Higher-order topological semimetal induced by altermagnet

doi:10.1088/1674-1056/ae6b35

Abstract Altermagnetism, characterized by momentum-dependent spin splitting in the absence of net magnetization, provides a fertile ground for realizing topological states. Here, we show that coupling a first-order topological insulator to a $d$-wave altermagnet leads to a higher-order topological semimetal phase. This phase simultaneously hosts gap-closing points, robust zero-energy edge states, and corner states. The altermagnetic order parameter governs the motion of the gap-closing points within the Brillouin zone, while the Néel vector determines the spatial localization of the corner states. By mapping out the phase diagram, we identify topological transitions between trivial, higher-order insulating, and higher-order topological semimetal phases. Our findings establish altermagnetic heterostructures as a tunable platform for engineering higher-order topological phases in two dimensions.

Keywords: altermagnet topological semimetal high-order topological phase

Received: 11 March 2026
Revised: 07 May 2026
Accepted manuscript online: 11 May 2026

PACS:	75.10.-b	(General theory and models of magnetic ordering)
	73.20.-r	(Electron states at surfaces and interfaces)
	03.65.Vf	(Phases: geometric; dynamic or topological)

Corresponding Authors: Sen Cui
E-mail: scui@ujs.edu.cn

Cite this article:

Dengfeng Wang(王登风), Xiang Ji(吉祥), and Sen Cui(崔森) Higher-order topological semimetal induced by altermagnet 2026 Chin. Phys. B 35 077510

