Recent Work

IN THE QUANTUM MATERIALS AREAS^†:

1. Cuprate high temperature superconductors
2. Iron-pnictide high temperature superconductors
3. Low dimensional quantum magnets
4. Topological insulators
5. Heavy fermions and heavy fermion superconductors
6. Dilute magnetic semiconductors and other materials
7. Instruments and Methods

1. Cuprate high temperature superconductors

[71] K.-J. Xu, J. He, S.-D. Chen, Y. He, S. N. Abadi, C. R. Rotundu, Y. S. Lee, D.-H. Lu, Q. Guo, O. Tjernberg, T.P. Devereaux, D.-H. Lee, M. Hashimoto, and Z.-X. Shen, Anomalous normal state gap in an electron-doped cuprate, arXiv:2309.10208, Science, (2024), accepted.

[70] J.-Y. Shan, M. Guo, J. B. Curtis, C. J. Roh, C. R. Rotundu, Y. S. Lee, P. Narang, T. W. Noh, E. Demler, and D. Hsieh, A dynamical magnetic phase transition induced by parametric magnon pumping, Physical Review B 19, 054302 (2024).

[69] K.-J. Xu, Q. Guo, M. Hashimoto, Z.-X. Li, S.-D. Chen, J. He, Y. He, C. Li, M. H. Berntsen, C. R. Rotundu, Y. S. Lee, T. P. Devereaux, A. Rydh, D.-H. Lu, D.-H. Lee, O. Tjernberg, and Z.-X. Shen, Bogoliubov Quasiparticle on the Gossamer Fermi Surface in Electron-Doped Cuprates, Nature Physics 19, 1834 (2023).

[68] J.-J. Wen, W. He, H. Jang, H. Nojiri, S. Matsuzawa, S. Song, M. Chollet, D. Zhu, Y.-J. Liu, M. Fujita, J. M. Jiang, C. R. Rotundu, C.-C. Kao, H.-C. Jiang, J.-S. Lee, and Y. S. Lee, Enhanced charge density wave with mobile superconducting vortices in La_1.885Sr_0.115CuO₄, Nature Communications 14, 733 (2023).

[67] K. L. Seyler, D. Van Beveren, A. Ron, C. R. Rotundu, Y. S. Lee, and D. Hsieh, Thermally controlled antiferromagnetic domain switching in a cuprate Mott insulator, Physical Review B 106, L140403 (2023), Editor's suggestion.

[66] J.-F. He, C. R. Rotundu, M. S. Scheurer, Y. He, M. Hashimoto, K. Xu, Y. Wang, E. W. Huang, T. Jia, S.-D. Chen, B. Moritz, D.-H. Lu, Y. S. Lee, T. P. Devereaux and Z.-X. Shen, “Antiferromagnetic” band folding and Fermi surface reconstruction in optimal-doped and overdoped Nd_2-xCe_xCuO₄ without long-range order, Proceedings of the National Academy of Sciences PNAS 116, 3449 (2019).

[65] M. Hepting, L. Chaix, E. W. Huang, R. Fumagalli, Y. Y. Peng, B. Moritz, K. Kummer, N. B. Brookes, W. C. Lee, M. Hashimoto, T. Sarkar, J. F. He, C. R. Rotundu, Y. S. Lee, R. L. Greene, L. Braicovich, G. Ghiringhelli, Z. X. Shen, T. P. Devereaux, and W. S. Lee, Three-dimensional collective charge excitations in electron-doped cuprate superconductors, Nature 563, 374 (2018).

[64] C. R. Rotundu, V. V. Struzhkin, M. S. Somayazulu, S. Sinogeikin, R. J. Hemley, R. L. Greene, High-pressure effects on single crystals electron-doped Pr_2-xCe_xCuO₄, Physical Review B 87, 024506 (2013).

2. Iron-pnictide high temperature superconductors

[63] H. Pfau, S. D. Chen, M. Hashimoto, N. Gauthier, C. R. Rotundu, J. C. Palmstrom, I. R. Fisher, S.-K. Mo, Z.-X. Shen, and D. Lu, Anisotropic quasiparticle coherence in nematic BaFe₂As₂ studied with strain-dependent ARPES, Physical Review B, 103, 165136 (2021).

