Tunable Weyl fermions and Fermi arcs in magnetized topological crystalline insulators
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摘要
Based on k · p analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped(Mn, Eu, Cr, etc.) Sn_(1-x)Pb_x(Te, Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry.Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization,temperature, surface potential, etc., opening up the possibility of manipulating Weyl points and rewiring the Fermi arcs.
Based on k · p analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped(Mn, Eu, Cr, etc.) Sn_(1-x)Pb_x(Te, Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry.Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization,temperature, surface potential, etc., opening up the possibility of manipulating Weyl points and rewiring the Fermi arcs.
Based on k · p analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped(Mn, Eu, Cr, etc.) Sn_(1-x)Pb_x(Te, Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry.Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization,temperature, surface potential, etc., opening up the possibility of manipulating Weyl points and rewiring the Fermi arcs.
引文
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[3]Nielsen H and Ninomiya M 1982 Phys.Lett.B 130 389
[4]Son D T and Spivak B Z 2013 Phys.Rev.B 88 104412
[5]Liu C X,Ye P and Qi X L 2013 Phys.Rev.B 87 235306
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[7]Witten E 2015 arXiv preprint arXiv:1510.07698
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[9]Weng H,Fang C,Fang Z,Bernevig B A and Dai X 2015 Phys.Rev.X5 011029
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[13]Lv B Q,Weng H M,Fu B B,Wang X P,Miao H,Ma J,Richard P,Huang X C,Zhao L X,Chen G F,et al.2015 Phys.Rev.X 5 031013
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[15]Yang L X,Liu Z K,Sun Y,Peng H,Yang H F,Zhang T,Zhou B,Zhang Y,Guo Y F,Rahn M,et al.2015 Nat.Phys.11 728
[16]Lu L,Fu L,Joannopoulos J D and Soljacic M 2013 Nat.Photon.7
[17]Lu L,Joannopoulos J D and Soljaˇci′c M 2014 Nat.Photon.8 821
[18]Lu L,Wang Z,Ye D,Ran L,Fu L,Joannopoulos J D and Soljaˇci′c M2015 Science 349 622
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[21]Xu G,Weng H,Wang Z,Dai X and Fang Z 2011 Phys.Rev.Lett.107186806
[22]Fang C,Gilbert M J,Dai X and Bernevig B A 2012 Phys.Rev.Lett.108 266802
[23]Witczak-Krempa W and Kim Y B 2012 Phys.Rev.B 85 045124
[24]Kim H J,Kim K S,Wang J F,Sasaki M,Satoh N,Ohnishi A,Kitaura M,Yang M and Li L 2013 Phys.Rev.Lett.111 246603
[25]Bulmash D,Liu C X and Qi X L 2014 Phys.Rev.B 89 081106
[26]Dubˇcek T,Kennedy C J,Lu L,Ketterle W,Soljaˇci′c M and Buljan H2015 Phys.Rev.Lett.114 225301
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[31]Wang Q,Xu Y,Lou R,Liu Z,Li M,Huang Y,Shen D,Weng H,Wang S and Lei H 2018 Nat.Commun.9 3681
[32]Fu L 2011 Phys.Rev.Lett.106 106802
[33]Hsieh T H,Lin H,Liu J,Duan W,Bansil A and Fu L 2012 Nat.Commun.3 982
