Electronic properties and surface states of RbNi2Se2

2025-05-03 0 0 6.99MB 12 页 10玖币

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Surajit Basaka,Przemysław Piekarzaand Andrzej Ptoka,∗

aInstitute of Nuclear Physics, Polish Academy of Sciences, ul. W. E. Radzikowskiego 152, 31-342 Kraków, Poland

ARTICLE INFO

Keywords:

DFT calculations

Electronic structure

Surface states

Hydrostatic pressure

Lifshitz transition

ABSTRACT

Iron-based superconductors, with the ThCr2Si2-type tetragonal structure (122 family), due to

the iron arsenide/selenide layers exhibit several characteristic electronic properties. For example,

multiband character mosty associated with the d-orbitals of iron and the quasi-two-dimensional

(2D) cylindrical Fermi surface. Moreover, external hydrostatic pressure leads to the isostructural

phase transition from the tetragonal to collapsed-tetragonal phase. In this paper, in relation

to the iron-based superconductors, we discuss the electronic properties of novel 122-family

member RbNi2Se2[Liu H. et al.,Phys. Rev. B 106, 094511 (2022)]. We show that the two

Fermi pockets exhibit quasi-2D character. Calculation of the surface spectral function for the

(001) surface shows that the surface states are realized independently on the surface termination.

Additionally, contrary to the iron-based 122 compounds, RbNi2Se2exhibits extraordinary

multiple isostructural phase transitions under pressure. Moreover, the Lifshizt transition occurs

under external pressure, which results into a strong modiﬁcation of the shapes of the Fermi

pockets.

1. Introduction

Discovered in 2008, the superconductors based on iron [1] opened a period of intensive experimental and theoretical

studies of this class of compounds [2–6]. These materials are characterized by the layered structure containing iron-

arsenide/selenide layers – where the iron square lattice is decorated by anions. As a consequence, the electronic

structure exhibits multiband properties and the characteristic quasi-two-dimensional (2D) cylindrical Fermi surface.

One of the examples of iron-based superconductors is a group of the ternary ThCr2Si2-type compounds (called

122 family) [7–20]. The 122-family members exhibit not only superconductivity, but also a wide range of physical

properties, e.g., antiferromagnetism [15–18], spin density waves [7–9], and structural phase transitions [11]. Moreover,

in the presence of external hydrostatic pressure, the isostructural transition from the tetragonal to collapsed-tetragonal

phase occurs [21–32].

Recently, the RhNi2Se2compound, showing the multi-gap superconducting properties below 𝑇𝑐= 1.2K, was

successfully synthesized [33]. Contrary to a large part of the iron-based materials [34], RhNi2Se2exhibits the Pauli

paramagnetic behavior. The initial measurements of the speciﬁc heat suggest enhancement of the eﬀective electronic

mass 𝑚∗= 6𝑚𝑒and a weak role of correlations.

In this paper, on the base of density functional theory (DFT) calculations, we discuss the electronic properties of

RbNi2Se2(the band structure and the Fermi surface). From the DFT band structure, we construct the tight banding

model in the basis of the Wannier orbitals and investigate the surface states. Mainly we discuss the surface termination

dependence of the surface states. Finally, we demonstrate the existence of the multiple-isostructural phase transitions

occuring under external hydrostatic pressure. The presented results can also be applicable for other 122-compounds

based on nickel, e.g. KNi2Se2[35], CsNi2Se2[36], or TlNi2Se2[37].

The paper is organized as follows. The computational details are present in Sec 2. Next, in Sec. 3we present and

discuss our results: electronic properties (Sec. 1), realized surface states (Sec. 3.2), and properties under hydrostatic

pressure (Sec. 3.3). Finally, a summary is provided in Sect. 4.

∗Corresponding author

surajit.basak@ifj.edu.pl (S. Basak); piekarz@wolf.ifj.edu.pl (P. Piekarz); aptok@mmj.pl (A. Ptok)

www.mmj.pl/~aptok/ (A. Ptok)

ORCID(s): 0000-0002-0669-0984 (S. Basak); 0000-0001-6339-2986 (P. Piekarz); 0000-0002-5566-2656 (A. Ptok)

S. Basak et al.: Preprint submitted to Elsevier Page 1 of 12

arXiv:2210.13280v3 [cond-mat.supr-con] 7 Aug 2024

Electronic properties and surface states of RbNi2Se2

2. Computational details

The electronic properties were calculated using QUANTUM ESPRESSO [38–40]. The calculations were performed

within the generalized gradient approximation (GGA) in the Perdew, Burke, and Ernzerhof (PBE) parameteriza-

tion [41] within PSLIBRARY [42]. In this study we used the experimental lattice parameters [33].

