Long Spin Coherence Lengths for Quantum Devices

M.J. Yang,¹ C.H. Yang,² and Y.B. Lyanda-Geller^1,3
1Electronics Science and Technology Division
²University of Maryland
³University of Illinois

Introduction: Electron spin in semiconductor quantum devices is currently attracting great attention—in part because of potential applications for quantum information and spintronics. The critical issue for quantum computation is to maintain electron spin coherence over quantum structures. The observation of spin interference phenomena, such as quantum beating in the conductivity of ring-shaped structures is a crucial challenge in making spin-coherent quantum devices possible. Long-range spin coherence can be tested by observation of the phenomena related to the phase in the electron wave function, and lately it has become a "holy grail" in many areas of modern physics.

Spin Berry's Phase: When the parameters of a quantum system are changed and then return to their original values, the wave function acquires dynamical and geometric phases. In contrast to the dynamical phase that records how long these changes take place, the geometric phase depends only on the path taken by the parameters of the system during these changes. Since the discovery by M. Berry,¹ the geometric phases have captured the imagination of physicists and have been demonstrated experimentally in optics and atomic physics. For electronic transport in solids, it has been proposed that conducting rings provide a physical setting in which the spin Berry phase can be observed due to intrinsic spin-orbit (SO) coupling.² In particular, for rings with Rashba SO coupling, the electron momentum defines a radial in-plane Zeeman-like magnetic field (B_in in Fig. 10). This results in energy splitting for fixed wave vector k ≠ 0. When electrons circumnavigate the ring in a perpendicular external magnetic field B_ext, the values of the total magnetic field () form a cone-shaped path, so that the Berry phase is half the solid angle of the cone.

Nanofabricated Ballistic Rings: We have recently achieved a breakthrough in nanofabrication³ at NRL. Among other opportunities, it has enabled us to create spin-coherent devices for observing the spin Berry phase. The novel device proposed and realized here has a one-collimating-contact (OCC) configuration, in which the current lead is tangent to a ring, as depicted in Fig. 10. The collimating contact between the lead and the ring allows most of electrons to move essentially without diffraction. We used AlSb/InAs/AlSb single quantum wells grown by molecular beam epitaxy to create these structures. Figure 11 is a schematic diagram of the structure and the electrostatic lateral confinement of the conducting channel. The newly developed nanofabrication technique utilizes the large difference of the surface properties of InAs from that of AlSb. We first define device patterns using electron-beam lithography, and remove the 3-nm InAs cap by wet-etching. This shallow etch process results in a drastic change of the band bending and creates a conducting electron channel in the InAs quantum well. We used this technique to process OCC rings with radii (r) of 150, 250, 350, and 500 nm. The right-hand inset in Fig. 12(a) shows an atomic force micrograph (AFM) of a 350-nm ring. The lithographic width of the wire is 95 nm, and the estimated conducting channel width is 70 nm. The magnetoresistance of a 500-nm ring is shown in the left-hand inset of Fig. 12(a). The data indicate that there are four transverse modes in the wire when B_ext < 2.3 T. The estimated longitudinal wavelengths for the first three transverse modes are 44, 50, and 66 nm, smaller than the contact size determined from atomic force microscopy (AFM) images. Because of the collimation effect, these modes do not enter the ring unless B_ext reaches 0.9 T, at which magnetic focusing becomes important.

Quantum Beating of the Aharonov-Bohm Oscillations: Figure 12(a) displays the Aharonov-Bohm (AB) interference effect in the resistance of 250 nm ring at 1.9 K. There are two distinct features in DR: (1) the unambiguous h/2e oscillations around zero B_ext, and (2) the quantum beating pattern with five visible transitions to the fundamental frequency h/e. The noticeable nodes, indicated by arrows in Fig. 12(a), are aperiodic on B_ext. The observed features in ΔR are the result of the superposition of two interference signals associated with two spin eigenstates. The double frequency in the vicinity of zero magnetic field is a result of two conditions; (1) the existence of two spin states at B_ext = 0, and simultaneously; (2) the π phase difference between dynamical phases of these two spin states after a single passage in this particular ring. In other rings that we have studied, the double-frequency signal manifests itself at different magnetic fields, determined by the ratios of the spin-orbit energy and the frequency of electron rotation in those rings. For example, the AB oscillations for a 350-nm ring, shown in Fig. 12(b), indicate that the phases of two spin states differ by 1.5 π after one passage of the ring.

Implications: The interplay of the Berry's and dynamical phases leads to transitions in AB conductance between double and single frequency oscillations. The spin Berry's phase has a profound impact on the AB oscillations. In our experiments, Berry's phase determines ΔR at low B_ext, shifts the occurrence of the first in-phase beating to the higher field for r = 250 nm, and results in a dramatic turnabout feature in r = 350 nm oscillations. The observations of quantum beating and double-frequency oscillations indicate a long spin coherent length, more than 3 μm at 1.9 K.

A ring with two spin-orbit states is an interesting example of quantum two-level systems, which are currently the focus of attention as the building blocks of quantum computers. This system can also generate other prospects for future quantum technologies. Our work shows that interference signals in nanostructures can be modified by creating contacts that filter electron modes. With the on-going effort to create electrical gates to these devices, we anticipate further achievements in controlling and manipulating spin-orbit states.

[Sponsored by ONR, NSA/ARDA, and DARPA]

References

¹ M.V. Berry, "Quantal Phase Factors Accompanying Dadiabatic Changes," Proc. R. Soc. London A 392, 45-57 (1984).
² A.G. Aronov and Y.B. Lyanda-Geller, "Spin-Orbit Berry Phase in Conducting Rings," Phys. Rev. Lett. 70, 343-346 (1993).
³ M.J. Yang, K.A. Cheng, C.H. Yang, and J.C. Culbertson, "A Nanofabrication Scheme for InAs/AlSb Heterostructures," Appl. Phys. Lett. 80, 1201-1203 (2002).