[34]Dziawa P,Kowalski B J,Dybko K,Buczko R,Szczerbakow A,Szot M,Lusakowska E,Balasubramanian T,Wojek B M,Bernsten M H,et al.2012 Nat.Mater.11 1023
[35]Tanaka Y,Ren Z,Sato T,Nakayama K,Souma S,Takahashi T,Segawa K and Ando Y 2012 Nat.Phys.8 800
[36]Xu S Y,Liu C,Alidoust N,Neupane M,Qian D,Belopolski I,Denlinger J D,Wang Y J,Lin H,Wray L A,et al.2012 Nat.Commun.31192
[37]Yan C,Liu J,Zang Y,Wang J,Wang Z,Wang P,Zhang Z D,Wang L,Ma X,Ji S,et al.2014 Phys.Rev.Lett.112 186801
[38]Zeljkovic I,Okada Y,Serbyn M,Sankar R,Walkup D,Zhou W,Liu J,Chang G,Wang Y J,Hasan M Z,et al.2015 Nat.Mater.14 318
[39]Cho G Y 2011 arXiv preprint arXiv:1110.1939
[40]Story T,Ga?la?zka,Frankel R B and Wolff P A 1986 Phys.Rev.Lett.56 777
[41]Bauer G 1986 in MRS Proceedings,Vol.89(Cambridge:Cambridge University Press)p.107
[42]G′orska M and Anderson J R 1988 Phys.Rev.B 38 9120
[43]Pascher H,R¨othlein P,Bauer G and von Ortenberg M 1989 Phys.Rev.B 40 10469
[44]Rothlein P,Pascher H,Bauer G and Tacke M 1990 Semicond.Sci.Technol.5 S147
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[48]Dietl T,′Sliwa C,Bauer G and Pascher H 1994 Phys.Rev.B 49 2230
[49]de Jonge W J M,Swagten H J M,Eltink S J E A and Stoffels N M J1990 Semicond.Sci.Technol.5 S131
[50]Story T,Grodzicka E,Witkowska B,Gorecka J and Dobrowolski W1992 Acta Physica Polonica A 82 879
[51]Eggenkamp P,Story T,Sw¨uste C,Swagten H and de Jonge W 1993Acta Physica Polonica A 84 641
[52]Eggenkamp P,Swagten H,Story T and de Jonge W 1995 J.Magn.Magn.Mater.140-144 2039
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[54]Mitchell D L and Wallis R F 1966 Phys.Rev.151 581
[55]Murakami S 2007 New J.Phys.9 356
[56]Okada Y,Serbyn M,Lin H,Walkup D,Zhou W,Dhital C,Neupane M,Xu S,Wang Y J,Sankar R,et al.2013 Science 341 1496
[57]Qian X,Fu L and Li J 2014 Nano Res.8 967
[58]Brodowska B,Dobrowolski W,Arciszewska M,Slynko E and Dugaev V 2006 J.Alloys Compd.423 205
[59]Fang C,Lu L,Liu J and Fu L 2015 arXiv preprint arXiv:1512.01552
[60]Lent C S,Bowen M A,Dow J D,Allgaier R S,Sankey O F and Ho ES 1986 Superlattices and Microstructures 2 491
[61]Liu J,Hsieh T H,Wei P,Duan W,Moodera J and Fu L 2014 Nat.Mater.13 178
[62]Liu J,Qian X and Fu L 2015 Nano Lett.15 2657
[63]Wojek B M,Buczko R,Safaei S,Dziawa P,Kowalski B J,Berntsen MH,Balasubramanian T,Leandersson M,Szczerbakow A,Kacman P,et al.2013 Phys.Rev.B 87 115106
[64]Safaei S,Kacman P and Buczko R 2013 Phys.Rev.B 88 045305
[65]Liu J,Duan W and Fu L 2013 Phys.Rev.B 88 241303
[66]Sancho M P L,Sancho J M L and Rubio J 1985 J.Phys.F:Metal Phys.15 851
[67]Fukuma Y,Asada H,Nishimura N and Koyanagi T 2003 J.Appl.Phys.93 4034
[68]Dziawa P,Knoff W,Domukhovski V,Domagala J,Jakiela R,Lusakowska E,Osinniy V,Swiatek K,Taliashvili B and Story T 2007Narrow Gap Semiconductors(Springer)pp.11-14
[69]Fukuma Y,Asada H,Moritake N,Irisa T and Koyanagi T 2007 Appl.Phys.Lett.91 092501
[70]Fukuma Y,Asada H,Miyawaki S,Koyanagi T,Senba S,Goto K and Sato H 2008 Appl.Phys.Lett.93 252502
[71]Dietl T 2010 Nat.Mater.9 965
[72]Hassan M,Springholz G,Lechner R,Groiss H,Kirchschlager R and Bauer G 2011 J.Crystal Growth 323 363