The DFT results of the electronic band structure calculation, performed for the primitive unit cell, were used to

ﬁnd the tight binding model in the basis of the maximally localized Wannier orbitals [43–45]. It was performed using

the WANNIER90 software [46–48]. In our calculations, we used the 6×6×6full 𝒌-point mesh, starting from the 𝑝

orbitals of Se, and from the 𝑠and 𝑑orbitals for Rb and Ni, respectively. Finally, the resulting 28-orbital tight binding

model of RbNi2Se2was applied to investigate the surface Green’s function for a semi-inﬁnite system [49], using

WANNIERTOOLS [50] software.

Properties of the system under external hydrostatic pressure were investigated using the projector augmented-wave

(PAW) potentials [51] implemented in the Vienna Ab initio Simulation Package (VASP) code [52–54] within the GGA

PBE. The energy cutoﬀ for the plane-wave expansion was set to 400 eV. Optimizations of structural parameters (lattice

constants and atomic positions) under pressure were performed in the conventional unit cell (containing two formula

units) using the 12 × 12 × 4 k–point grid in the Monkhorst–Pack scheme [55]. The convergence criteria were set to be

10−6 eV and 10−8 eV for ionic and electronic degrees of freedom, respectively.

3. Results and discussion

RbNi2Se2crystallizes in the ThCr2Si2-type structure (symmetry I4/mmm, space group No. 139) [33]. In the

absence of any external pressure, the lattice parameters were experimentally measured to be 𝑎=𝑏= 3.9272 Å,

and 𝑐= 13.8650. In this cell three nonequivalent atoms Rb, Ni, and Se are placed at the crystallographic sites:

2𝑎(0,0,0),4𝑑(0,1∕2,1∕4) and 4𝑒(0.0, 𝑧Se), respectively. Experimentally, the free parameter at the position of Se atom

was determined to be 𝑧Se = 0.3498. The lattice parameters are comparable to the parameters of the isostructural

KFe2As2superconductor [30].

Figure 1: The electronic band structure of RbNi2Se2. The results in the absence and presence of spin–orbit coupling are

represented by orange and blue lines, respectively. Inset presents the Brillouin zone and its high symmetry points.

3.1. Band structure and Fermi surface

The electronic band structure (in the absence and presence of the spin–orbit coupling) is presented in Fig. 1. In

relation to the 122 iron-based compounds, e.g. KFe2As2[30], the Fermi level is shifted to the higher energies. This is

associated with the three “extra” electrons in the system (due to the Fe→Ni and As→Se substitutions). Nevertheless, the

Fermi level is still located within the range of energies related to the d-orbitals [33]. This behaviour is also well visible

in the partial density of states, presented in Fig. 2. For energies from −6 to 1eV, the Se p-orbitals and Ni d-orbitals

contribute the most. The group of the d-orbitals are mostly locallized between −3 and 1eV, and constitute a group

of bands well separated from rest of the spectrum by the gaps (around −3 eV and 1eV, see Fig. 1). Similar situation

was previously reported for FeSe [56], where bands related to the Fe d-orbitals were well separated. Contrary to this,

S. Basak et al.: Preprint submitted to Elsevier Page 2 of 12

Electronic properties and surface states of RbNi2Se2

Figure 2: The total and partial electronic density of states of RbNi2Se2.

in the case of KFe2As2, the bands were not separated due to the strong mixing with As p-orbitals [56]. In the case of

RbNi2Se2, the Se p-orbitals are mostly localized at energies from −6 eV to −3 eV, and show only a small contribution

close to the Fermi energy. For bands above 2eV, the strong mixing of orbitals is observed, without dominant role of

any of them.

In relation to the 122 iron-based superconductors [30], the Fermi level is shifted to the higher energies. As a

consequence, the strong modiﬁcation of the Fermi surface with respect to the 122 iron-based systems is observed

(Fig. 3). There are three Fermi pockets with hole-like character. One pocket exhibits exactly three dimensional character

[Fig. 3(c)], while two pockets along the X–P path exhibit quasi-2D character [Fig. 3(d) and (e)]. It is worth mentioning

that in the case of KFe2As2, the quasi-2D pockets are centered along the Γ–Z path, while along the X–P path there are

four small pockets [30].

The multiband character of this compound can aﬀect its superconducting properties. Initial investigations of

the superconducting states predicted two-gap BCS-like superconductivity [33]. However, RbNi2Se2exhibits a weak

Figure 3: The general view (a) and view from the top (b) of the Fermi surface of RbNi2Se2. Panels (c)–(e) present the

separated Fermi pockets.

S. Basak et al.: Preprint submitted to Elsevier Page 3 of 12

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摘要：

ElectronicpropertiesandsurfacestatesofRbNi2Se2SurajitBasaka,PrzemysławPiekarzaandAndrzejPtoka,∗aInstituteofNuclearPhysics,PolishAcademyofSciences,ul.W.E.Radzikowskiego152,31-342Kraków,PolandARTICLEINFOKeywords:DFTcalculationsElectronicstructureSurfacestatesHydrostaticpressureLifshitztransitionABSTRA...

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Electronic properties and surface states of RbNi2Se2

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