Ⅱ-Ⅵ族稀磁半导体微纳结构中的激子磁极化子及其发光
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摘要
自旋是基本粒子(电子、光子)角动量的内在形式.固体中体现自旋特征的集体电子行为如拓扑绝缘体等是当前凝聚态物理领域关注的焦点,是基态行为.激子作为电子空穴对的激发态且寿命很短,可复合发光,它是否能体现自旋极化主导的行为?对此人们的认识远不如针对基态的电子.激子磁极化子(exciton magnetic polaron, EMP)是由磁性半导体微结构中铁磁自旋耦合态与自由激子相互作用形成的复合元激发,但其研究很有限.本文概述了我们在稀磁半导体微纳米结构中的EMP及其发光动态学光谱、自旋极化激子凝聚态的形成方面取得的一些进展,展望了未来可能在自旋光电子器件、磁控激光、光致磁性等量子技术方面的潜在应用.
Spin is an intrinsic nature of the angular momentum of elementary particle like electron and photon. Currently the collective spin behaviors of the multi-electrons in condensed matter, such as GMR, CMR and topological insulator which are the behaviors of ground state, have been a research focus in the condensed matter physics, due to the fact that the collective spin is related to electronic transports. Exciton is another type of bosonic quasiparticle, an excited state of electronhole pair in solid, which has a short lifetime and can recombine to emit light. Whether excitons can also exhibit the spin-polarized dominance before they recombine, has not been understood yet. It is proposed that excitons form condensate by themselves or light binding. Can coupled spins conduce to the formation of the exciton condensate in solid? Excitonic magnetic polaron(EMP) is the composite exciton of ferromagnetically coupled spins and free excitons in magnetic semiconductors, which may lead to ferromagnetic Bose-Einstein condensate(BEC) due to the binding of collective spins in a microstructure, like the photon binding excitons(exciton polaritons) in an optical cavity However,this subject has not been a research focus yet. Here in this paper, we review the progress of the EMP formation, its dynamic behaviors and spin polarized collective EMP emission and lasing in II-VI dilute magnetic semiconductor microstructures in our group Besides, we also present some expectations for the applications or advances in the quantum phenomena such as spin-related emission and lasing, spin induced BEC, photon induced magnetism and Hall effect, etc.Even more achievements of EMP could be expected in the future.
Spin is an intrinsic nature of the angular momentum of elementary particle like electron and photon. Currently the collective spin behaviors of the multi-electrons in condensed matter, such as GMR, CMR and topological insulator which are the behaviors of ground state, have been a research focus in the condensed matter physics, due to the fact that the collective spin is related to electronic transports. Exciton is another type of bosonic quasiparticle, an excited state of electronhole pair in solid, which has a short lifetime and can recombine to emit light. Whether excitons can also exhibit the spin-polarized dominance before they recombine, has not been understood yet. It is proposed that excitons form condensate by themselves or light binding. Can coupled spins conduce to the formation of the exciton condensate in solid? Excitonic magnetic polaron(EMP) is the composite exciton of ferromagnetically coupled spins and free excitons in magnetic semiconductors, which may lead to ferromagnetic Bose-Einstein condensate(BEC) due to the binding of collective spins in a microstructure, like the photon binding excitons(exciton polaritons) in an optical cavity However,this subject has not been a research focus yet. Here in this paper, we review the progress of the EMP formation, its dynamic behaviors and spin polarized collective EMP emission and lasing in II-VI dilute magnetic semiconductor microstructures in our group Besides, we also present some expectations for the applications or advances in the quantum phenomena such as spin-related emission and lasing, spin induced BEC, photon induced magnetism and Hall effect, etc.Even more achievements of EMP could be expected in the future.