[2]Wan X,Turner A M,Vishwanath A and Savrasov S Y 2011 Phys.Rev.B 83 205101
[3]Nielsen H and Ninomiya M 1982 Phys.Lett.B 130 389
[4]Son D T and Spivak B Z 2013 Phys.Rev.B 88 104412
[5]Liu C X,Ye P and Qi X L 2013 Phys.Rev.B 87 235306
[6]Potter A C,Kimchi I and Vishwanath A 2014 Nat.Commun.5
[7]Witten E 2015 arXiv preprint arXiv:1510.07698
[8]Young S M,Zaheer S,Teo J C Y,Kane C L,Mele E J and Rappe A M2012 Phys.Rev.Lett.108 140405
[9]Weng H,Fang C,Fang Z,Bernevig B A and Dai X 2015 Phys.Rev.X5 011029
[10]Huang S M,Xu S Y,Belopolski I,Lee C C,Chang G,Wang B,Alidoust N,Bian G,Neupane M,Bansil A,et al.2015 Nat.Commun.6
[11]Xu S Y,Belopolski I,Alidoust N,Neupane M,Zhang C,Sankar R,Huang S M,Lee C C,Chang G,Wang B,et al.2015 Science 349 613
[12]Xu S Y,Alidoust N,Belopolski I,Yuan Z,Bian G,Chang T R,Zheng H,Strocov V N,Sanchez D S,Chang G,et al.2015 Nat.Phys.11 748
[13]Lv B Q,Weng H M,Fu B B,Wang X P,Miao H,Ma J,Richard P,Huang X C,Zhao L X,Chen G F,et al.2015 Phys.Rev.X 5 031013
[14]Lv B Q,Xu N,Weng H M,Ma J Z,Richard P,Huang X C,Zhao L X,Chen G F,Matt C E,Bisti F,et al.2015 Nat.Phys.11 724
[15]Yang L X,Liu Z K,Sun Y,Peng H,Yang H F,Zhang T,Zhou B,Zhang Y,Guo Y F,Rahn M,et al.2015 Nat.Phys.11 728
[16]Lu L,Fu L,Joannopoulos J D and Soljacic M 2013 Nat.Photon.7
[17]Lu L,Joannopoulos J D and Soljaˇci′c M 2014 Nat.Photon.8 821
[18]Lu L,Wang Z,Ye D,Ran L,Fu L,Joannopoulos J D and Soljaˇci′c M2015 Science 349 622
[19]Burkov A A,Hook M D and Balents L 2011 Phys.Rev.B 84 235126
[20]Burkov A A and Balents L 2011 Phys.Rev.Lett.107 127205
[21]Xu G,Weng H,Wang Z,Dai X and Fang Z 2011 Phys.Rev.Lett.107186806
[22]Fang C,Gilbert M J,Dai X and Bernevig B A 2012 Phys.Rev.Lett.108 266802
[23]Witczak-Krempa W and Kim Y B 2012 Phys.Rev.B 85 045124
[24]Kim H J,Kim K S,Wang J F,Sasaki M,Satoh N,Ohnishi A,Kitaura M,Yang M and Li L 2013 Phys.Rev.Lett.111 246603
[25]Bulmash D,Liu C X and Qi X L 2014 Phys.Rev.B 89 081106
[26]Dubˇcek T,Kennedy C J,Lu L,Ketterle W,Soljaˇci′c M and Buljan H2015 Phys.Rev.Lett.114 225301
[27]Borisenko S,Evtushinsky D,Gibson Q,Yaresko A,Kim T,Ali MN,Buechner B,Hoesch M and Cava R J 2015 arXiv preprint arXiv:1507.04847
[28]Chang G,Xu S Y,Zheng H,Singh B,Hsu C H,Belopolski I,Sanchez D S,Bian G,Alidoust N,Lin H,et al.2016 arXiv preprint arXiv:1603.01255
[29]Yang K Y,Lu Y M and Ran Y 2011 Phys.Rev.B 84 075129
[30]Liu E,Sun Y,Kumar N,Muechler L,Sun A,Jiao L,Yang S Y,Liu D,Liang A,Xu Q,et al.2018 Nat.Phys.14 1125
[31]Wang Q,Xu Y,Lou R,Liu Z,Li M,Huang Y,Shen D,Weng H,Wang S and Lei H 2018 Nat.Commun.9 3681
[32]Fu L 2011 Phys.Rev.Lett.106 106802
[33]Hsieh T H,Lin H,Liu J,Duan W,Bansil A and Fu L 2012 Nat.Commun.3 982
[34]Dziawa P,Kowalski B J,Dybko K,Buczko R,Szczerbakow A,Szot M,Lusakowska E,Balasubramanian T,Wojek B M,Bernsten M H,et al.2012 Nat.Mater.11 1023
[35]Tanaka Y,Ren Z,Sato T,Nakayama K,Souma S,Takahashi T,Segawa K and Ando Y 2012 Nat.Phys.8 800
[36]Xu S Y,Liu C,Alidoust N,Neupane M,Qian D,Belopolski I,Denlinger J D,Wang Y J,Lin H,Wray L A,et al.2012 Nat.Commun.31192