[1] Šmejkal L, Sinova J and Jungwirth T 2022 Phys. Rev. X 12 040501
[2] Šmejkal L, Sinova J and Jungwirth T 2022 Phys. Rev. X 12 031042
[3] Bai L, Feng W, Liu S, Šmejkal L, Mokrousov Y and Yao Y 2024 Adv. Funct. Mater. 34 2409327
[4] Jiang Y, Song Z, Zhu T, Fang Z, Weng H, Liu Z X, Yang J and Fang C 2024 Phys. Rev. X 14 031039
[5] McClarty P A and Rau J G 2024 Phys. Rev. Lett. 132 176702
[6] Rimmler B H, Pal B and Parkin S S P 2024 Nat. Rev. Mater. 10 109
[7] Song C, Bai H, Zhou Z, Han L, Reichlova H, Dil J H, Liu J, Chen X and Pan F 2025 Nat. Rev. Mater. 10 473
[8] Zhang F, Cheng X, Yin Z, Liu C, Deng L, Qiao Y, Shi Z, Zhang S, Lin J, Liu Z, Ye M, Huang Y, Meng X, Zhang C, Okuda T, Shimada K, Cui S, Zhao Y, Cao G H, Qiao S, Liu J and Chen C 2025 Nat. Phys. 21 760
[9] Zhu Z H, Strempfer J, Rao R R, Occhialini C A, Pelliciari J, Choi Y, Kawaguchi T, You H, Mitchell J F, Shao-Horn Y and Comin R 2019 Phys. Rev. Lett. 122 017202
[10] Šmejkal L, González-Hernández R, Jungwirth T and Sinova J 2020 Sci. Adv. 6 eaaz8809
[11] Bai H, Han L, Feng X Y, Zhou Y J, Su R X, Wang Q, Liao L Y, Zhu W X, Chen X Z, Pan F, Fan X L and Song C 2022 Phys. Rev. Lett. 128 197202
[12] Fedchenko O, Minár J, Akashdeep A, D’Souza SW, Vasilyev D, Tkach O, Odenbreit L, Nguyen Q, Kutnyakhov D, Wind N, Wenthaus L, Scholz M, Rossnagel K, Hoesch M, Aeschlimann M, Stadtmüller B, Kläui M, Schönhense G, Jungwirth T, Hellenes A B, Jakob G, Šmejkal L, Sinova J and Elmers H J 2024 Sci. Adv. 10 eadj4883
[13] Amin O J, Dal Din A, Golias E, Niu Y, Zakharov A, Fromage S C, Fields C J B, Heywood S L, Cousins R B, Maccherozzi F, Krempaský J, Dil J H, Kriegner D, Kiraly B, Campion R P, Rushforth A W, Edmonds K W, Dhesi S S, Šmejkal L, Jungwirth T and Wadley P 2024 Nature 636 348
[14] Gonzalez Betancourt R D, Zubáč J, Geishendorf K, Ritzinger P, R°užičková B, Kotte T, Zelezný J, Olejník K, Springholz G, Büchner B, Thomas A, Výborný K, Jungwirth T, Reichlová H and Kriegner D 2024 npj Spintronics 2 45
[15] Lee S, Lee S, Jung S, Jung J, Kim D, Lee Y, Seok B, Kim J, Park B G, Šmejkal L, Kang C J and Kim C 2024 Phys. Rev. Lett. 132 036702
[16] Reimers S, Odenbreit L, Šmejkal L, Strocov V N, Constantinou P, Hellenes A B, Jaeschke Ubiergo R, Campos W H, Bharadwaj V K, Chakraborty A, Denneulin T, Shi W, Dunin-Borkowski R E, Das S, Kläui M, Sinova J and Jourdan M 2024 Nat. Commun. 15 2116
[17] Zhou Z, Cheng X, Hu M, Chu R, Bai H, Han L, Liu J, Pan F and Song C 2025 Nature 638 645
[18] Yang G, Li Z, Yang S, Li J, Zheng H, ZhuW, Pan Z, Xu Y, Cao S, Zhao W, Jana A, Zhang J, Ye M, Song Y, Hu L H, Yang L, Fujii J, Vobornik I, Shi M, Yuan H, Zhang Y, Xu Y and Liu Y 2025 Nat. Commun. 16 1442
[19] Reichlova H, Lopes Seeger R, González-Hernández R, Kounta I, Schlitz R, Kriegner D, Ritzinger P, Lammel M, Leiviskä M, Birk Hellenes A, Olejník K, Petriček V, Doležal P, Horak L, Schmoranzerova E, Badura A, Bertaina S, Thomas A, Baltz V, Michez L, Sinova J, Goennenwein S T B, Jungwirth T and Šmejkal L 2024 Nat. Commun. 15 4961
[20] Leiviskä M, Rial J, Bad’ura A, Seeger R L, Kounta I, Beckert S, Kriegner D, Joumard I, Schmoranzerová E, Sinova J, Gomonay O, Thomas A, Goennenwein S T B, Reichlová H, Šmejkal L, Michez L, Jungwirth T and Baltz V 2024 Phys. Rev. B 109 224430
[21] Badura A, CamposWH, Bharadwaj V K, Kounta I, Michez L, Petit M, Rial J, Leiviskä M, Baltz V, Krizek F, Kriegner D, Zelezný J, Zemen J, Telkamp S, Sailler S, Lammel M, Jaeschke-Ubiergo R, Hellenes A B, González-Hernández R, Sinova J, Jungwirth T, Goennenwein S T B, Šmejkal L and Reichlova H 2025 Nat. Commun. 16 7111