引文
[1]Wolf S A,Awschalom D D,Buhrman R A,Daughton J M,von Molnár S,Roukes M L,Chtchelkanova A Y,Treger D M 2001 Science 294 1488
[2]Dietl T 2010 Nat.Mater.9 965
[3]Merkulov I A,Yakovlev D R,Keller A,Ossau W,Geurts J,Waag A,Landwehr G,Karczewski G,Wojtowicz T,Kossut J 1999 Phys.Rev.Lett.83 1431
[4]Bhattacharjee A K,Benoit Guillaume C 1997 Phys.Rev.B:Condens.Matter 55 10613
[5]Norberg N S,Parks G L,Salley G M,Gamelin D R 2006J.Am.Chem.Soc.128 13195
[6]Beaulac R,Schneider L,Archer P I,Bacher G,Gamelin D R 2009 Science 325 973
[7]Schwartz D A,Norberg N S,Nguyen Q P,Parker J M,Gamelin D R 2003 J.Am.Chem.Soc.125 13205
[8]Bhattacharjee A K 2007 Phys.Rev B:Condens.Matter76 075305
[9]Kavokin A,Gil B,Bigenwald P 1998 Phys.Rev.B:Condens.Matter 57 4261
[10]Eisenstein J P,MacDonald A H 2004 Nature 432 691
[11]Su,J J,MacDonald A H 2008 Nature Phys.4 799
[12]K?opotowski?,Cywiński?,Wojnar P,Voliotis V,Fronc K,Kazimierczuk T,Golnik A,Ravaro M,Grousson R,Karczewski G,Wojtowicz T 2011 Phys.Rev.B:Condens.Matter 83 081306
[13]Mackh G,Ossau W,Yakovlev D R,Waag A,Landwehr G,Hellmann R,G?bel E O 1994 Phys.Rev.B:Condens.Matter 49 10248
[14]Cui X Y,Medvedeva J E,Delley B,Freeman A J,Newman N,Stampfl C 2005 Phys.Rev.Lett.95 256404
[15]Raebiger H,Lany S,Zunger A 2007 Phys.Rev.Lett.99167203
[16]Ivanov V A,Pashkova O N,Ugolkova E A,Sanygin VP,Galéra R M 2008 Inorg.Mater.44 1041
[17]Zou B S,Liu R B,Wang F F,Pan A L,Cao L,Wang ZL 2006 J.Phys.Chem.B 110 12865
[18]Bulakh B,Khomenkova L,Kushnirenko V,Markevich I2004 Europ.Phys.J.:Appl.Phys.27 305
[19]Schmitt-Rink S,Chemla D S,Miller D A B 1989 Adv.Phys.38 89
[20]Johnson J C,Yan H,Yang P,Saykally R J 2003 J.Phys.Chem.B 107 8816
[21]Johnson J C,Knutsen K P,Yan H,Law M,Zhang Y,Yang P,Saykally R J 2004 Nano Lett.4 197
[22]Klingshirn C 1992 J.Cryst.Growth 117 753
[23]Griffin A,Snoke D W,Stringari S 1996 BoseEinstein Condensation(Cambridge:Cambridge University Press)
[24]Godde T,Reshina I I,Ivanov S V,Akimov I A,Yakovlev D R,Bayer M 2010 Phys.Status Solidi(b)247 1508
[25]Wang R P,Xu G,Jin P 2004 Phys.Rev.B:Condens.Matter 69 113303
[26]Liu R,Shi L,Zou B 2014 ACS Appl.Mat.Interf.6 10353
[27]Rashba E,Sturge M 1982 Excitons(North Holland:Amsterdam)
[28]Liu R B,Zou B S 2011 Chin.Phys.B 20 47104
[29]Pokatilov E P,Fomin V M,Devreese J T,Balaban SN,Klimin S N 2000 Phys.Rev.B:Condens.Matter 612721