[62] H. Pfau, H. Soifer, J. A. Sobota, A. Gauthier, C. R. Rotundu, J. C. Palmstrom, I. R. Fisher, H. Lin, G.-Y. Chen, H.-H. Wen, Z.-X. Shen, and P. S. Kirchmann, Low work function in the 122-family of iron-based superconductors, Physical Review Materials, 4, 034801 (2020).

[61] H. Pfau, S. Chen, M. Yi, M. Hashimoto, C. R. Rotundu, J. C. Palmstrom, T. Chen, P.-C. Dai, J. Straquadine, A. Hristov, R. J. Birgeneau, I. R. Fisher, D. Lu, and Z.-X. Shen, Momentum dependence of the nematic order parameter in iron-based superconductors, Physical Review Letters 123, 066402 (2019).

[60] H. Pfau, C. R. Rotundu, J. Palmstrom, M. Hashimoto, D. Lu, A.F. Kemper, I. R. Fisher, and Z.-X. Shen, Detailed band structure of twinned and detwinned BaFe₂As₂ studied with angle-resolved photoemission spectroscopy, Physical Review B 99, 035118 (2019), Editor's suggestion.

[59] C. R. Rotundu, T. R. Forrest, N. E. Phillips, and R. J. Birgeneau, Method for Accurate Determination of the Electron Contribution: Specific Heat of Ba_0.59K_0.41Fe₂As₂, Chapter in book “High T_c superconductors and related transition metal oxides”, Dedicated to Prof. K. Alex Müller on the Occasion of his 90^th Birthday, Editors Annette Bussmann-Holder, Hugo Keller, Antonio Bianconi, Springer Series in Materials Science Volume 255, pages 277-297 (2017).

[58] T. R. Forrest, P. N. Valdivia, C. R. Rotundu, E. Bourret-Courchesne, and R. J. Birgeneau, The effects of post-growth annealing on the structural and magnetic properties of BaFe₂As₂, Journal of Physics: Condensed Matter 28, 115702 (2016).

[57] C. R. Rotundu, Comment on “Retention of the tetragonal to orthorhombic structural transition in F-substituted SmFeAsO: a new phase diagram for SmFeAs(O_1-xF_x)”, Physical Review Letters 110, 209701 (2013).

[56] J. Zhao, C. R. Rotundu, K. Marty, M. Matsuda, Y. Zhao, C. Setty, E. Bourret-Courchesne, J. Hu, D.-H. Lee, and R. J. Birgeneau, Effect of electron correlations on the spin excitations in isovalently doped iron based superconductor Ba(Fe_1-xRu_x)₂As₂, Physical Review Letters 110, 147003 (2013).

[55] D. M. Pajerowski, C. R. Rotundu, J. W. Lynn, R. J. Birgeneau, Measurement of Ba(Fe_1-xCo_x)₂As₂ critical-magnetic exponents for x = 0.039, 0.022, and 0.021, Physical Review B 87, 134507 (2013).

[54] C. R. Rotundu, W. Tian, K. C. Rule, T. R. Forrest, J. Zhao, J. L. Zarestky, and R. J. Birgeneau, A neutron scattering study of the under-doped Ba_1-xK_xFe₂As₂, x=0.09 and 0.17 self-flux grown single crystals and the universality of the tricritical point, Physical Review B 85, 144506 (2012).

[53] C. R. Rotundu and R. J. Birgeneau, First and second order magnetic and structural phase transitions in BaFe_2(1-x)Co_2xAs₂, Physical Review B 84, 092501 (2011).

[52] C. R. Rotundu, B. Freelon, S. D. Wilson, G. Pinuellas, A. Kim, E. Bourret-Courchesne, N. E. Phillips, and R. J. Birgeneau, Heat capacity of Ba_1-xK_xFe₂As₂, x=0 and 0.41, Journal of Physics: Conference Series 273, 012103 (2011).

[51] B. Freelon, Y. S. Liu, Y. Liu, C. R. Rotundu, S. D. Wilson, J. H. Guo, J. Chen, W. Yang, C. L. Chang, P. A. Glans, P. M. Shirage, A. Iyo, and R. J. Birgeneau, Electronic structure of PrFeAsO_1-δ: An investigation using X-ray absorption and emission spectroscopy, Journal of Physics: Conference Series 273, 012092 (2011).