[22] Jiang B, Hu M, Bai J, Song Z, Mu C, Qu G, LiW, ZhuW, Pi H,Wei Z, Sun Y J, Huang Y, Zheng X, Peng Y, He L, Li S, Luo J, Li Z, Chen G, Li H, Weng H and Qian T 2025 Nat. Phys. 21 754
[23] Ouassou J A, Brataas A and Linder J 2023 Phys. Rev. Lett. 131 076003
[24] Zhu D, Zhuang Z Y, Wu Z and Yan Z 2023 Phys. Rev. B 108 184505
[25] Sun C, Brataas A and Linder J 2023 Phys. Rev. B 108 054511
[26] Brekke B, Sukhachov P, Giil H G, Brataas A and Linder J 2024 Phys. Rev. Lett. 133 236703
[27] Wang Q, Wu D W, Guo G H, Long M Q and Wang Y P 2024 Chin. Phys. B 33 097507
[28] Antonenko D S, Fernandes R M and Venderbos J W F 2025 Phys. Rev. Lett. 134 096703
[29] Lin H J, Zhang S B, Lu H Z and Xie X C 2025 Phys. Rev. Lett. 134 136301
[30] Zhu Y, Liu S, Cui Q, Jiang J, Yang H, Zhou T and Liu B 2025 Appl. Phys. Lett. 127 082401
[31] Li J, Li W, Hu Y, Guo X, Chen M, Li S, Chen X and Wu S 2025 Appl. Phys. Lett. 127 132401
[32] González J W, Gallardo R A, Vidal-Silva N and León A M 2026 Chin. Phys. Lett. 43 020705
[33] Feng Z, Zhou X, Šmejkal L,Wu L, Zhu Z, Guo H, González-Hernández R, Wang X, Yan H, Qin P, Zhang X, Wu H, Chen H, Meng Z, Liu L, Xia Z, Sinova J, Jungwirth T and Liu Z 2022 Nat. Electron. 5 735
[34] Sato T, Haddad S, Fulga I C, Assaad F F and Van Den Brink J 2024 Phys. Rev. Lett. 133 086503
[35] Chen R,Wang Z M,Wu K, Sun H P, Zhou B,Wang R and Xu D H 2025 Phys. Rev. Lett. 135 096602
[36] Zhang S B, Hu L H and Neupert T 2024 Nat. Commun. 15 1801
[37] Chakraborty D and Black-Schaffer A M 2024 Phys. Rev. B 110 L060508
[38] Chakraborty D and Black-Schaffer A M 2025 Phys. Rev. B 112 014516
[39] Li Y X and Liu C C 2023 Phys. Rev. B 108 205410
[40] Ghorashi S A A, Hughes T L and Cano J 2024 Phys. Rev. Lett. 133 106601
[41] Li Y X, Liu Y and Liu C C 2024 Phys. Rev. B 109 L201109
[42] Li Y X 2024 Phys. Rev. B 109 224502
[43] Guo X, Zhang M H and Yao D X 2025 Chin. Phys. Lett. 42 120703
[44] Bose A, Vadnais S and Paramekanti A 2024 Phys. Rev. B 110 205120
[45] Li J, Liu J, Yang X and Tang H K 2025 arXiv:2505.12342
[46] Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
[47] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[48] Mesaros A and Ran Y 2013 Phys. Rev. B 87 155115
[49] Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005
[50] Bansil A, Lin H and Das T 2016 Rev. Mod. Phys. 88 021004
[51] Kudo K, Yoshida T and Hatsugai Y 2019 Phys. Rev. Lett. 123 196402
[52] Ghorashi S A A, Li T and Hughes T L 2020 Phys. Rev. Lett. 125 266804
[53] Ghorashi S A A, Hughes T L and Rossi E 2020 Phys. Rev. Lett. 125 037001
[54] Wang H X, Lin Z K, Jiang B, Guo G Y and Jiang J H 2020 Phys. Rev. Lett. 125 146401
[55] Tiwari A, Li M H, Bernevig B A, Neupert T and Parameswaran S A 2020 Phys. Rev. Lett. 124 046801
[56] Xi W, Zhang Z H, Gu Z C and Chen W Q 2021 Sci. Bull. 66 1731
[57] Liu T, He J J, Yang Z and Nori F 2021 Phys. Rev. Lett. 127 196801
[58] Cao Y, Li Y and Yang X 2021 Phys. Rev. B 103 075126
[59] Proctor M, Blanco de Paz M, Bercioux D, García-Etxarri A and Arroyo Huidobro P 2021 Appl. Phys. Lett. 118 091105
[60] Song L, Yang H, Cao Y and Yan P 2022 Nat. Commun. 13 5601
[61] Li Y, Ji X, Chen Y, Yan X and Yang X 2022 Phys. Rev. B 106 195425
[62] Zheng Z, Yin J, Wen J and Yu D 2022 Appl. Phys. Lett. 120 144101
[63] Jahin A, Tiwari A and Wang Y 2022 SciPost Phys. 12 053
[64] Xiong Z, Lin Z K, Wang H X, Liu S, Qian Y and Jiang J H 2023 Phys. Rev. B 108 085141
[65] Guo S, Huang J, Huang R, Zhuang F, Su S, Lin Z, Qiu W, Su J and Wang X 2024 Appl. Phys. Lett. 124 073104
[66] Ji X, Geng H, Akhtar N and Yang X 2025 Phys. Rev. B 111 195419