[30]Butov L V,Lai C W,Ivanov A L,Gossard A C,Chemla D S 2002 Nature 417 47
[31]Tang Z K,Wong G K L,Yu P,Kawasaki M,Ohtomo A,Koinuma H,Segawa Y 1998 Appl.Phys.Lett.72 3270
[32]Cao L,Miao Y,Zhang Z,Xie S S,Yang G Z,Zou B S2005 J.Chem.Phys.123 024702
[33]L?venich R,Sch?fer W,Kner P,Chemla D S 1997 Physica Status Solidi(a)164 347
[34]Dietl T,Ohno H,Matsukura F,Cibert J,Ferrand D 2000Science 287 1019
[35]Sharma P,Gupta A,Rao K V,Owens F J,Sharma R,Ahuja R,Guillen J M O,Johansson B,Gehring G A2003 Nat.Mater.2 673
[36]Jin Z W,Yoo Y Z,Sekiguchi T,Chikyow T,Ofuchi H,Fujioka H,Oshima M,Koinuma H 2003 Appl.Phys.Lett.83 39
[37]Norberg N S,Kittilstved K R,Amonette J E,Kukkadapu R K,Schwartz D A,Gamelin D R 2004 J.Am.Chem.Soc.126 9387
[38]Furdyna J K 1988 J.Appl.Phys.64 R29
[39]Takahashi M 2004 Phys.Rev.B:Condens.Matter 70035207
[40]Mizokawa T,Nambu T,Fujimori A,Fukumura T,Kawasaki M 2002 Phys.Rev.B:Condens.Matter 65085209
[41]Demokritov S O,Demidov V E,Dzyapko O,Melkov GA,Serga A A,Hillebrands B,Slavin A N 2006 Nature443 430
[42]Maksimov A A,Bacher G,McDonald A,Kulakovskii VD,Forchel A,Becker C R,Landwehr G,Molenkamp LW 2000 Phys.Rev.B:Condens.Matter 62 R7767
[43]Seufert J,Bacher G,Scheibner M,Forchel A,Lee S,Dobrowolska M,Furdyna J K 2001 Phys.Rev.Lett.88027402
[44]Sun L,Chen Z,Ren Q,Yu K,Bai L,Zhou W,Xiong H,Zhu Z Q,Shen X 2008 Phys.Rev.Lett.100 156403
[45]Xie W,Dong H,Zhang S,Sun L,Zhou W,Ling Y,Lu J,Shen X,Chen Z 2012 Phys.Rev.Lett.108 166401
[46]Liu R,Pan A,Fan H,Wang F,Shen Z,Yang G,Xie S,Zou B 2007 J.Phys.:Condens.Matter 19 136206
[47]Leung Y H,Kwok W M,Djuri?i?A B,Phillips D L,Chan W K 2005 Nanotechnology 16 579
[48]Paredes B,Widera A,Murg V,Mandel O,F?lling S,Cirac I,Shlyapnikov G V,H?nsch T W,Bloch I 2004Nature 429 277
[49]Kinoshita T,Wenger T,Weiss D S 2004 Science 3051125
[50]Eisenstein J P,MacDonald A H 2004 Nature 432 691
[51]Kamran M A,Liu R,Shi L,Li Z,Marzi T,Sch?ppner C,Farle M,Zou B S 2014 Nanotechnology 25 385201
[52]Kamran M A,Liu R,Shi L,Zou B S,Zhang Q 2013 J.Phys.Chem.C 117 17777
[53]Zuo T,Sun Z,Zhao Y,Jiang X,Gao X 2010 J.Am.Chem.Soc.132 6618
[54]Pradhan N,Peng X 2007 J.Am.Chem.Soc.129 3339
[55]Hazarika A,Layek A,De S,Nag A,Debnath S,Mahadevan P,Chowdhury A,Sarma D D 2013 Phys.Rev.Lett.110 267401
[56]Erwin S C,Zu L J,Haftel M I,Efros A L,Kennedy TA,Norris D J 2005 Nature 436 91
