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In a semi-infinite crystal, the periodic potential is destroyed at the surface, and the electronic wave functions exponentially decay from the surface to both sides. Such localized electronic states in the vicinity of the surface are known as Tamm surface states. In analogy to the electronic Tamm states, in recent years, optical Tamm states have been found at the surface of the truncated photonic crystal composed of two kinds of dielectrics. Very recently, novel types of optical Tamm states including backward Tamm states in which the phase velocity and the group velocity of optical waves are in the opposite direction have been discovered in the photonic structures containing metamaterials. In fact, the concepts in electronic field and photonic field can inspire each other. Many unique phenomena in photonic systems can also be mapped to the electronic systems. In this paper, we study the novel types of electronic Tamm states in electronic systems, inspired by the novel types of optical Tamm states in photonic structures. #br#At first, comparing Maxwell equations with Schrodinger equations, one can see a correspondence between the parameters in electromagnetic system and the parameters in the electronic system. In particular, Hg1-xCdxTe semiconductors with special electronic band structures can realize various electronic materials in analogy to the optical metamaterials with various values of permittivity and permeability. By tuning the parameter x of Hg1-xCdxTe, we obtain a variety of metamaterial-like electronic materials, in analogy to the single-negative metamaterials, the double-negative metamaterials and the near-zero-index metamaterials in optical systems. Then, inspired by the one-dimensional heterostructures with metamaterials that generate optical Tamm states, we design a one-dimensional electronic heterostructure consisting of Hg0.847Cd0.153Te and CdTe/HgTe superlattice. When Hg0.847Cd0.153Te is analogous to the double-negative metamaterial, we find the backward electronic Tamm states in which the phase velocity and the group velocity of electronic waves are in the opposite directions. When Hg0.847Cd0.153Te is analogous to the near-zero-index metamaterial, we find a novel electronic Tamm states in which the amplitude of the electronic probability decays very slowly in Hg0.847Cd0.153Te. The discovery of these new types of electronic Tamm states enlarges our knowledge of electronic surface states.
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Keywords:
- electronic Tamm states /
- band inversion /
- Hg1-xCdxTe
[1] Tamm I Y 1932 Phys. Z. Sowjetunion 1 733
[2] Ohno H, Mendez E E, Brum J A, Hong J M, Agulló R F, Chang L L, Esaki L 1990 Phys. Rev. Lett. 64 2555
[3] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
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[5] Yeh P, Yariv A, Cho A Y 1978 Appl. Phys. Lett. 32 104
[6] Yeh P 1988 Optical Waves in Layered Media (New York: Wiley) pp337-344
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[14] Cheianov V V, Vladimir F, Altshuler B L 2007 Science 315 1252
[15] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
[16] Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772
[17] Zandbergen S R, Michiel J A 2010 Phys. Rev. Lett. 104 043903
[18] Jelinek L, Baena J D, Voves J, Marquesn R 2011 New J. Phys. 13 083011
[19] Kane E O 1957 J. Phys. Chem. Sol. 1 249
[20] Bastard G 1988 Wave Mechanics Applied to Semiconductor Heterostructures (New York: Wiley) pp41-48
[21] Kowalczyk S P, Cheng J T, Kraut E A 1986 Phys. Rev. Lett. 56 1605
[22] Johnson N F, Hui P M, Ehrenreich H 1988 Phys. Rev. Lett. 61 1993
[23] Mecabih L, Amrane N, Belgoumene B 2000 Physica A 276 495
[24] Yu Y F, Lu C, Wei L Y, Lin S 2012 Chin. Phys. B 21 017804
[25] Jiang H T, Chen H, Li H Q, Zhang Y W 2004 Phys. Rev. E 69 066607
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[1] Tamm I Y 1932 Phys. Z. Sowjetunion 1 733
[2] Ohno H, Mendez E E, Brum J A, Hong J M, Agulló R F, Chang L L, Esaki L 1990 Phys. Rev. Lett. 64 2555
[3] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[4] John S 1987 Phys. Rev. Lett. 58 2486
[5] Yeh P, Yariv A, Cho A Y 1978 Appl. Phys. Lett. 32 104
[6] Yeh P 1988 Optical Waves in Layered Media (New York: Wiley) pp337-344
[7] Veselago V G 1968 Sov. Phys. Usp. 10 509
[8] Pendry J B, Holden A J, Stewart W J 1996 Phys. Rev. Lett. 76 4773
[9] Pendry J B, Holden A J, Robbins D J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
[10] Monticone F, Alù A 2014 Chin. Phys. B 23 047809
[11] Martorell J, Sprung D W L, Morozov G V 2006 Pure Appl. Opt. 8 630
[12] Malkova N, Ning C Z 2006 Phys. Rev. B 73 113113
[13] Namdar A, Shadrivov I V, Kivshar Y S 2007 Phys. Rev. A 75 053812
[14] Cheianov V V, Vladimir F, Altshuler B L 2007 Science 315 1252
[15] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
[16] Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772
[17] Zandbergen S R, Michiel J A 2010 Phys. Rev. Lett. 104 043903
[18] Jelinek L, Baena J D, Voves J, Marquesn R 2011 New J. Phys. 13 083011
[19] Kane E O 1957 J. Phys. Chem. Sol. 1 249
[20] Bastard G 1988 Wave Mechanics Applied to Semiconductor Heterostructures (New York: Wiley) pp41-48
[21] Kowalczyk S P, Cheng J T, Kraut E A 1986 Phys. Rev. Lett. 56 1605
[22] Johnson N F, Hui P M, Ehrenreich H 1988 Phys. Rev. Lett. 61 1993
[23] Mecabih L, Amrane N, Belgoumene B 2000 Physica A 276 495
[24] Yu Y F, Lu C, Wei L Y, Lin S 2012 Chin. Phys. B 21 017804
[25] Jiang H T, Chen H, Li H Q, Zhang Y W 2004 Phys. Rev. E 69 066607
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