[67] Liu L, Sun Q F and Zhang Y T 2025 arXiv:2502.13535
[68] Khalaf E 2018 Phys. Rev. B 97 205136
[69] Yan Z 2019 Phys. Rev. Lett. 123 177001
[70] Tiwari A, Jahin A and Wang Y 2020 Phys. Rev. Res. 2 043300
[71] Xie B,Wang H X, Zhang X, Zhan P, Jiang J H, Lu M and Chen Y 2021 Nat. Rev. Phys. 3 520
[72] Wang Z, Meng Y, Yan B, Zhao D, Yang L, Chen J, Cheng M, Xiao T, Shum P P, Liu G G, Yang Y, Chen H, Xi X, Zhu Z X, Xie B and Gao Z 2025 Nat. Commun. 16 3122
[73] Yang X, Feng Y, Wahab A and Geng H 2026 Phys. Rev. A 113 023506
[74] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B 96 245115
[75] Yan Z 2019 Phys. Rev. B 100 205406
[76] Zhao W, Yang M, Xu R, Du X, Li Y, Zhai K, Peng C, Pei D, Gao H, Li Y, Xu L, Han J, Huang Y, Liu Z, Yao Y, Zhuang J, Du Y, Zhou J, Chen Y and Yang L 2023 Nat. Commun. 14 8089
[77] Luo X W and Zhang C 2019 Phys. Rev. Lett. 123 073601
[78] Ren Y, Qiao Z and Niu Q 2020 Phys. Rev. Lett. 124 166804
[79] Roy B and Juričić V 2021 Phys. Rev. B 104 L180503
[80] Ji X, Ding W, Chen Y and Yang X 2024 Phys. Rev. B 109 125420
[81] Vazifeh M M and Franz M 2013 Phys. Rev. Lett. 111 027201
[82] Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X and Bernevig B A 2015 Nature 527 495
[83] Sun X Q, Zhang S C and Wang Z 2015 Phys. Rev. Lett. 115 076802
[84] Yan Z and Wang Z 2016 Phys. Rev. Lett. 117 087402
[85] Yan B and Felser C 2017 Annu. Rev. Condens. Matter Phys. 8 337
[86] Yesilyurt C, Siu Z B, Tan S G, Liang G, Yang S A and JalilMB A 2017 Appl. Phys. Lett. 111 063101
[87] Armitage N P, Mele E J and Vishwanath A 2018 Rev. Mod. Phys. 90 015001
[88] Geishendorf K, Schlitz R, Vir P, Shekhar C, Felser C, Nielsch K, Goennenwein S T B and Thomas A 2019 Appl. Phys. Lett. 114 092403
[89] Shen J, Zeng Q, Zhang S, TongW, Ling L, Xi C,Wang Z, Liu E,Wang W, Wu G and Shen B 2019 Appl. Phys. Lett. 115 212403
[90] Da H, Song Q, Ye H and Yan X 2021 Appl. Phys. Lett. 119 081103
[91] Tang K,Wen Z, Lau Y C, Sukegawa H, Seki T and Mitani S 2021 Appl. Phys. Lett. 118 062402
[92] Bierhance G, Markou A, Gueckstock O, Rouzegar R, Behovits Y, Chekhov A L, Wolf M, Seifert T S, Felser C and Kampfrath T 2022 Appl. Phys. Lett. 120 082401
[93] Matsuo T, Higo T, Nishio-Hamane D and Nakatsuji S 2022 Appl. Phys. Lett. 121 013103
[94] Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
[95] Qian X, Liu J, Fu L and Li J 2014 Science 346 1344
[96] Yan Z, Song F and Wang Z 2018 Phys. Rev. Lett. 121 096803
[97] Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J and Jarillo-Herrero P 2018 Science 359 76
[98] Li Y Y and Zhang S B 2025 Phys. Rev. B 111 045106
[99] Godinho J, Reichlová H, Kriegner D, Novák V, Olejník K, Kašpar Z, Šobán Z, Wadley P, Campion R P, Otxoa R M, Roy P E, Zelezný J, Jungwirth T and Wunderlich J 2018 Nat. Commun. 9 4686
[100] Park I J, Lee T, Das P, Debnath B, Carman G P and Lake R K 2019 Appl. Phys. Lett. 114 142403
[101] Mahmood A, Echtenkamp W, Street M, Wang J L, Cao S, Komesu T, Dowben P A, Buragohain P, Lu H, Gruverman A, Parthasarathy A, Rakheja S and Binek C 2021 Nat. Commun. 12 1674
[102] Zhang P, Chou C T, Yun H, McGoldrick B C, Hou J T, Mkhoyan K A and Liu L 2022 Phys. Rev. Lett. 129 017203
[103] Grigorev V, Filianina M, Lytvynenko Y, Sobolev S, Pokharel A R, Lanz A P, Sapozhnik A, Kleibert A, Bodnar S, Grigorev P, Skourski Y, Kläui M, Elmers H J, Jourdan M and Demsar J 2022 ACS Nano 16 20589
[104] Guo H, Lin Z, Lu J, Yun C, Han G, Sun S, Wu Y, Yang W, Xiao D, Zhu Z, Peng L, Ye Y, Hou Y, Yang J and Luo Z 2025 Nat. Commun. 16 8911

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