Eu-4f orbitals (for EuK44, EuRb44, EuCs44),

Orbital Selective Bandwidth renormalization

To understand the effect of rare earth doping on bandwidths of different orbital derived bands, we present bandwidths of the hole like bands having different orbital characters. Bandwidth of different hole like bands is defined as the difference in energy between the top of the respective hole like band (at Γ-point) and first minima of the same band in Γ-M direction [78]. Due to very much mixed character of the bands it is not reasonable to assign a single orbital character to any particular

Conclusions

A comprehensive electronic structure study on all family members of 1144 Fe based superconducting materials in presence of electron correlation and spin orbit coupling suggests several important aspects. The electronic band structure have a number of hole like as well as electron like bands, each having multiple orbital characters mainly of Fe-3d orbitals but also from As-4pz i.e., electronic structure is multi-band multi-orbital nature. This leads to multi Fermi sheets (usually six hole like

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contribution

Numerical simulations and data analysis in the paper were carried out by Abyay Ghosh. GGA + U + SOC calculations were performed by S. Sen. The problem was formulated and conceptualized by Haranath Ghosh. The manuscript was written by Abyay Ghosh which was corrected and reformulated by H. Ghosh.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

We thank Computer Centre, RRCAT for providing computational facilities. AG acknowledges the HBNI, RRCAT for financial support and encouragements.

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