{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:04:32Z","timestamp":1760231072773,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We studied the emergence of the quantum spin Hall (QSH) states for the pseudo-gap (PG) phase of Bi2212 bilayer system, assumed to be D-density wave (DDW) ordered, starting with a strong Rashba spin-orbit coupling (SOC) armed, and the time reversal symmetry (TRS) complaint Bloch Hamiltonian. The presence of strong SOC gives rise to non-trivial, spin-momentum locked spin texture tunable by electric field. The emergence of quantum anomalous Hall effect with TRS broken Chiral DDW Hamiltonian of Das Sarma et al. is found to be possible.<\/jats:p>","DOI":"10.3390\/sym14081746","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T23:49:56Z","timestamp":1661212196000},"page":"1746","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fledgling Quantum Spin Hall Effect in Pseudo Gap Phase of Bi2212"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1944-7526","authenticated-orcid":false,"given":"Udai Prakash","family":"Tyagi","sequence":"first","affiliation":[{"name":"Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kakoli","family":"Bera","sequence":"additional","affiliation":[{"name":"Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Partha","family":"Goswami","sequence":"additional","affiliation":[{"name":"Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"94503","DOI":"10.1103\/PhysRevB.63.094503","article-title":"Hidden order in the cuprates","volume":"63","author":"Chakravarty","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"22501","DOI":"10.1088\/0034-4885\/74\/2\/022501","article-title":"Quantum oscillations and key theoretical issues in high temperature superconductors from the perspective of density waves","volume":"74","author":"Chakravarty","year":"2011","journal-title":"Rep. Prog. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"017004","DOI":"10.1103\/PhysRevLett.112.017004","article-title":"Fermi-liquid computation of the phase diagram of high-Tc cuprate superconductors with an orbital antiferro-magnetic pseudogap","volume":"112","author":"Laughlin","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","first-page":"210384","article-title":"A theoretical approach to pseudogap and superconducting transitions in hole-doped cuprates","volume":"2013","author":"Goswami","year":"2013","journal-title":"Sch. Res. Not."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"174508","DOI":"10.1103\/PhysRevB.78.174508","article-title":"Anomalous Nernst effect from a chiral d-density-wave state in underdoped cuprate superconductors","volume":"78","author":"Zhang","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1126\/science.aao0980","article-title":"Revealing hidden spin-momentum locking in a high-temperature cuprate superconductor","volume":"362","author":"Gotlieb","year":"2018","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1038\/374434a0","article-title":"Importance of phase fluctuations in superconductors with small superfluid density","volume":"374","author":"Emery","year":"1995","journal-title":"Nature"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"137002","DOI":"10.1103\/PhysRevLett.105.137002","article-title":"Carrier-concentration dependence of the pseudo-gap ground state of superconducting Bi2Sr2\u2212xLaxCuO6+\u03b4 revealed by Cu-nuclear magnetic resonance in very high magnetic fields","volume":"105","author":"Kawasaki","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.physrep.2006.05.006","article-title":"Inhomogeneous superconductivity and the pseudo-gap state of novel superconductors","volume":"431","author":"Kresin","year":"2006","journal-title":"Phys. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"216401","DOI":"10.1103\/PhysRevLett.108.216401","article-title":"Strong coupling superconductivity, pseudo-gap, and Mott transition","volume":"108","author":"Sordi","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1103\/PhysRevLett.86.1070","article-title":"Renormalization of spectral line shape and dispersion below Tc in Bi2Sr2CaCu2O 8+\u03b4","volume":"86","author":"Kaminski","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"045104","DOI":"10.1103\/PhysRevB.82.045104","article-title":"Physics of the Pseudogap in 8-site Cluster Dynamical Mean Field Theory: Photoemission, Raman scattering, in-plane and c-axis conductivity","volume":"82","author":"Lin","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1146\/annurev-conmatphys-031113-133829","article-title":"Crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein Condensation and the Unitary Fermi Gas","volume":"5","author":"Randeria","year":"2014","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.aop.2017.10.001","article-title":"A Holographic Model for Pseudogap in BCS-BEC Crossover (I): Pairing Fluctuations, Double-Trace Deformation and Dynamics of Bulk Bosonic Fluid","volume":"387","author":"DeWolfe","year":"2017","journal-title":"Ann. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1038\/nature12165","article-title":"Bounding the pseudo- gap with a line of phase transitions in YBCO","volume":"498","author":"Shekhter","year":"2013","journal-title":"Nature"},{"key":"ref_16","first-page":"031017","article-title":"Amperean pairing and the pseudo-gap phase of cuprate superconductors","volume":"4","author":"Lee","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"064502","DOI":"10.1103\/PhysRevB.101.064502","article-title":"Modelling the pseudo-gap metallic state in cuprates: Quantum disordered pair density wave","volume":"101","author":"Dai","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1038\/nature17411","article-title":"Detection of Cooper pair density wave in Bi2Sr2CaCu2O8+\u03b4","volume":"532","author":"Hamidian","year":"2016","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1103\/PhysRevB.100.224511","article-title":"Fractionalized pair density wave in the pseudo-gap phase of cuprate superconductors","volume":"100","author":"Chakraborty","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1038\/nphys4205","article-title":"Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy","volume":"13","author":"Sato","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_21","unstructured":"Hsu, C. (2022, June 23). A Study of d-Density Wave States in Strongly Correlated Electron Systems, UCLA Electronic Theses and Dissertations, UCLA. 2014. Available online: https:\/\/escholarship.org\/uc\/item\/5vd202j4."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"180519","DOI":"10.1103\/PhysRevB.65.180519","article-title":"Effects of magnetic field on the d-density-wave order in the cuprates","volume":"65","author":"Nguyen","year":"2002","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1088\/0034-4885\/62\/1\/002","article-title":"The pseudogap in high-temperature superconductors: An experimental survey","volume":"62","author":"Timusk","year":"1999","journal-title":"Rep. Prog. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhao, A., Gu, Q., Haugan, T.J., Bullard, T.J., and Klemm, R.A. (2022). Quantum spin Hall effect in two-dimensional metals without spin-orbit coupling. arXiv.","DOI":"10.1088\/1361-648X\/ac9720"},{"key":"ref_25","first-page":"7327","article-title":"Spinorbit qubit in a semiconductor nanowire","volume":"468","author":"Frolov","year":"2010","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7420","DOI":"10.1038\/nature11559","article-title":"Circuit quantum electro-dynamics with a spin qubit","volume":"490","author":"Petersson","year":"2012","journal-title":"Nature"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev-conmatphys-033117-054144","article-title":"Topological materials: Quantum Anomalous Hall Systems","volume":"9","author":"He","year":"2018","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"054519","DOI":"10.1103\/PhysRevB.72.054519","article-title":"One-band tight-binding model parametrization of the high-Tc cuprates including the effect of kz dispersion","volume":"72","author":"Markiewicz","year":"2005","journal-title":"Phys. Rev. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1016\/0022-3697(95)00269-3","article-title":"LDA energy bands, low energy Hamiltonians, t\u2032, t\u2033,t\u2534(k) and J\u2534","volume":"56","author":"Andersen","year":"1995","journal-title":"Phys. Chem. Solids"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"087002","DOI":"10.1103\/PhysRevLett.102.087002","article-title":"Tuning the interlayer spacing of high Tc Bi based superconductors by intercalation: Measuring the penetration depth and two-dimensional superfluidity","volume":"102","author":"Baker","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1038\/nature04973","article-title":"Interplay of electron\u2013lattice interactions and superconductivity in Bi2Sr2CaCu2O8+\u03b4","volume":"442","author":"Lee","year":"2006","journal-title":"Nature"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1038\/nature07400","article-title":"Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+\u03b4","volume":"456","author":"Yang","year":"2008","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"247201","DOI":"10.1103\/PhysRevLett.116.247201","article-title":"Dzyaloshinskii-Moriya interaction as a consequence of a Doppler shift due to spin-orbit-induced intrinsic spin current","volume":"116","author":"Kikuchi","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"195312","DOI":"10.1103\/PhysRevB.74.195312","article-title":"Time reversal polarization and a Z2 adiabatic spin pump","volume":"74","author":"Fu","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/B978-0-444-63314-9.00001-9","article-title":"Chapter 1\u2014Topological Band Theory and the \u21242 Invariant","volume":"6","author":"Kane","year":"2013","journal-title":"Contemp. Concepts Condens. Matter Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"116401","DOI":"10.1103\/PhysRevLett.104.116401","article-title":"Collective Modes of a Helical Liquid","volume":"104","author":"Raghu","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"13485","DOI":"10.1038\/ncomms13485","article-title":"Spin injection and inverse Edelstein effect in the surface states of topological Kondo insulator SmB6","volume":"7","author":"Song","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"021903","DOI":"10.1063\/1.4942494","article-title":"The Z2 index of disordered topological insulators with time reversal symmetry","volume":"57","author":"Katsura","year":"2016","journal-title":"J. Math. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"031903","DOI":"10.1063\/1.5026964","article-title":"The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors","volume":"59","author":"Katsura","year":"2018","journal-title":"J. Math. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"205141","DOI":"10.1103\/PhysRevB.87.205141","article-title":"Criticality of metal-topological insulator transition driven by disorder","volume":"87","author":"Yamakage","year":"2013","journal-title":"Phys. Rev. B."