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We have measured weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations in the two-dimensional electron gas formed in InGaAs/AlInAs heterostructures. This system possesses strong spin-orbit coupling and a high Landé factor. Phase-coherence lengths of 2 - 4 μm at 1.5 - 4.2 K are extracted from the magnetoconductance measurements. The analysis of the coherence-sensitive data reveals that the temperature dependence of the decoherence rate complies with the dephasing mechanism originating from electron-electron interactions in all three experiments. Distinct beating patterns superimposed on the Aharonov-Bohm oscillations are observed over a wide range of magnetic fields, up to 0.7 Tesla at the relatively high temperature of 1.5 K. The possibility that these beats are due to the interplay between the Aharonov-Bohm phase and the Berry one, different for electrons of opposite spins in the presence of strong spin-orbit and Zeeman interactions in ring geometries, is carefully investigated. It appears that our data are not explained by this mechanism; rather, a few geometrically-different electronic paths within the ring’s width can account for the oscillations’ modulations.

The electronic characteristic scale on which quantum interference can occur in a meso-scopic sample is the phase-coherence length

Here we focus on nanostructures in which the electrons are subjected to significant spin-orbit coupling, and report on studies of weak antilocalization (WAL) effects, uni- versal conductance fluctuations (UCF), and Aharonov-Bohm (AB) oscillations in the magnetoresistance data of mesoscopic samples of InGaAs/AlInAs. This material is well- known for its strong Rashba-type spin-orbit interaction [^{−11} eV m [

The spin-orbit interaction, coupling the momentum of the electron to its spin, in conjunction with a Zeeman field gives rise to Berry phases [

However, one should exercise caution when adopting the interpretation based on the effect of Berry phases for beating patterns superimposed on Aharonov-Bohm oscilla- tions. First, the Aharonov-Bohm oscillations appear at arbitrarily small magnetic fields, while the effect of the Berry phase reaches its full extent only in the adiabatic limit, realized when both

The remaining part of the paper is organized as follows. Section 2 describes the samples’ preparation and the measurements techniques. Section 3 includes the results of the measurements of the antilocalization effects (Section 3.1), the universal con- ductance fluctuations (Section 3.2), and the Aharonov-Bohm oscillations (Section 3.3). In each subsection we list the values of the coherence length extracted from the data. In the last subsection there we combine the results of all measurements to produce the dependence of the dephasing rate in our samples on the temperature (Section 3.4), from which we draw the conclusion that it is electron-electron scattering that dephases the interference in our InGaAs/AlInAs heterostructures. Section 4 presents our at- tempts to explain the beating pattern of the AB oscillations displayed in Section 3.3. Our conclusions are summarized in Section 5.

Three types of samples were prepared, all comprising a single basic material. The schematic drawing of the layers in the InGaAs/AlInAs heterostructures used in our studies is given in ^{5} cm^{2}/(V sec) were deduced from resistivity and Hall-effect measurements taken at 4.2 K. These values were calculated for the samples which have a significant contribution of the parallel conduction of low mobility layers below the 2DEG in the quantum well, and therefore are different from the actual values of the mobility and carrier density of electrons in that quantum well.

Measuring each of the coherence effects requires samples of different geometry. We have used a ^{4}He cryostat at temperatures in the range of

Weak-localization corrections to the average conductivity arise from interference between pairs of time-reversed paths that return to their origin. Application of a mag- netic field that destroys time-reversal symmetry suppresses the interference and thus increases the conductivity. Antilocalization appears in systems in which the electrons are subjected to (rather strong) spin-orbit coupling. Then, the interference-induced correction to the conductivity is reduced, because the contribution of time-reversed paths corresponding to wave functions of opposite spins’ projections is negative, while that of the equal spin-direction time-reversed paths remains positive. The reason is that upon following a certain closed path, the electron’s spin is rotated by

