{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T03:52:14Z","timestamp":1784605934069,"version":"3.55.0"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T00:00:00Z","timestamp":1703721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"QuantiXLie Centre of Excellence","award":["KK.01.1.1.01.0004"],"award-info":[{"award-number":["KK.01.1.1.01.0004"]}]},{"name":"QuantiXLie Centre of Excellence","award":["IZSEZ0_217543"],"award-info":[{"award-number":["IZSEZ0_217543"]}]},{"name":"Scientific Exchange","award":["KK.01.1.1.01.0004"],"award-info":[{"award-number":["KK.01.1.1.01.0004"]}]},{"name":"Scientific Exchange","award":["IZSEZ0_217543"],"award-info":[{"award-number":["IZSEZ0_217543"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate a single-particle density of states in the three-dimensional system described by effective two-band Hamiltonian, which describes a ground state in two distant electronic phases: the semimetalic nodal-loop phase and the insulating gapped phase. An analysis of valence bands and Fermi surfaces in both phases indicates that the density of states crucially depends on the parameter in the Hamiltonian of the system that controls a topological alternation of the Fermi surface. The signature of that alternation is expected to play an important role in all quantities closely related to the density of electronic states, such as charge transport and the optical conductivity of the system for example.<\/jats:p>","DOI":"10.3390\/sym16010038","type":"journal-article","created":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T09:35:21Z","timestamp":1703756121000},"page":"38","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Density of States in the 3D System with Semimetallic Nodal-Loop and Insulating Gapped Phase"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6997-3183","authenticated-orcid":false,"given":"Zoran","family":"Rukelj","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Science, University of Zagreb, Bijeni\u010dka 32, 10000 Zagreb, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2102-0285","authenticated-orcid":false,"given":"Ivan","family":"Kup\u010di\u0107","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, University of Zagreb, Bijeni\u010dka 32, 10000 Zagreb, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5696-3752","authenticated-orcid":false,"given":"Danko","family":"Radi\u0107","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, University of Zagreb, Bijeni\u010dka 32, 10000 Zagreb, Croatia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,28]]},"reference":[{"key":"ref_1","first-page":"1414631","article-title":"Symmetry demanded topological nodal-line materials","volume":"3","author":"Yang","year":"2018","journal-title":"Adv. Phys. X"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1126\/science.1133734","article-title":"Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells","volume":"314","author":"Bernevig","year":"2006","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1103\/PhysRevLett.42.1698","article-title":"Solitons in Polyacetylene","volume":"42","author":"Su","year":"1979","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","unstructured":"Peierls, R.E. (1955). Quantum Theory of Solids, Clarendon Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"205802","DOI":"10.1088\/0953-8984\/24\/20\/205802","article-title":"Nonlinear optical response in gapped graphene","volume":"24","author":"Jafari","year":"2012","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1103\/PhysRev.71.622","article-title":"The Band Theory of Graphite","volume":"71","author":"Wallace","year":"1947","journal-title":"Phys. Rev."},{"key":"ref_7","first-page":"205426-1-15","article-title":"Damping effects in doped graphene: The relaxation-time approximation","volume":"90","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"165111","DOI":"10.1103\/PhysRevB.94.165111","article-title":"Dirac cone tilt on interband optical background of type-I and type-II Weyl semimetals","volume":"94","author":"Carbote","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"153412","DOI":"10.1103\/PhysRevB.80.153412","article-title":"Merging of Dirac points in a two-dimensional crystal","volume":"80","author":"Montambaux","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"195412","DOI":"10.1103\/PhysRevB.100.195412","article-title":"Dynamical conductivity of the Fermi arc and the Volkov-Pankratov states on the surface of Weyl semimetals","volume":"100","author":"Mukherjee","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"176402","DOI":"10.1103\/PhysRevLett.124.176402","article-title":"Magneto-Optics of a Weyl Semimetal beyond the Conical Band Approximation: Case Study of TaP","volume":"124","author":"Polatkan","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"245121","DOI":"10.1103\/PhysRevB.89.245121","article-title":"Chiral anomaly and optical absorption in Weyl semimetals","volume":"89","author":"Ashby","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"305801","DOI":"10.1088\/0953-8984\/25\/30\/305801","article-title":"Strong light\u2013matter interaction in systems described by a modified Dirac equation","volume":"25","author":"Peres","year":"2013","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"476","DOI":"10.3390\/quantum4040034","article-title":"Topological Properties of the 2D 2-Band System with Generalized W-Shaped Band Inversion","volume":"4","author":"Rukelj","year":"2022","journal-title":"Quantum Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"155150","DOI":"10.1103\/PhysRevB.96.155150","article-title":"Optical conductivity of three and two dimensional topological nodal-line semimetals","volume":"96","author":"Barati","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"053024","DOI":"10.1088\/1367-2630\/ac696d","article-title":"DC and optical signatures of the reconstructed Fermi surface for electrons with parabolic band","volume":"24","author":"Rukelj","year":"2022","journal-title":"New J. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Dressel, M., and Gr\u00fcner, G. (2002). Electrodynamics of Solids: Optical Properties of Electrons in Matter, Cambridge University Press.","DOI":"10.1017\/CBO9780511606168"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"121113","DOI":"10.1103\/PhysRevB.93.121113","article-title":"Drumhead surface states and topological nodal-line fermions in TlTaSe2","volume":"93","author":"Bian","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jare.2019.12.001","article-title":"Novel topological nodal lines and exotic drum-head-like surface states in synthesized CsCl-type binary alloy TiOs","volume":"22","author":"Wang","year":"2020","journal-title":"J. Adv. Res."},{"key":"ref_20","unstructured":"Ashcroft, N.W., and Mermin, N. (1976). Solid State Physics, Saunders Collage."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"035441","DOI":"10.1103\/PhysRevB.100.035441","article-title":"Signatures of merging Dirac points in optics and transport","volume":"100","author":"Carbote","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"155151","DOI":"10.1103\/PhysRevB.108.155151","article-title":"Dynamical conductivity of a two-dimensional weakly doped Holstein system","volume":"108","author":"Rukelj","year":"2023","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"117106","DOI":"10.1088\/1674-1056\/25\/11\/117106","article-title":"Topological nodal line semimetals","volume":"25","author":"Fang","year":"2016","journal-title":"Chin. Phys. B"},{"key":"ref_24","first-page":"2065216","article-title":"Quantum transport in topological nodal-line semimetals","volume":"7","author":"Yang","year":"2022","journal-title":"Adv. Phys. X"},{"key":"ref_25","unstructured":"Kandel, S., Gumbs, G., and Berman, O.L. (2023). Advances in Nanosheets, IntechOpen."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:43:20Z","timestamp":1760132600000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,28]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010038"],"URL":"https:\/\/doi.org\/10.3390\/sym16010038","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,28]]}}}