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Vertical electron transport in semiconductor superlattice has been the focus of science and technology during the past two decades due to the potential application of superlattice in terahertz devices. When driven by electromagnetic field, many novel phenomena have been found in superlattice. Here we study the chaotic electron transport in miniband superlattice driven by dc+ac electric fields along the growth axis (z-axis) and a magnetic field tilted to z-axis using semiclassical equations of motion in the preflence of dissipation. We calculate the electron momentum by changing the magnetic field or amplitude of the terahertz field. It is shown that the momentum py(t) of miniband electron exhibits complicated oscillation modes while changing the control parameters. Poincaré bifurcation diagram and power spectrum are adopted to analyze the nonlinear electron states. Poincaré bifurcation diagram is obtained by plotting pym = py(mTac) (with m = 1, 2, 3,… and Tac the period of ac terahertz field) as functions of ac amplitude E1 after the transients decay. The periodic and aperiodic regions can be distinguished from each other since there are a large number of points in the chaotic regions. When the magnetic field is increased from 1.5 to 2 T, the Poincaré bifurcation diagram changes dramatically due to the strong effect of magnetic field on electron motion. The oscillating state of py(t) may be changed between periodic and chaotic syates. Power spectra of electron momentum py for different values of E1 (= 2.06, 2.18, 2.388, and 2.72) are calculated for a deep insight into the nonlinear oscillating mode. It is found that the power spectra of n-periodic states show peaks at frequencies ifac/n (with i = 1, 2, 3,…); the power spectra of chaotic states are very irregular with a large number of peaks. We demonstrate that the dissipation and resonance between Bloch oscillation frequency and cyclotron frequency play an important role in the electron transport process. We attribute the emerging of periodic and chaotic states in a superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode related to Bloch oscillation and cyclotron oscillation. In the case of ωB≠iωc, the time-dependent electron motion is chaotic in most regions of the parameter space. Results of the preflent paper are useful for designing terahertz devices based on the semiconductor superlattices.
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Keywords:
- terahertz /
- superlattice /
- chaos /
- bifurcation
[1] Lei X L, Horing N J M, Cui H L 1991 Phys. Rev. Lett. 66 3277
[2] Waschke C, Roskos H G, Schwedler R, Leo K, Kurz H, K. Köhler 1993 Phys. Rev. Lett. 70 3319
[3] Winnerl S, Schomburg E, Brandl S, Kus O, Renk K F, Wanke M C, Allen S J, Ignatov A A, Ustinov V, Zhukov A, Kop’ev P S 2000 Appl. Phys. Lett. 77 1259
[4] Sun B, Wang J, Ge W, Wang Y, Jiang D, Zhu H, Wang H, Deng Y, Feng S 1999 Phys. Rev. B 60 8866
[5] Wacker A 2002 Phys. Rep. 357 1
[6] Zhang Q Y, Tian Q 2002 Acta Phys. Sin. 51 1804 (in Chinese) [张启义, 田强 2002 物理学报 51 1804]
