Effective tight-binding model for renormalized band structure of Sr{}_{\scriptsize{\textup{2}}}RuO{}_{\scriptsize{\textup{4}}}

Effective tight-binding model for renormalized band structure of SrRuO

V. B. Zabolotnyy    D. V. Evtushinsky Institute for Solid State Research, IFW-Dresden, P. O. Box 270116, D-01171 Dresden, Germany    A. A. Kordyuk Institute of Metal Physics of National Academy of Sciences of Ukraine, 03142 Kyiv, Ukraine Institute for Solid State Research, IFW-Dresden, P. O. Box 270116, D-01171 Dresden, Germany    T. K. Kim111Present address: Diamond Light Source Ltd., Didcot, Oxfordshire, OX11 0DE, United Kingdom Institute for Solid State Research, IFW-Dresden, P. O. Box 270116, D-01171 Dresden, Germany    E. Carleschi Department of Physics, University of Johannesburg, P. O. Box 524, Auckland Park 2006, South Africa    B. P. Doyle Department of Physics, University of Johannesburg, P. O. Box 524, Auckland Park 2006, South Africa    R. Fittipaldi CNR-SPIN, and Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, I-84084 Fisciano (Salerno) Italy    M. Cuoco CNR-SPIN, and Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, I-84084 Fisciano (Salerno) Italy    A. Vecchione CNR-SPIN, and Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, I-84084 Fisciano (Salerno) Italy    S. V. Borisenko Institute for Solid State Research, IFW-Dresden, P. O. Box 270116, D-01171 Dresden, Germany
July 19, 2019
Abstract

We derive an effective quasiparticle tight-binding model which is able to describe with high accuracy the low-energy electronic structure of SrRuO obtained by means of low temperature angle resolved photoemission spectroscopy. Such approach is applied to determine the momentum and orbital dependent effective masses and velocities of the electron quasiparticles close to the Fermi level. We demonstrate that the model can provide, among the various computable physical quantities, a very good agreement with the specific heat coefficient and the plasma frequency. Its use is underlined as a realistic input in the analysis of the possible electronic mechanisms related to the superconducting state of SrRuO.

pacs:
79.60.-i, 74.25.Jb, 74.70.-b, 71.15.Mb
preprint: xxx

Since its discovery, the nature of the superconducting state of SrRuO remains in the focus of the solid state research Carlo323 (); Puetter27010 (); Maeno011009 (); Wysokinski077004 (). An accurate description of the low energy electronic structure is a fundamental step for understanding the collective properties of complex materials. This is also the case for the superconducting phase of SrRuO. There are generally two ways to get access at the electronic structure of a given material. On one side, ab initio density functional theory (DFT) can provide quasiparticle spectrum at all energies, although it is known to be not suitable for properly accounting the effects of electron correlations. To this end, DFT calculations are often taken as a platform for a more elaborate treatment of correlation effects as, for instance, in DFT+DMFT (dynamical mean-field theory) approaches, or other many-body theories. Such methods, in the attempt to build up an accurate quantitative description of correlated materials, usually includes the Coulomb interaction within tight-binding (TB) models based on a localized Wannier basis from the DFT states. The complexity in dealing with the high and low energy sector of correlated materials on equal footing leads to deviations between the theoretical predictions and the experimental observations. These can manifest themselves, for instance, in the difficulty to capture the observed band renormalization, to quantitatively reproduce the relative band positions Geck046403 (), etc.

On the other hand, there are different experimental methods to probe directly and indirectly the electronic structure. For instance, the thermodynamical properties can provide average information on the physical quantities at the Fermi level (FL) such as density of states. Otherwise, by means of de Haas–van Alphen or Shubnikov–de Haas measurements via the analysis of the resonance frequencies of the cyclotron motion it is possible to map the Fermi surface and to extract the effective masses at the FL, assuming that suitable conditions for the applied magnetic field and the degree of purity of the samples are given. For the Compton scattering probe, which recently gained popularity with layered superconductors, one has to face the reconstruction of a 2D electron density from a set of experimentally measured Compton profiles Hiraoka100501 (); Hiraoka094511 (); Mijnarends2381 (); AlSawai115109 (); Utfeld064509 (); Sakurai06052011 (). In this framework, in terms of band mapping Krasovskii045432 (), angle-resolved photoelectron spectroscopy (ARPES) appears to be the most direct momentum and energy resolving technique for determination of the electronic structure.

Concerning the SrRuO, though for the first ARPES measurements it was not easy to disentangle the contributions of the surface states from the bulk ones Yokoya3009 (), the improvement of the experimental analysis allowed to get a general agreement between photoemission and bulk probes Bergemann639 (); Hiraoka100501 (). Interestingly, the recent observation of an anomalous splitting of the surface bands renewed interest in the study of SrRuO electronic structure Zabolotnyy063039 (). While various reports on integrated quantities (like average Fermi velocities or effective masses) characterizing the band structure of SrRuO are available in the literature, a detailed quantitative description of the low energy electronic structure of SrRuO as measured by ARPES is still missing. In this paper, starting from low temperature high resolution ARPES observations, we aim at providing an effective TB model to quantitatively describe the dispersion of the renormalized low energy quasiparticles of SrRuO, following an approach that is similar to what has already been done for the layered dichalcogenides -TaSe and -NbSeInosov125112 (); Inosov125027 ().

Effective TB models, i.e. a representation of the electronic structure within a certain energy region close to the FL in terms of atomic-like orbitals, is a powerful method often used to analyze the essential mechanisms governing the physical behavior of complex materials. Moreover, one of the basic advantages of a TB model is that it allows the band structure to be computed on very fine meshes in the Brillouin zone at low computational cost, which, furthermore, greatly facilitates calculation of transport, superconducting and other properties determined by peculiarities of the Fermi surface and the dispersion of low energy electronic bands Mazin5223 ().

