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Experimental Observations of Geometric Phases in Mesoscopic Narrow-Gap Semiconductor Systems R. B. Lillianfeld1, R. L. Kallaher1, J. J. Heremans1, Hong Chen2, N. Goel3, S. J. Chung3, M. B. Santos3, W. Van Roy4, G. Borghs4 1 Department of Physics, Virginia Tech, Blacksburg, VA, USA, 2 Department of Physics, University of North Florida, Jacksonville, FL, USA, 3 Department of Physics, University of Oklahoma, Norman, OK, USA, 4 IMEC (Leuven, Belgium) We experimentally investigate quantum interference in closed loop structures fabricated on ntype narrow bandgap semiconductor quantum wells with strong spin-orbit interaction (SOI). We discuss our results in terms of four quantum mechanical phases: the Aharonov-Bohm (AB) phase [1], the Altshuler-Aronov-Spivak (AAS) effect [2], the Berry’s phase [3,4,5] due to evolution of the spin degree of freedom, and the Aharonov-Casher phase [6,7,8]. Ring arrays were fabricated by electron beam lithography on an InAs two-dimensional electron system in an InAs/AlGaSb heterostructure (inset Fig. 1). In the arrays we observe both AB oscillations periodic in one flux quantum, ΦAB=h/e, as well as AAS oscillations periodic in ΦAAS=h/2e (Fig. 1) for 0.4K<T<10K. The h/e oscillations persist into the integer quantum Hall regime. Analysis of the structure of the h/e and h/2e Fourier components reveals the different physical mechanisms underlying AB and AAS oscillations. The Fourier spectra reveal a splitting at the h/e peaks (inset Fig. 1), which has been observed previously in other systems and attributed to a SOI induced Berry’s phase [3,4,5]. The magnitude of the splitting depends on the Rashba coefficient, allowing a comparison, as in [3], with the coefficient derived from Shubnikov-de Haas oscillations. In contrast to the InAs/AlGaSb system, we only observe h/2e oscillations in a hexagonal antidot lattice fabricated on an InSb two-dimensional electron system in InSb/InAlSb. A periodic change in oscillation amplitude as function of front-gate voltage could be observed. Modulations in oscillation amplitude by the gate voltage have been previously reported and have been attributed to the Aharonov-Casher phase [7,8]. The observed periodicity in gate voltage in the InSb two-dimensional electron system is similarly compatible with an interpretation based on the Aharonov-Casher phase in narrow gap systems under strong SOI [8]. Supported by DOE DE-FG02-08ER46532, and NSF DMR-0520550. Fig. 1: The low field magnetoresistance in a ring array fabricated on InAs/AlGaSb. Upper right inset: SEM image of part of a ring array. Lower inset: Fourier transform (FFT) of a low field data set showing splitting of the h/e peak. 1) Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959). 2) B.L. Altshuler, A.G. Aronov and B.Z. Spivak, JETP Lett. 33, 94 (1981). 3) B. Grbić, R. Leturcq, T. Ihn, K. Ensslin, D. Reuter and A. Wieck, Phys. Rev. Lett. 99, 176803 (2007). 4) N. Kang, E. Abe, Y. Hashimoto, Y. Iye and S. Katsumoto, J. Phys. Soc. Jpn. 76, 083704 (2007). 5) J. Yau, E.P. De Poortere and M. Shayegan, Phys. Rev. Lett. 88, 146801 (2002). 6) Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984). 7) M. König et al., Phys. Rev. Lett. 96, 076804 (2006). 8) T. Bergsten, T. Kobayashi, Y. Sekine and J. Nitta, Phys. Rev. Lett. 97, 196803 (2006).