Download Aharonov-Bohm-type quantum interference effects in narrow gap

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.
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