[50] C. R. Rotundu, B. Freelon, T. R. Forrest, S. D. Wilson, P. N. Valdivia, G. Pinuellas, A. Kim, Z. Islam, J.-W. Kim, E. Bourret-Courchesne, N. E. Phillips, and R. J. Birgeneau, Heat capacity study of BaFe₂As₂: effects of annealing, Physical Review B 82, 144525 (2010).

[49] S. D. Wilson, C. R. Rotundu, Z. Yamani, P. N. Valdivia, B. Freelon, E. Bourret-Courchesne and R. J. Birgeneau, Universal magnetic and structural behaviors in the iron pnictides, Physical Review B 81, 014501 (2010), Editors' Suggestion, Featured by the Virtual Journal of Applications of Superconductivity volume 18, issue 2.

[48] S. D. Wilson, Z. Yamani, C. R. Rotundu, B. Freelon, P. N. Valdivia, E. Bourret-Courchesne, J. W. Lynn, S. Chi, J. Fernandez-Baca, T. Hong, and R. J. Birgeneau, Antiferromagnetic critical fluctuations in BaFe₂As₂, Physical Review B 82, 144502 (2010).

[47] B. Freelon, Y. Liu, C. R. Rotundu, S. D. Wilson, J. Guo, J.-L. Chen, W. Yang, C. Chang, P. A. Glans, P. Shirage, A. Iyo, and R. J. Birgeneau, X-ray absorption and emission spectroscopy study of the effect of doping on the low energy electronic structure of PrFeAsO_1-δ, Journal of the Physical Society of Japan 79, 074716 (2010).

[46] C. R. Rotundu, D. T. Keane, B. Freelon, S. D. Wilson, A. Kim, P. N. Valdivia, E. Bourret-Courchesne and R. J. Birgeneau, Phase diagram of PrFeAsO_1-xF_x superconductor, Physical Review B 80, 144517 (2009), Featured by the Virtual Journal of Applications of Superconductivity volume 17, issue 8.

[45] S. D. Wilson, Z. Yamani, C. R. Rotundu, B. K. Freelon, E. Bourret-Courchesne, and R. J. Birgeneau, Neutron diffraction study of the magnetic and structural phase transitions in BaFe₂As₂, Physical Review B 79, 184519 (2009), Featured by the Virtual Journal of Applications of Superconductivity volume 16, issue 11.

[44] D. R. Garcia, C. Jozwiack, C. G. Hwang, A. Fedorov, S. M. Hanrahan, S. D. Wilson, C. R. Rotundu, B. K. Freelon, R. J. Birgeneau, E. Bourret-Courchesne and A. Lanzara, Core-level and valence band study using angle-integrated photoemission on LaO_0.9F_0.1FeAs, Physical Review B 78, 245119 (2008), Featured by the Virtual Journal of Applications of Superconductivity volume 16, issue 1.

3. Low dimensional quantum magnets

[43] C. R. Rotundu, J. Wen, W. He, Y. Choi, D. Haskel, and Y. S. Lee, Enhancement and destruction of spin-Peierls physics in a one-dimensional quantum magnet under pressure, Physical Review B 97, 054415 (2018).

[42] H. Tsujii, C. R. Rotundu, B. Andraka, Y. Takano, H. Kageyama, and Y. Ueda, Specific heat of the S=1/2 two-dimensional Shastry-Sutherland antiferromagnet SrCu₂(BO₃)₂ in high magnetic fields, Journal of the Physical Society of Japan 80, 043707 (2011).

[41] M. Hagiwara, H. Tsujii, C. R. Rotundu, B. Andraka, Y. Takano, T. Suzuki, and S. Suga, Field Induced Tomonaga-Luttinger liquid of a quasi-one-dimensional S=1 antiferromagnet, Modern Physics Letters B 21, No 16, 965 (2007), Brief invited review paper.

[40] H. Tsujii, C. R. Rotundu, T. Ono, H. Tanaka, B. Andraka, K. Ingersent, and Y. Takano, Thermodynamics of the up-up-down phase of the S=1/2 triangular-lattice antiferromagnet Cs₂CuBr₄, Physical Review B 76, 060406(R) (2007).