[37]Yan C,Liu J,Zang Y,Wang J,Wang Z,Wang P,Zhang Z D,Wang L,Ma X,Ji S,et al.2014 Phys.Rev.Lett.112 186801
[38]Zeljkovic I,Okada Y,Serbyn M,Sankar R,Walkup D,Zhou W,Liu J,Chang G,Wang Y J,Hasan M Z,et al.2015 Nat.Mater.14 318
[39]Cho G Y 2011 arXiv preprint arXiv:1110.1939
[40]Story T,Ga?la?zka,Frankel R B and Wolff P A 1986 Phys.Rev.Lett.56 777
[41]Bauer G 1986 in MRS Proceedings,Vol.89(Cambridge:Cambridge University Press)p.107
[42]G′orska M and Anderson J R 1988 Phys.Rev.B 38 9120
[43]Pascher H,R¨othlein P,Bauer G and von Ortenberg M 1989 Phys.Rev.B 40 10469
[44]Rothlein P,Pascher H,Bauer G and Tacke M 1990 Semicond.Sci.Technol.5 S147
[45]Galazka R R,palek J,Lewicki A,Crooker B C,Karczewski G and Story T 1991 Phys.Rev.B 43 11093
[46]Hofmann W,Fichtel U,Pascher H,Frank N and Bauer G 1992 Phys.Rev.B 45 8742
[47]Bauer G,Pascher H and Zawadzki W 1992 Semicond.Sci.Technol.7703
[48]Dietl T,′Sliwa C,Bauer G and Pascher H 1994 Phys.Rev.B 49 2230
[49]de Jonge W J M,Swagten H J M,Eltink S J E A and Stoffels N M J1990 Semicond.Sci.Technol.5 S131
[50]Story T,Grodzicka E,Witkowska B,Gorecka J and Dobrowolski W1992 Acta Physica Polonica A 82 879
[51]Eggenkamp P,Story T,Sw¨uste C,Swagten H and de Jonge W 1993Acta Physica Polonica A 84 641
[52]Eggenkamp P,Swagten H,Story T and de Jonge W 1995 J.Magn.Magn.Mater.140-144 2039
[53]Geist F,Herbst W,Mej′?a-Garc′?a C,Pascher H,Rupprecht R,Ueta Y,Springholz G,Bauer G and Tacke M 1997 Phys.Rev.B 56 13042
[54]Mitchell D L and Wallis R F 1966 Phys.Rev.151 581
[55]Murakami S 2007 New J.Phys.9 356
[56]Okada Y,Serbyn M,Lin H,Walkup D,Zhou W,Dhital C,Neupane M,Xu S,Wang Y J,Sankar R,et al.2013 Science 341 1496
[57]Qian X,Fu L and Li J 2014 Nano Res.8 967
[58]Brodowska B,Dobrowolski W,Arciszewska M,Slynko E and Dugaev V 2006 J.Alloys Compd.423 205
[59]Fang C,Lu L,Liu J and Fu L 2015 arXiv preprint arXiv:1512.01552
[60]Lent C S,Bowen M A,Dow J D,Allgaier R S,Sankey O F and Ho ES 1986 Superlattices and Microstructures 2 491
[61]Liu J,Hsieh T H,Wei P,Duan W,Moodera J and Fu L 2014 Nat.Mater.13 178
[62]Liu J,Qian X and Fu L 2015 Nano Lett.15 2657
[63]Wojek B M,Buczko R,Safaei S,Dziawa P,Kowalski B J,Berntsen MH,Balasubramanian T,Leandersson M,Szczerbakow A,Kacman P,et al.2013 Phys.Rev.B 87 115106
[64]Safaei S,Kacman P and Buczko R 2013 Phys.Rev.B 88 045305
[65]Liu J,Duan W and Fu L 2013 Phys.Rev.B 88 241303
[66]Sancho M P L,Sancho J M L and Rubio J 1985 J.Phys.F:Metal Phys.15 851
[67]Fukuma Y,Asada H,Nishimura N and Koyanagi T 2003 J.Appl.Phys.93 4034
[68]Dziawa P,Knoff W,Domukhovski V,Domagala J,Jakiela R,Lusakowska E,Osinniy V,Swiatek K,Taliashvili B and Story T 2007Narrow Gap Semiconductors(Springer)pp.11-14
[69]Fukuma Y,Asada H,Moritake N,Irisa T and Koyanagi T 2007 Appl.Phys.Lett.91 092501
[70]Fukuma Y,Asada H,Miyawaki S,Koyanagi T,Senba S,Goto K and Sato H 2008 Appl.Phys.Lett.93 252502
[71]Dietl T 2010 Nat.Mater.9 965
[72]Hassan M,Springholz G,Lechner R,Groiss H,Kirchschlager R and Bauer G 2011 J.Crystal Growth 323 363