[57]Yang G,Xu G,Chen B,Zou S,Liu R,Zhong H,Zou B2013 Chem.Mater.25 3260
[58]Bhattacharyya S,Estrin Y,Rich D H,Zitoun D,Koltypin Y,Gedanken A 2010 J.Phys.Chem.C 11422002
[59]Gumlich H E,Moser R,Neumann E 1967 Phys.Status Solidi(b)24 K13
[60]Nag A,Cherian R,Mahadevan P,Gopal A V,Hazarika A,Mohan A,Vengurlekar A S,Sarma D D 2010 J.Phys.Chem.C 114 18323
[61]Cui X Y,Delley B,Freeman A J,Stampfl C 2007 Phys.Rev.B:Condens.Matter 76 045201
[62]Durst A C,Bhatt R N,Wolff P A 2002 Phys.Rev.B:Condens.Matter 65 235205
[63]Wojtowicz T,Kole?nik S,Miotkowski I,Furdyna J K1993 Phys.Rev.Lett.70 2317
[64]Beaulac R,Feng Y,May J W,Badaeva E,Gamelin DR,Li X 2011 Phys.Rev.B:Condens.Matter 84 195324
[65]Delikanli S,He S,Qin Y,Zhang P,Zeng H,Zhang H,Swihart M 2008 Appl.Phys.Lett.93 132501
[66]Kisliuk P,Chang N C,Scott P L,Pryce M H L 1969Phys.Rev.184 367
[67]Spano F C,Silva C 2014 Annu.Rev.Phys.Chem.65477
[68]Muhammad A K,Zhang Y Y,Liu R B,Shi L J,Zou BS 2014 Chin.Phys.Lett.31 067802
[69]Zou S,Kamran M A,Shi L J,Liu R B,Guo S,Kavokin A,Zou B S 2016 ACS Photon.3 1809
[70]Bonanni A,Navarro-Quezada A,Li T,Wegscheider M,Matěj Z,HolyV,Lechner R T,Bauer G,Rovezzi M,D’Acapito F,Kiecana M,Sawicki M,Dietl T 2008 Phys.Rev.Lett.101 135502
[71]Zhang Y B,Assadi M H N,Li S 2009 J.Phys.:Condens.Matter 21 175802
[72]Oka Y,Shen J,Takabayashi K,Takahashi N,Mitsu H,Souma I,Pittini R 1999 J.Lumin.83 83
[73]Godlewski M,Yatsunenko S,Khachapuridze A,Ivanov V Y,Go?acki Z,Karczewski G,Bergman P J,Klar P J,Heimbrodt W,Phillips M R 2004 J.Alloy.Compd.38045
[74]Chang K,Peeters F M 2003 Phys.Rev.B:Condens.Matter 68 205320
[75]Katayama K,Miyajima K,Ashida M,Itoh T 2012 J.Phys.:Condens.Matter 24 325801
[76]Dey A,Yarlagadda S 2014 Phys.Rev.B:Condens.Matter 89 064311
[77]Butov L V,Filin A I 1998 Phys.Rev.B:Condens.Matter 58 1980
[78]Snoke D W 2011 Adv.Condens.Matter Phys.2011938609
[79]Moskalenko S A,Liberman M A,Dumanov E V 2011 J.Nanoelectron.Optoelectron.6 393
[80]Hague J P,Kornilovitch P E 2010 Phys.Rev.B:Condens.Matter 82 094301
[81]Hague J P,Kornilovitch P E,Samson J H,Alexandrov A S 2007 Phys.Rev.Lett.98 037002
[82]Voigt J,Spiegelberg F,Senoner M 1979 Phys.Status Solidi 91 189
[83]Bandres M A,Wittek S,Harari G,Parto M,Ren J,Segev M,Christodoulides D N,Khajavikhan M 2018 Science 359 4005