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ziegler, K. (2019). Metal\u2013Insulator Transition in Three-Dimensional Semiconductors. Symmetry, 11.","DOI":"10.3390\/sym11111345"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Kim, D.J., Xia, J., and Fisk, Z. (2013). Topological surface state in the Kondo Insulator Samarium Hexaboride. arXiv.","DOI":"10.1038\/nmat3913"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"127002","DOI":"10.1103\/PhysRevLett.100.127002","article-title":"Polar Kerr-Effect Measurements of the High-Temperature YBa2Cu3O6+x Superconductor: Evidence for Broken Symmetry near the Pseudogap Temperature","volume":"100","author":"Xia","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"eaar1998","DOI":"10.1126\/sciadv.aar1998","article-title":"Dynamics of correlation-frozen antinodal quasiparticles in superconducting cuprates","volume":"4","author":"Cilento","year":"2018","journal-title":"Sci. Adv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/nnano.2014.16","article-title":"Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3","volume":"9","author":"Li","year":"2014","journal-title":"Nat. Nanotechnol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"196601","DOI":"10.1103\/PhysRevLett.113.196601","article-title":"Spin-Electricity Conversion Induced by Spin Injection into Topological Insulators","volume":"113","author":"Shiomi","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1038\/s41565-017-0014-x","article-title":"A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%","volume":"13","author":"Yoneda","year":"2018","journal-title":"Nat. Nanotechnol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"047202","DOI":"10.1103\/PhysRevLett.96.047202","article-title":"Coherent single electron spin control in a slanting Zeeman field","volume":"96","author":"Tokura","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"165319","DOI":"10.1103\/PhysRevB.74.165319","article-title":"Electric-dipole-induced spin resonance in quantum dots","volume":"74","author":"Golovach","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"195302","DOI":"10.1103\/PhysRevB.78.195302","article-title":"Theory of electron dipole spin resonance in quantum dots: Mean field theory with Gaussian fluctuations and beyond","volume":"78","author":"Rashba","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1143\/JPSJ.12.570","article-title":"Statistical-Mechanical Theory of Irreversible Processes. 1. General theory and simple applications in magnetic and conduction problems","volume":"12","author":"Kubo","year":"1957","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"114961","DOI":"10.1016\/j.physe.2021.114961","article-title":"Non-equilibrium spin polarization in magnetic two-dimensional electron gas with k-linear and k-cubed Dresselhaus spin-orbit coupling","volume":"135","author":"Krzyzewska","year":"2022","journal-title":"Physica E"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"146801","DOI":"10.1103\/PhysRevLett.90.146801","article-title":"Nonballistic Spin-Field-Effect Transistor","volume":"90","author":"Schliemann","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"160403","DOI":"10.1103\/PhysRevLett.105.160403","article-title":"Spin-orbit coupled spinor Bose-Einstein condensate","volume":"105","author":"Wang","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"53403","DOI":"10.1103\/PhysRevA.81.053403","article-title":"Generalized Rashba-Dresselhaus spin-orbit coupling for cold atoms","volume":"81","author":"Juzeliunas","year":"2010","journal-title":"Phys. Rev. A."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1103\/RevModPhys.83.1523","article-title":"Colloquium: Artificial gauge potentials for neutral atoms","volume":"83","author":"Dalibard","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1038\/nphys2933","article-title":"Hidden spin-polarization in inversion-symmetric bulk crystal","volume":"10","author":"Zhang","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"155405","DOI":"10.1103\/PhysRevB.94.155405","article-title":"High-temperature large-gap quantum anomalous Hall insulating state in ultrathin double perovskite films","volume":"94","author":"Baidya","year":"2016","journal-title":"Phys. Rev. B."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"5944","DOI":"10.1021\/acsnano.0c10435","article-title":"Moire pattern in 2D materials: A review","volume":"15","author":"He","year":"2021","journal-title":"ACS Nano"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"26084","DOI":"10.1038\/srep26084","article-title":"Evolution of Moir\u00e9 Profiles from van der Waals Superstructures of Boron Nitride Nanosheets","volume":"6","author":"Liao","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"157401","DOI":"10.1103\/PhysRevLett.125.157401","article-title":"Designing all-electric subwavelength meta-sources for Near-field photonic routings","volume":"125","author":"Long","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"3226","DOI":"10.1038\/ncomms4226","article-title":"Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes","volume":"5","author":"Kapitanova","year":"2014","journal-title":"Nat. Commun."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1746\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:13:37Z","timestamp":1760141617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1746"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,22]]},"references-count":62,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081746"],"URL":"https:\/\/doi.org\/10.3390\/sym14081746","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,8,22]]}}}