Measuring the magnetoconductivity as a function of the magnetic field allows for an accurate estimate of the phase-breaking length

from zero, one observes a decreasing conductivity originating from the suppression of antilocalization, followed by an increase due to the destruction of localization. Indeed, the line shapes at small magnetic fields measured at 1.4 K and 4.2 K, are nicely fitted to the curves calculated from the theoretical expression derived in Refs. [

where

These parameters comprise

The comparison of the data with Equation (1) has yielded

As seen in

Equation (1) derived in Refs. [

Finally we note that for

Like weak localization and weak antilocalization effects, the universal conductance fluc- tuations of a mesoscopic system result from interference of the electronic wave func- tions corresponding to pairs of time-reversed paths. As such, these fluctuations are do- minated by the phase-coherence length

where

The phase-coherence length is derived from the magnetic correlation field

where

(

where

The resistance of the shorter Hall bar, measured at 1.52 K and at 4.2 K, is shown in

Perhaps the most conspicuous manifestation of the Aharonov-Bohm effect [

The average area of the two rings we measured (see Section 2 and ^{−1}. The magnetoresistance of our ring A as a function

of the magnetic field measured at 1.5 K is portrayed in ^{−1}, consistent with the estimated periodicity for the AB oscillations. On top of these, one sees beats, with a frequency of about 40 Tesla^{−1}. These observations are consistent with the Fourier transform of the resistance, shown in ^{−1}. Panel (b), based on data points from the range 0.65 - 0.7 Tesla, has two peaks, at ^{−1} and at ^{−1}. Analysis of data between these ranges shows a gradual decrease of the (average) AB frequency and a gradual increase of the splitting between the two peaks. Although the coherence length of our rings is of the order of the ring circumference (see below), ^{−1}, probably corresponding to the second harmonic of the AB oscillations.

The splitting of the main peak in the power spectrum is the hallmark of the beating pattern [

The Fourier transforms of the magnetoresistance of our sample B are similar to those shown in

magnetic fields has been chosen because it contains mainly an amplitude of only a “single” harmonic. According to Ref. [

where

The dephasing rate of the electrons,

It is related to the coherence length by

Using the diffusion coefficient,

The two-dimensional electronic density of states, _{0.25}In_{0.75}As to be

The symbols in

The combined effect of strong spin-orbit and Zeeman interactions, in the adiabatic limit, is expected to induce a Berry phase on the spin part of the electronic wave function. The possibility that this geometrical phase can be detected in power spectra of the magnetoconductance oscillations of mesoscopic rings has been pursued quite actively, both theoretically and experimentally (see Section 1 for a brief survey). An interesting (theoretical) observation has been made in Ref. [

Our data are not sufficient to examine this observation. We have therefore analyzed the simpler expression given in Ref. [^{1} subjected to strong spin-orbit and Zeeman interactions,

This expression is valid in the adiabatic limit, pertaining to the case where, as mentioned in Section 1, both

where

where

The effective electron mass

For our samples’ parameters

The two panels in

(13), the Berry phase is of order

^{−1}. In our samples

cally, one has

ing beats have even smaller frequencies, of order 0.14 Tesla^{−1} and 1 Tesla^{−1}, respectively. These frequencies seem consistent with the envelopes of the fast oscillations in

We have measured weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations in the two-dimensional electron gas formed in InGaAs/ AlInAs heterostructures. This system possesses strong spin-orbit coupling and a high Landé factor. Phase-coherence lengths of

Distinct beating patterns superimposed on the Aharonov-Bohm oscillations are ob- served over a wide range of magnetic fields, up to 0.7 Tesla at the relatively high tem- perature of 1.5 K. The Berry phase is much smaller than the AB phase, and therefore cannot be responsible for these beats. Qualitatively, the theory of Aronov and Lyanda- Geller [

We thank Y. Lyanda-Geller for very useful comments. This work was partially support- ed by the Israeli Science Foundation (ISF) grant 532/12 and grant 252/11, and by the infrastructure program of Israel Ministry of Science and Technology under contract 3-11173.

Tzarfati, L.H., Hevroni, R., Aharony, A., Entin-Wohlman, O., Karpovski, M., Shelukhin, V., Umansky, V. and Palevski, A. (2017) Dephasing Mea- surements in InGaAs/AlInAs Heterostructures: Manifestations of Spin-Orbit and Zee- man Interactions. Journal of Modern Physics, 8, 110-125. http://dx.doi.org/10.4236/jmp.2017.81010