[39] M. Hagiwara, H. Tsujii, C. R. Rotundu, B. Andraka, Y. Takano, N. Tateiwa, T. C. Kobayashi, T. Suzuki, and S. Suga, Tomonaga-Luttinger liquid in a quasi-one-dimensional S=1 antiferromagnet observed by specific heat measurements, Physical Review Letters 96, 147203 (2006).

[38] H. Tsujii, C. R. Rotundu, T. Ono, B. Andraka, H. Tanaka, and Y. Takano, Magnetic phase diagram of the quasi-two-dimensional S=1/2 antiferromagnet Cs₂CuBr₄, AIP Conference Proceedings, Volume 850 (LT24), 1093 (2006).

[37] M. Hagiwara, H. Tsujii, C. R. Rotundu, B. Andraka, and Y. Takano, Evidence for a Tomonaga-Luttinger phase in a S=1 bond-alternating antiferromagnetic chain, AIP Conference Proceedings, Volume 850 (LT24), 1043 (2006).

4. Topological insulators

[36] Y. Huang J. D. Querales-Flores, S. W. Teitelbaum, J. Cao, T. Henighan, H. Liu, M. Jiang, G. De la Peña, V. Krapivin, J. Haber, T. Sato, M. Chollet, D. Zhu, T. Katayama, R. Power, M. Allen, C. R. Rotundu, T. P. Bailey, C. Uher, M. Trigo, P. S. Kirchmann, É. D. Murray, Z.-X. Shen, I. Savić, S. Fahy, J. A. Sobota, and D. A. Reis, Ultrafast measurements of mode-specific deformation potentials of Bi₂Te₃ and Bi₂Se₃, Physical Review X 13, 041050 (2023).

[35] J. A. Sobota, S. W. Teitelbaum, Y. Huang, J. D. Querales-Flores, R. Power, M. Allen, C. R. Rotundu, T. P. Bailey, C. Uher, T. Henighan, M. Jiang, D. Zhu, M. Chollet, T. Sato, M. Trigo, É. D. Murray, I. Savić, S. Fahy, P. S. Kirchmann, S. Fahy, D. A. Reis, and Z.-X. Shen, Influence of local symmetry on lattice dynamics coupled to topological surface states, Physical Review B 107, 014305 (2023), Editor's suggestion.

[34] D. Baykusheva, A. Chacón, J. Lu, T. P. Bailey, J. A. Sobota, H. Soifer, P. S. Kirchmann, C. R. Rotundu, C. Uher, T. F. Heinz, D. A. Reis, and S. Ghimire, All-optical probe of three-dimensional topological insulators based on high-harmonic generation by circularly-polarized laser fields, Nano Letters 21, 8970 (2021).

[33] A. Gauthier, J. A. Sobota, N. Gauthier, K.-J. Xu, Heike Pfau, C. R. Rotundu, Z.-X. Shen, and P. S. Kirchmann, Tuning time and energy resolution in time-resolved photoemission spectroscopy, Journal of Applied Physics 128, 093101 (2020).

[32] H. Soifer, A. Gauthier, A. F. Kemper, C. R. Rotundu, S. Yang, H. Xiong, D. Lu, M. Hashimoto, P. S. Kirchmann, J. A. Sobota, Z.-X. Shen, Band resolved imaging of photocurrent in a topological insulator, Physical Review Letters 122, 167401 (2019).

[31] C. Jozwiak, J. A. Sobota, K. Gotlieb, A. F. Kemper, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, D.-H. Lee, Z.-X. Shen, A. Lanzara, Spin-polarized surface resonances accompanying topological surface state formation, Nature Communications 7, 13143 (2016).

[30] C. Jozwiak, C.-H. Park, K. Gotlieb, D.-H. Lee, S. G. Louie, J. D. Denlinger, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, and A. Lanzara, Photoelectron spin-flipping and texture manipulation realized in a topological insulator, Nature Physics 9, 293 (2013), Featured in the News & Views and in the Science Daily.

[29] C. Jozwiak, Y. L. Chen, A. V. Fedorov, J. G. Analytis, C. R. Rotundu, A. K. Schmid, J. D. Denlinger, Y.-D. Chuang, D.-H. Lee, I. R. Fisher, R. J. Birgeneau, Z.-X. Shen, Z. Hussain, and A. Lanzara, Widespread spin polarization effects in photoemission from topological insulators, Physical Review B 84, 165113 (2011).