[84]Bliokh K Y,Rodríguez-Fortu?o F J,Nori F,Zayats AV 2015 Nature Photon.9 796
[2]Dietl T 2010 Nat.Mater.9 965
[3]Merkulov I A,Yakovlev D R,Keller A,Ossau W,Geurts J,Waag A,Landwehr G,Karczewski G,Wojtowicz T,Kossut J 1999 Phys.Rev.Lett.83 1431
[4]Bhattacharjee A K,Benoit Guillaume C 1997 Phys.Rev.B:Condens.Matter 55 10613
[5]Norberg N S,Parks G L,Salley G M,Gamelin D R 2006J.Am.Chem.Soc.128 13195
[6]Beaulac R,Schneider L,Archer P I,Bacher G,Gamelin D R 2009 Science 325 973
[7]Schwartz D A,Norberg N S,Nguyen Q P,Parker J M,Gamelin D R 2003 J.Am.Chem.Soc.125 13205
[8]Bhattacharjee A K 2007 Phys.Rev B:Condens.Matter76 075305
[9]Kavokin A,Gil B,Bigenwald P 1998 Phys.Rev.B:Condens.Matter 57 4261
[10]Eisenstein J P,MacDonald A H 2004 Nature 432 691
[11]Su,J J,MacDonald A H 2008 Nature Phys.4 799
[12]K?opotowski?,Cywiński?,Wojnar P,Voliotis V,Fronc K,Kazimierczuk T,Golnik A,Ravaro M,Grousson R,Karczewski G,Wojtowicz T 2011 Phys.Rev.B:Condens.Matter 83 081306
[13]Mackh G,Ossau W,Yakovlev D R,Waag A,Landwehr G,Hellmann R,G?bel E O 1994 Phys.Rev.B:Condens.Matter 49 10248
[14]Cui X Y,Medvedeva J E,Delley B,Freeman A J,Newman N,Stampfl C 2005 Phys.Rev.Lett.95 256404
[15]Raebiger H,Lany S,Zunger A 2007 Phys.Rev.Lett.99167203
[16]Ivanov V A,Pashkova O N,Ugolkova E A,Sanygin VP,Galéra R M 2008 Inorg.Mater.44 1041
[17]Zou B S,Liu R B,Wang F F,Pan A L,Cao L,Wang ZL 2006 J.Phys.Chem.B 110 12865
[18]Bulakh B,Khomenkova L,Kushnirenko V,Markevich I2004 Europ.Phys.J.:Appl.Phys.27 305
[19]Schmitt-Rink S,Chemla D S,Miller D A B 1989 Adv.Phys.38 89
[20]Johnson J C,Yan H,Yang P,Saykally R J 2003 J.Phys.Chem.B 107 8816
[21]Johnson J C,Knutsen K P,Yan H,Law M,Zhang Y,Yang P,Saykally R J 2004 Nano Lett.4 197
[22]Klingshirn C 1992 J.Cryst.Growth 117 753
[23]Griffin A,Snoke D W,Stringari S 1996 BoseEinstein Condensation(Cambridge:Cambridge University Press)
[24]Godde T,Reshina I I,Ivanov S V,Akimov I A,Yakovlev D R,Bayer M 2010 Phys.Status Solidi(b)247 1508
[25]Wang R P,Xu G,Jin P 2004 Phys.Rev.B:Condens.Matter 69 113303
[26]Liu R,Shi L,Zou B 2014 ACS Appl.Mat.Interf.6 10353
[27]Rashba E,Sturge M 1982 Excitons(North Holland:Amsterdam)
[28]Liu R B,Zou B S 2011 Chin.Phys.B 20 47104
[29]Pokatilov E P,Fomin V M,Devreese J T,Balaban SN,Klimin S N 2000 Phys.Rev.B:Condens.Matter 612721
[30]Butov L V,Lai C W,Ivanov A L,Gossard A C,Chemla D S 2002 Nature 417 47