TB models with the corresponding sets of parameters as derived from the first-principles calculations of SrRuO have been reported earlier Mazin733 (); Liebsch1591 (); Morr5978 (); Mishonov305 (); Mazin5223 (); Noce2659 (); Noce19971713 (), and used to calculate the magnetic response Braden064522 (); Morr5978 (), the Hall coefficient Noce2659 () and the photoemission spectra Liebsch1591 (). Unlike the previous examples, where unrenormalized band structure was captured, TB models were also successfully applied to parameterize the dynamics of quasiparticles, as in the case of graphene Grueneis205425 (), for the reconstructed diamond surface C(111)21 Marsili205414 () or in iron arsenides Beaird140507 (). Here we combine our experimental data with a quasiparticle tight-binding approach to produce an accurate description of quasiparticle dispersion in single layer ruthenate SrRuO in the vicinity of the FL.

High-quality SrRuO single crystals used in this work have been grown by the flux-feeding floating-zone technique with Ru self-flux Fittipaldi70180 (); Mao20001813 (). The composition and structure of the samples have been characterized by X-ray and electron backscatter diffraction. All the diffraction peaks had the expected (001) Bragg reflections of the SrRuO phase, confirming the absence of any spurious phase. The purity of the crystals is supported by a.c. susceptibility and resistivity measurements demonstrating a narrow superconducting transition with =1.34 K, which is a signature of a low impurity concentration Kikugawa237 (). Photoemission data were collected at the BESSY 1 ARPES station equipped with a SCIENTA R4000 analyzer and a Janis He cryostat Borisenko720159 (); BorisenkoJove (). Further details on the experimental geometry can be found elsewhere Zabolotnyy024502 (); Inosov212504 ().

Before presenting the modeling of the SrRuO electronic structure it is worth pointing out a few aspects which have to be considered with care in the attempt of deriving a TB description of the experimental data Inosov125112 (); Inosov125027 (); Kordyuk064504 (); Evtushinsky147201 (). Indeed, electronic structure of SrRuO as seen in photoemission experiment can be regarded as a superposition of two sets of features, one corresponding to the bulk bands, and the other one to the surface bands Ingle205114 (); Zabolotnyy063039 (). While the momentum disparity between the corresponding surface and bulk features is comparatively small at the FL, the difference becomes notable at higher binding energies because of the unequal renormalization of the surface and bulk bands Ingle205114 (); Zabolotnyy024502 (); Zabolotnyy063039 (). To illustrate this issue in Fig. Effective tight-binding model for renormalized band structure of SrRuO we show a cut through the pocket, where the surface and bulk bands are well resolved, so that their MDC dispersions can be fit and traced down to about 50 meV in binding energy. We find that the velocity of the bulk band projected on the cut direction is about 1 eVÅ, and does not vary much within the first 50 meV below the FL. However, for the surface band, contrary to the expectations expressed in Ref. Ingle205114, , we find an abrupt change in the band velocity located at about 17 meV binding energy.

(a) Experimental Fermi surface of Sr
Dispersion of the quasiparticle TB bands (a) and the derived quasiparticle density of states (b) in the vicinity of the FL.
0.032 0.145 0.016 0.081 0.039 0.005 0.000 0.122
mass type total year
(this study) 5.4 4.8 16.7 26.9
Cyclotron thermodynamic Bergemann2001371 (); Bergemann639 () 3.3 7.0 16.0 26.3 2001
Cyclotron thermodynamic Andrew385 () 3.4 7.5 14.6 25.5 1998
Cyclotron thermodynamic Mackenzie3786 () 3.4 6.6 12. 22.0 1998
Cyclotron thermodynamic Mackenzie1996510 () 3.2 6.6 12.0 21.8 1996
Cyclotron resonance Bergemann639 () 2.1 4.3 5.8 12.2 2003
Cyclotron resonance Hill3374 () 4.3 5.8 9.7 19.8 2000
Fig. 3: Dispersion of the quasiparticle TB bands (a) and the derived quasiparticle density of states (b) in the vicinity of the FL.
Fig. 3: Dispersion of the quasiparticle TB bands (a) and the derived quasiparticle density of states (b) in the vicinity of the FL.
Fig. 2: (a) Experimental Fermi surface of SrRuO with superimposed TB contours. (b) Intensity distribution similar the Fermi surface map shown in (a) but taken 30 meV below the FL. (c) Comparison of experimental intensity distribution for several energy–momentum cuts with fitting quasiparticle dispersion. Cuts position in momentum space is marked by small arrows in panel (b).
Fig. 2: (a) Experimental Fermi surface of SrRuO with superimposed TB contours. (b) Intensity distribution similar the Fermi surface map shown in (a) but taken 30 meV below the FL. (c) Comparison of experimental intensity distribution for several energy–momentum cuts with fitting quasiparticle dispersion. Cuts position in momentum space is marked by small arrows in panel (b).
Fig. 1: Surface and bulk bands (a) and their MDC dispersions (b). The projections of the band velocities were estimated by fitting a line to a straight segments of experimental dispersion. Since the cut is not perpendicular to the Fermi surface locus, the total in-plane velocities are actually larger.
Fig. 1: Surface and bulk bands (a) and their MDC dispersions (b). The projections of the band velocities were estimated by fitting a line to a straight segments of experimental dispersion. Since the cut is not perpendicular to the Fermi surface locus, the total in-plane velocities are actually larger.
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