5. Heavy fermions and heavy fermion superconductors

[28] B. Andraka, A. Ross, and C. R. Rotundu, Signatures of a hybridization gap in magnetic susceptibility of Ce_1-xLa_xOs₄Sb₁₂, Journal of Physics: Condensed Matter 23, 405601 (2011).

[27] B. Andraka, C. R. Rotundu, P. Kumar, and H. Tsujii, Investigation of heavy fermion state and superconductivity in Pr_1-xLa_xOs₄Sb₄ by the upper critical field slope at T_c, Journal of Physics: Condensed Matter 22, 345701 (2010).

[26] B. Andraka, C. R. Rotundu, and K. Ingersent, Search for heavy quasiparticles in the resistivity of PrOs₄Sb₁₂ in magnetic fields: Comparison with Pr_0.7La_0.3Os₄Sb₁₂, Physical Review B 81, 054509 (2010).

[25] B. Andraka, M. E. McBriarty, C. R. Rotundu, Low-temperature anomalies in the specific heat of PrOs₄Sb₁₂, Physical Review B 81, 024517 (2010).

[24] B. Andraka, C. R. Rotundu, Y. Takano and H. Tsujii, Dilute limit of heavy fermions: evidence for coherent nature of CeAl₃, Journal of Physics: Condensed Matter 21, 495601 (2009).

[23] B. Andraka, C. R. Rotundu, K Ingersent, and P Schlottmann, Resistivity and magnetoresistance of La-doped CeOs₄Sb₁₂ and PrOs₄Sb₁₂, Journal of the Physics Society of Japan 77, Sup. A, 148 (2008), Invited paper.

[22] C. R. Rotundu, B. Andraka, and P. Schlottmann, Exotic Kondo-hole Ce_1-xLa_xOs₄Sb₁₂ band resistivity and magnetoresistance, Physical Review B 76, 054416 (2007).

[21] C. R. Rotundu, K. Ingersent, and B. Andraka, Cristalline electric field contribution to the magnetoresistance of Pr_1-xLa_xOs₄Sb₁₂, Physical Review B 75, 104504 (2007).

[20] C. R. Rotundu, and B. Andraka, La-alloying study of CeCoGe₂: magnetic susceptibility and specific-heat measurements, Physical Review B 74, 224423 (2006).

[19] C. R. Rotundu, and B. Andraka, Anomalous low temperature state of CeOs₄Sb₁₂: magnetic field and La-impurity study, Physical Review B 73, 144429 (2006).

[18] C. R. Rotundu, P. Kumar, and B. Andraka, Collective heavy fermion state and superconductivity in Pr_1-xLa_xOs₄Sb₁₂: a specific heat study, Physical Review B 73, 014515 (2006).

[17] C. R. Rotundu, and B. Andraka, Crystalline electric field effects in Pr_1-xLa_xOs₄Sb₁₂, AIP Conference Proceedings, Volume 850 (LT24), 653 (2006).

[16] C. R. Rotundu, and B. Andraka, Magnetoresistance of PrOs₄Sb₁₂: search for the evidence for heavy fermion behavior, Journal of Applied Physics 97, 10A927 (2005).

[15] C. R. Rotundu, B. Andraka, Z. Fisk, G. R. Stewart, and Y. Takano, Magnetic field study of the "hidden order" in UCd₁₁, Journal of Applied Physics 97, 10A912 (2005).

[14] R. Pietri, C. R. Rotundu, B. Andraka, B. Daniels, and K. Ingersent, Absence of Kondo lattice coherence effects in Ce_0.6La_0.4Pb₃: magnetic field study, Journal of Applied Physics 97, 10A510 (2005).

[13] C. R. Rotundu, H. Tsujii, Y. Takano, B. Andraka, H. Sugawara, Y. Aoki, and H. Sato, High magnetic field phase diagram of PrOs₄Sb₁₂ Physical Review Letters 92, 037203 (2004).

[12] C. R. Rotundu, D. Mixson, G. R. Stewart, and B. Andraka, Specific heat of U_1-xY_xRu₂Si₂; 0≤x≤0.5: search for a hidden order, Journal of Magnetism and Magnetic Materials 272-276, e123 (2004).

