Spontaneous valley polarization of electrons- A breakthrough in valleytronics?
Electrons in solids can have two spins, up-spin and down-spin, giving rise to a spin degree of freedom. Leveraging the availability of two spins, a major technological field, namely spintronics, emerged with applications in memory and processing devices.
it turns out that besides spin, electrons in numerous solids such as Si, AlAs, and monolayer materials such as MoS2, WSe2 harbor a valley degree of freedom. This is because electrons can occupy multiple conduction band minima that have the same energy. The availability of valley degree of freedom also gave rise to an emerging field, ‘valleytronics’ recently.
However, to make a valleytronic memory device, there are several technological and physical challenges. Even though the spin polarization of an interacting system enjoyed immense theoretical and experimental attention, valley polarization in such systems remained uncharted territory for the physics community. For example, it would be great to have control over valley polarization just by applying a gate voltage. This will allow the electrical manipulation of the memory device that is the most convenient in the technological context. In our recent work, we precisely achieve this feat: control over valley polarization via a gate voltage.
Our platform is an AlAs 2D electron system where the spin and valley degree of freedoms are not interlocked as in MoS2 or WSe2. This presents us with an unprecedented opportunity to control spin and valley separately.
We start with a system where the electrons occupy two valleys (let’s call them X and Y). This is because X and Y have the same energy. As we apply a gate voltage and lower the density below 6 x 10¹⁰ 1/cm², suddenly the valleys split up in energy. We find that Y valley becomes lower in energy compared to the X valley if we change the density very slightly to below 6 x 10¹⁰ 1/cm². Consequently, all the electrons (who were distributed between X and Y equally) now spontaneously transfer to the Y valley. This means that the valley polarization can be controlled by a gate voltage conveniently. Only a small change in gate voltage is required to transfer all the electrons from two to one valley, i.e. to change the valley polarization from 0 to 1.
Alongside the valleytronic application, our findings bring significantly new physics to the table. It turns out that the reason for the spontaneous valley polarization is electron-electron interaction. Above 6 x 10¹⁰ 1/cm², electron-electron interaction is dominated by the kinetic energy of the system. Therefore, the electrons prefer to spread between the two valleys, thus lowering the kinetic energy. Below 6 x 10¹⁰ 1/cm², the interaction switches to being dominated by inter-valley exchange interaction. Subsequently, electrons prefer to go all in one valley to minimize the inter-valley exchange. This is analogous to Bloch ferromagnetism predicted in the context of spins, discussed in my previous post.
Our finding, therefore, establishes an analogy between spin and valley degrees of freedom. Intriguingly, as discussed in my previous post, spontaneous spin polarization requires 2 x 10¹⁰ 1/cm² density, a factor of 3 lower compared to the density for spontaneous valley polarization. Further theoretical efforts are required to understand why valley polarization occurs at a higher density.
Please read more about our work in Phys. Rev. Lett. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.116601?ft=1