[31]Tang Z K,Wong G K L,Yu P,Kawasaki M,Ohtomo A,Koinuma H,Segawa Y 1998 Appl.Phys.Lett.72 3270
[32]Cao L,Miao Y,Zhang Z,Xie S S,Yang G Z,Zou B S2005 J.Chem.Phys.123 024702
[33]L?venich R,Sch?fer W,Kner P,Chemla D S 1997 Physica Status Solidi(a)164 347
[34]Dietl T,Ohno H,Matsukura F,Cibert J,Ferrand D 2000Science 287 1019
[35]Sharma P,Gupta A,Rao K V,Owens F J,Sharma R,Ahuja R,Guillen J M O,Johansson B,Gehring G A2003 Nat.Mater.2 673
[36]Jin Z W,Yoo Y Z,Sekiguchi T,Chikyow T,Ofuchi H,Fujioka H,Oshima M,Koinuma H 2003 Appl.Phys.Lett.83 39
[37]Norberg N S,Kittilstved K R,Amonette J E,Kukkadapu R K,Schwartz D A,Gamelin D R 2004 J.Am.Chem.Soc.126 9387
[38]Furdyna J K 1988 J.Appl.Phys.64 R29
[39]Takahashi M 2004 Phys.Rev.B:Condens.Matter 70035207
[40]Mizokawa T,Nambu T,Fujimori A,Fukumura T,Kawasaki M 2002 Phys.Rev.B:Condens.Matter 65085209
[41]Demokritov S O,Demidov V E,Dzyapko O,Melkov GA,Serga A A,Hillebrands B,Slavin A N 2006 Nature443 430
[42]Maksimov A A,Bacher G,McDonald A,Kulakovskii VD,Forchel A,Becker C R,Landwehr G,Molenkamp LW 2000 Phys.Rev.B:Condens.Matter 62 R7767
[43]Seufert J,Bacher G,Scheibner M,Forchel A,Lee S,Dobrowolska M,Furdyna J K 2001 Phys.Rev.Lett.88027402
[44]Sun L,Chen Z,Ren Q,Yu K,Bai L,Zhou W,Xiong H,Zhu Z Q,Shen X 2008 Phys.Rev.Lett.100 156403
[45]Xie W,Dong H,Zhang S,Sun L,Zhou W,Ling Y,Lu J,Shen X,Chen Z 2012 Phys.Rev.Lett.108 166401
[46]Liu R,Pan A,Fan H,Wang F,Shen Z,Yang G,Xie S,Zou B 2007 J.Phys.:Condens.Matter 19 136206
[47]Leung Y H,Kwok W M,Djuri?i?A B,Phillips D L,Chan W K 2005 Nanotechnology 16 579
[48]Paredes B,Widera A,Murg V,Mandel O,F?lling S,Cirac I,Shlyapnikov G V,H?nsch T W,Bloch I 2004Nature 429 277
[49]Kinoshita T,Wenger T,Weiss D S 2004 Science 3051125
[50]Eisenstein J P,MacDonald A H 2004 Nature 432 691
[51]Kamran M A,Liu R,Shi L,Li Z,Marzi T,Sch?ppner C,Farle M,Zou B S 2014 Nanotechnology 25 385201
[52]Kamran M A,Liu R,Shi L,Zou B S,Zhang Q 2013 J.Phys.Chem.C 117 17777
[53]Zuo T,Sun Z,Zhao Y,Jiang X,Gao X 2010 J.Am.Chem.Soc.132 6618
[54]Pradhan N,Peng X 2007 J.Am.Chem.Soc.129 3339
[55]Hazarika A,Layek A,De S,Nag A,Debnath S,Mahadevan P,Chowdhury A,Sarma D D 2013 Phys.Rev.Lett.110 267401
[56]Erwin S C,Zu L J,Haftel M I,Efros A L,Kennedy TA,Norris D J 2005 Nature 436 91