[11] H. Tsujii, C. R. Rotundu, Y. Takano, B. Andraka, Y. Aoki, H. Sugawara, and H. Sato, High field phase diagram of PrOs₄Sb₁₂, Journal of Magnetism and Magnetic Materials 272-276, 173 (2004).

6. Dilute magnetic semiconductors and other materials

[10] C. R. Rotundu, S. Jiang, X. Deng, Y. Qian, S. Khan, D. G. Hawthorn, G. Kotliar, N. Ni, Physical properties and electronic structure of a new barium titanate suboxide Ba_1+δTi_13-δO₁₂ (δ=0.11), APL Materials 3, 041517 (2015), invited paper.

[9] Q. S. Zeng, C. R. Rotundu, W. L. Mao, Y. M. Xiao, P. Chow, H.-K. Mao, X. J. Chen, J. H. Dai, C. L. Qin, and J. Z. Jiang, Low temperature transport properties of Ce-Al metallic glasses, Journal of Applied Physics 109, 113716 (2011).

[8] L. Kilanski, I. V. Fedorchenko, M. Górska, E Dynovska, M Wójcik, B J Kowalski, W Dobrowolski, J R Anderson, C. R. Rotundu, S A Varnavskiy, W Dobrowolski, and S F Marenkin, Paramagnetic regime in Zn_1-xMn_xGeAs₂ diluted magnetic semiconductor, Phys. Status Solidi B 248, 1601 (2011).

[7] L. Kilanski, M. Górska, W. Dobrowolski, E. Dynowska, M. Wójcik, B. J. Kowalski, J. R. Anderson, C. R. Rotundu, D. K. Maude, S. A. Varnavskiy, I. V. Fedorchenko, and S. F. Marenkin, Magnetism and magnetotransport of strongly disordered Zn_1-xMn_xGeAs₂ semiconductor: The role of nanoscale magnetic clusters, Journal of Applied Physics 108, 073925 (2010).

[6] W. Knoff, V. Domukhovski, K. Dybko, P. Dziawa, M. Górska, R. Jakieła, E. Łusakowska, B. Taliashvili, T. Story, A. Reszka, J. R. Anderson and C. R. Rotundu, Magnetic Properties of Epitaxial (Ge,Mn)Te Thin Films with Varying Crystal Stoichiometry, Acta Physica Polonica 114, No 5 , 1159 (2008).

[5] L. Kilanski, M. Górska, V. Domukhovski, W. Dobrowolski, J. R. Anderson, C. R. Rotundu, S. A. Varniavskii, and S. F. Marenkin, Zn_1-x(Mn,Co)_xGeAs₂ Ferromagnetic semiconductor: magnetic and transport properties, Acta Physica Polonica A 114, No 5, 1151 (2008).

7. Instruments and Methods

[4] X. Han, J. Qu, S. Sakamoto, D. Liu, D. Guan, J. Liu, H. Li, C. R. Rotundu, C. Jozwiak, Z. Hussain, Z.-X. Shen, and J. A. Sobota, Development of deflector mode for spin-resolved time-of-flight photoemission spectroscopy, Review of Scientific Instruments 94, 103906 (2023)

[3] C. R. Rotundu, T. R. Forrest, N. E. Phillips, and R. J. Birgeneau, Specific heat of Ba_0.59K_0.41Fe₂As₂, and a new method for identifying the electron contribution: two electron bands with different energy gaps in the superconducting state, Journal of the Physical Society of Japan 84, 114701 (2015).

[2] C. R. Rotundu, T. Ćuk, R. L. Greene, Z.-X. Shen, R. J. Hemley, and V. V. Struzhkin, High pressure diamond anvil cell resistivity apparatus for quasi-hydrostatic compression experiments, Review of Scientific Instruments 84, 063903 (2013).

[1] B. Freelon, Y. H. Liu, J. Chen, C. R. Rotundu, P. Valdivia, S. D. Wilson, G. Sui, E. Bourret-Courchesne, W. Yang, J. H. Guo, and R. J. Birgeneau, Soft X-ray absorption spectroscopy investigations of 1111 and 122 iron pnictides, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment A 649, 197 (2011).

^{†. From all the in preparation papers only the ones in a form close to submission are listed here.↩}