[7] Hyart T, Mattas J, Alekseev K N 2009 Phys. Rev. Lett. 103 117401
[8] Wang R Z, Yuan R, Song X M, Wei J S, Yan H 2009 Acta Phys. Sin. 58 3437 (in Chinese) [王如志, 袁瑞, 宋雪梅, 魏金生, 严辉 2009 物理学报 58 3437]
[9] Wang C, Cao J C 2012 J. Appl. Phys. 111 053711
[10] Li W, Reidler I, Aviad Y, Huang Y, Song H, Zhang Y, Rosenbluh M, Kanter I 2013 Phys. Rev. Lett. 111 044102
[11] Ignatov A A 2014 J. Appl. Phys. 116 084506
[12] Unterrainer K, Keay B J, Wanke M C, Allen S J, Leonard D, Medeiros-Ribeiro G, Bhattacharya U, Rodwell M J W 1996 Phys. Rev. Lett. 76 2973
[13] Lei X L 1997 J. Appl. Phys. 82 718
[14] Aguado R, Platero G 1998 Phys. Rev. Lett. 81 4971
[15] Bauer T, Kolb J, Hummel A B, Roskos H G, Kosevich Y, Klaus Köhler 2002 Phys. Rev. Lett. 88 086801
[16] Kosevich Y A, Hummel A B, Roskos H G, Köhler K 2006 Phys. Rev. Lett. 96 137403
[17] Bulashenko O M, Bonilla L L 1995 Phys. Rev. B 52 7849
[18] Zhang Y, Kastrup J, Klann R, Ploog K H, Grahn H T 1996 Phys. Rev. Lett. 77 3001
[19] Cao J C, Liu H C, Lei X L 2000 Phys. Rev. B 61 5546
[20] Fromhold T M, Patane à, Bujkiewicz S, Wilkinson P B, Fowler D, Sherwood D, Stapleton S P, Krokhin A A, Eaves L, Henini M, Sankeshwar N S, Sheard F W 2004 Nature 428 726
[21] Wang C, Wang F, Cao J C 2014 Chaos 24 033109
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[1] Lei X L, Horing N J M, Cui H L 1991 Phys. Rev. Lett. 66 3277
[2] Waschke C, Roskos H G, Schwedler R, Leo K, Kurz H, K. Köhler 1993 Phys. Rev. Lett. 70 3319
[3] Winnerl S, Schomburg E, Brandl S, Kus O, Renk K F, Wanke M C, Allen S J, Ignatov A A, Ustinov V, Zhukov A, Kop’ev P S 2000 Appl. Phys. Lett. 77 1259
[4] Sun B, Wang J, Ge W, Wang Y, Jiang D, Zhu H, Wang H, Deng Y, Feng S 1999 Phys. Rev. B 60 8866
[5] Wacker A 2002 Phys. Rep. 357 1
[6] Zhang Q Y, Tian Q 2002 Acta Phys. Sin. 51 1804 (in Chinese) [张启义, 田强 2002 物理学报 51 1804]
[7] Hyart T, Mattas J, Alekseev K N 2009 Phys. Rev. Lett. 103 117401
[8] Wang R Z, Yuan R, Song X M, Wei J S, Yan H 2009 Acta Phys. Sin. 58 3437 (in Chinese) [王如志, 袁瑞, 宋雪梅, 魏金生, 严辉 2009 物理学报 58 3437]
[9] Wang C, Cao J C 2012 J. Appl. Phys. 111 053711
[10] Li W, Reidler I, Aviad Y, Huang Y, Song H, Zhang Y, Rosenbluh M, Kanter I 2013 Phys. Rev. Lett. 111 044102
[11] Ignatov A A 2014 J. Appl. Phys. 116 084506
[12] Unterrainer K, Keay B J, Wanke M C, Allen S J, Leonard D, Medeiros-Ribeiro G, Bhattacharya U, Rodwell M J W 1996 Phys. Rev. Lett. 76 2973
[13] Lei X L 1997 J. Appl. Phys. 82 718
[14] Aguado R, Platero G 1998 Phys. Rev. Lett. 81 4971
[15] Bauer T, Kolb J, Hummel A B, Roskos H G, Kosevich Y, Klaus Köhler 2002 Phys. Rev. Lett. 88 086801
[16] Kosevich Y A, Hummel A B, Roskos H G, Köhler K 2006 Phys. Rev. Lett. 96 137403
[17] Bulashenko O M, Bonilla L L 1995 Phys. Rev. B 52 7849
[18] Zhang Y, Kastrup J, Klann R, Ploog K H, Grahn H T 1996 Phys. Rev. Lett. 77 3001
[19] Cao J C, Liu H C, Lei X L 2000 Phys. Rev. B 61 5546
[20] Fromhold T M, Patane à, Bujkiewicz S, Wilkinson P B, Fowler D, Sherwood D, Stapleton S P, Krokhin A A, Eaves L, Henini M, Sankeshwar N S, Sheard F W 2004 Nature 428 726
[21] Wang C, Wang F, Cao J C 2014 Chaos 24 033109
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