[57]Yang G,Xu G,Chen B,Zou S,Liu R,Zhong H,Zou B2013 Chem.Mater.25 3260
[58]Bhattacharyya S,Estrin Y,Rich D H,Zitoun D,Koltypin Y,Gedanken A 2010 J.Phys.Chem.C 11422002
[59]Gumlich H E,Moser R,Neumann E 1967 Phys.Status Solidi(b)24 K13
[60]Nag A,Cherian R,Mahadevan P,Gopal A V,Hazarika A,Mohan A,Vengurlekar A S,Sarma D D 2010 J.Phys.Chem.C 114 18323
[61]Cui X Y,Delley B,Freeman A J,Stampfl C 2007 Phys.Rev.B:Condens.Matter 76 045201
[62]Durst A C,Bhatt R N,Wolff P A 2002 Phys.Rev.B:Condens.Matter 65 235205
[63]Wojtowicz T,Kole?nik S,Miotkowski I,Furdyna J K1993 Phys.Rev.Lett.70 2317
[64]Beaulac R,Feng Y,May J W,Badaeva E,Gamelin DR,Li X 2011 Phys.Rev.B:Condens.Matter 84 195324
[65]Delikanli S,He S,Qin Y,Zhang P,Zeng H,Zhang H,Swihart M 2008 Appl.Phys.Lett.93 132501
[66]Kisliuk P,Chang N C,Scott P L,Pryce M H L 1969Phys.Rev.184 367
[67]Spano F C,Silva C 2014 Annu.Rev.Phys.Chem.65477
[68]Muhammad A K,Zhang Y Y,Liu R B,Shi L J,Zou BS 2014 Chin.Phys.Lett.31 067802
[69]Zou S,Kamran M A,Shi L J,Liu R B,Guo S,Kavokin A,Zou B S 2016 ACS Photon.3 1809
[70]Bonanni A,Navarro-Quezada A,Li T,Wegscheider M,Matěj Z,HolyV,Lechner R T,Bauer G,Rovezzi M,D’Acapito F,Kiecana M,Sawicki M,Dietl T 2008 Phys.Rev.Lett.101 135502
[71]Zhang Y B,Assadi M H N,Li S 2009 J.Phys.:Condens.Matter 21 175802
[72]Oka Y,Shen J,Takabayashi K,Takahashi N,Mitsu H,Souma I,Pittini R 1999 J.Lumin.83 83
[73]Godlewski M,Yatsunenko S,Khachapuridze A,Ivanov V Y,Go?acki Z,Karczewski G,Bergman P J,Klar P J,Heimbrodt W,Phillips M R 2004 J.Alloy.Compd.38045
[74]Chang K,Peeters F M 2003 Phys.Rev.B:Condens.Matter 68 205320
[75]Katayama K,Miyajima K,Ashida M,Itoh T 2012 J.Phys.:Condens.Matter 24 325801
[76]Dey A,Yarlagadda S 2014 Phys.Rev.B:Condens.Matter 89 064311
[77]Butov L V,Filin A I 1998 Phys.Rev.B:Condens.Matter 58 1980
[78]Snoke D W 2011 Adv.Condens.Matter Phys.2011938609
[79]Moskalenko S A,Liberman M A,Dumanov E V 2011 J.Nanoelectron.Optoelectron.6 393
[80]Hague J P,Kornilovitch P E 2010 Phys.Rev.B:Condens.Matter 82 094301
[81]Hague J P,Kornilovitch P E,Samson J H,Alexandrov A S 2007 Phys.Rev.Lett.98 037002
[82]Voigt J,Spiegelberg F,Senoner M 1979 Phys.Status Solidi 91 189
[83]Bandres M A,Wittek S,Harari G,Parto M,Ren J,Segev M,Christodoulides D N,Khajavikhan M 2018 Science 359 4005
[84]Bliokh K Y,Rodríguez-Fortu?o F J,Nori F,Zayats AV 2015 Nature Photon.9 796