Semiconductor Spintronics and Quantum Computation

The unique interplay between semiconducting bulk properties and ferromagnetism via exchange interaction, first discovered in europium chalcogenides (e.g. EuO) and semiconducting spinels (e.g. CdCr₂Se₄), attracted much attention and studied extensively in the 1960’s and 70’s [1,2]. The interest in this first generation of ferromagnetic semiconductors gradually waned in the 80’s, partly due to the difficulty associated with the preparation of single crystals and partly due to its low ferromagnetic transition temperatures, which made it difficult for practical room temperature applications.

Experiments to explore the transfer of a spin-polarized electric current within small devices have been ongoing for nearly 30 years. But attaining the same level of exquisite control over the transport of spin in micro- or nanoscale devices, as currently exists for the flow of charge in conventional electronic devices, remains elusive. Much has been learned since the time of the first demonstrations of spin polarized tunneling by Tedrow and Meservey. During this period we have witnessed the transformation of spin-based electronic devices from laboratory experiments to the realm of commercially available products. This has been driven especially, just in this past decade, by the robust phenomena of giant magnetoresistance (GMR) [1]. Even more recently, magnetic tunnel junction devices, involving transport of spin polarized electrons across interfaces, have proceeded to commercial development [2]. Meanwhile, spin injection devices — and by “injection” we here denote transferal of spin-polarized carriers into an otherwise nonmagnetic conductor (or semiconductor) — have not reached a similar, commercially viable, state of maturation. In fact, it is fair to say that, at present, even the fundamental physics and materials science of the spin injection process remains in need of significant elucidation.

Spin polarized transport in semiconductors presently attracts a great deal of interest. For the past five years or so, several research groups have tried to achieve efficient injection of spin polarized electrons into non-magnetic semiconductors using ferromagnetic metals as spin injecting contacts. All these experiments have failed to produce conclusive results; the reasons for this lack of success were outlined in Chap. 2 and in [1]. The main outcome of the theory for spin injection given in Chap. 2 is that the spin polarization a in the semiconductor is simply not proportional to the bulk spin polarization β in the ferromagnet. This is mainly due to the different conductivities of semiconductor (σ _sc ) and ferromagnet (σ _fm ) and to the short spin scattering length λ _fm in the ferromagnet.

The drive to build a framework for coherent semiconductor spintronic devices provides a strong motivation for understanding the coherent evolution of spin states in semiconductors [1,2]. The fundamental aim in this context is to discover regimes in which carefully prepared quantum states based upon spin can evolve coherently long enough to allow the storage, manipulation and transport of quantum information in devices. Such devices might exploit, for instance, the interference between two coherently-occupied spin states whose time variation occurs at a frequency ΔE/h, where ΔE is their energy separation. Since typical spin splittings in semiconductors are in the range of meV, the rapidly varying oscillations of a classical observable such as the spin orientation (magnetization) can occur at GHz-THz frequencies, providing the basis for ultrafast devices. Another possibility is that this quantum interference may actually be used as part of a calculation within the context of quantum computing algorithms [3]. It is hence crucial to develop experimental tools that probe spin coherence in semiconductors and that allow one to map out schemes for its manipulation, storage and transport. The previous chapter formulated the theoretical foundations underlying coherent spin dynamical phenomena in semiconductors and introduced specific mechanisms that may be responsible for spin relaxation and spin decoherence, pointing out the important physical distinctions between longitudinal and transverse spin relaxation times (T ₁ and T ₂, respectively) [4]. We note that it is the latter timescale that is of direct relevance to coherent spin devices and hence we focus on experimental techniques that probe the transverse spin relaxation time in semiconductors.

Direct-gap semiconductors interact extremely strongly with light, absorbing energy in the promotion of electrons into the conduction band. The lifetime of the photoexcited electrons is several nanoseconds, set by competing processes of radiative and non-radiative recombination. Of increasing interest in the last decade, is the phase of the photoexcited electrons (or the interband coherence) induced by the oscillating optical field (Fig. 6.1). The time for this phase memory to be lost is much shorter than the carrier lifetime, typically less than 100 fs in bulk materials at room temperature, and is controlled by the range of possible phase scattering events accessible to the carriers. By freezing out the lattice vibrations at low temperatures, and quantum confining the carriers in volumes smaller than their de Broglie wavelengths, it is possible to reduce the phase scattering. Such confinement produces quasi-atomic energy levels whose separation restricts the events that can cause phase scattering. However even in fully-confining semiconductor quantum dots at liquid helium temperatures (see Chap. 9), the phase decay is only slowed by a factor of 200 [1]. Thus although such quantum dot systems have been suggested as all-solid-state elements for quantum computing applications, they are still prone to dephasing events which cause errors.

Spintronics and Quantum Computation are both newly minted terms, and concepts, in physics. Depending on your point of view, they are almost exactly the same, or they are completely different. They both may be defined as a concept for using discrete, quantized degrees of freedom in a physical device to perform information-processing functions. But from this point of overlap, these two concepts are both more and less than the other. Spintronics concerns itself, of course, only with spins, spins in the solid state; quantum computing encompasses almost every possible quantum phenomenon in nature. But within its narrower setting, spintronics has a broader agenda, to facilitate and improve all possible forms of information processing using spin-based devices. Quantum computing actually has a narrower agenda: to devise and implement quantum-coherent strategies for computation and communication.

Coherent manipulation, filtering, and measurement of electronic spin in quantum dots and other nanostructures are new technologies which have promising applications both in conventional and in quantum information processing and transmission. We review the spintronics proposal for quantum computing, in which electron spins in quantum confined structures play the role of the quantum bits (qubits), and discuss the essential requirements for such an implementation. We describe several realizations of one- and twoqubit quantum gates and of state preparation and measurement, based on an all-electrical scheme to control the dynamics of spin. We discuss recently proposed schemes for using a single quantum dot as a spin filter and spin read-out device, and show how the decoherence time can be measured in a transport set-up. We address the issue of spin decoherence due to non-uniform hyperfine interactions with nuclei and show that for electrons confined to dots the spin decay is non-exponential. Finally, we discuss methods for producing and detecting the spin-entanglement of electronic EPR pairs, being an important resource for quantum communication.

Quantum cryptography has emerged as a significant field of study over the last fifteen years, because it offers the promise of private communication whose security is assured by the laws of quantum mechanics. Most implementations of quantum cryptography so far have used a protocol introduced by Bennet and Brassard, generally known as BB84 [1]. The message can be encoded on the polarization state of single photons, with a random choice between two non-orthogonal polarization bases when the photons are sent and received. Since an eavesdropper does not know what bases have been chosen, any measurement she makes will impose a detectable back-action on the states of the transmitted photons. Using error correction and privacy amplification, the communicating parties can distill the transmitted message into a secure key, about which the eavesdropper knows arbitrarily little.