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Valleytronics
Valleytronics is a developing field in quantum computing and electronic engineering that takes advantage of quantum properties of specific energy minima/maxima in a material's electronic structure. These valley-states chosen through the manipulation of electrons by magnetic and electric fields. Named the valley degree of freedom, it is robust to background noise, making it an appealing method for computing and processing quantum information. Valleytronics have formed in many materials: semiconductors, transition metal dichalcogenides (TMDs), and topological insulators.

Theory
Bounded by electric bonds, atoms build the crystal structure of materials, determining an electron's conduction property: drift current, diffusion, and magnetic moment. In semiconducting materials, the conduction band contains discrete packets of crystal momentum states where an electron can exist based on its energy. These momentum states are "polarized" into "valleys" where charge carriers are trapped in an energy well. Analogous to the Pauli exclusion principle, and the coulomb blockade effect, valley blockades occur in 2D semiconductors, wherein electrons prefer existing in these momentum states of their crystal lattice. By having one or more valley-states in a conduction band, quantum properties, superposition and entanglement of valley-states occur. Quantum properties form in pseudo spins, a net magnetic moment induced by the orbital angular momentum of the crystal when it is in a specific valley state.

Methods of Control
Experimental attempts, realizing valley-states noted the following phenomena. These caused the development of devices that harness and are wary of their effects.

Valley polarization
Transition metal dichalcogenides systems are light-dependent, demonstrating the ability to choose valley-states. Wherein right circularly polarized light couples to the +K valley and left circularly polarized light couples to −K valley. This valley polarization, η, can be experimentally read out by measuring the circularly polarized components of the emitted photoluminescence intensity, PL(σ±), and can be expressed as

η = (PL (σ +) - PL (σ -)) / (PL (σ +) + PL (σ -)

Valley polarization amounts to having the ability to read and process quantum information as these valley-states k- and k+ perform as up and down states.

Valley Hall Effect
When charge carriers from different valleys are present to an electric field perpendicular to their motion, they exhibit Hall currents in opposite directions. Hall currents are intrinsically a quantum phenomenon, with the realization of discrete hall current. Specifically, the valley hall effect generates current with charge carriers with up/down spin directly related to a valley-state. The valley hall effect is critical for spin transportation and spin polarization. Furthermore, measuring the Hall current allows for the differentiation of valley states, making it an attractive degree of freedom for developing quantum information processing. The first demonstration of the valley Hall effect in monolayer MoS2 shows this exciting property. In MoS2, optical polarization information (σ) converts to electrical information (hall voltage).

Zeeman Effect
In valleytronic materials, like transition metal dichalcogenides (TMDs) or monolayer semiconductors, electrons can occupy different energy levels. The Zeeman effect refers to splitting energy levels due to the interaction between the magnetic moment of electrons and an external magnetic field. When a magnetic field is applied, the energy levels of the different valleys shift, causing a valley splitting. Meaning that electrons in distinct valleys will have different energy levels. Valley splitting is the method of using magnetic fields to determine a valley-state.

The main problem with these control methods is that they last in the order of pico-nanosecond time. Most valleytronic research focuses on developing materials and devices that use or lengthen this excitation time.

Applications
Researchers and engineers utilizing these methods of control, developing novel methods of computing information processing and energy efficiency.

Valley transistors
As we are at the end of Moore's law, new methods of processing information must overcome the ordinary transistor. More compact, energy-efficient, and robust models have appeared in valleytronics. In FET transistors, the source is where the current enters, the drain is where it exits, and the gate controls the flow by modulating the conductivity of the semiconductor channel between them. Valley transistors use the same concepts, but polarized light dictates a channel's conductive property instead of voltage. MoS2, a 2D-dimensional material, is a critical aspect of these devices that serves as the channel for conducting. In order to transport the information of the valley-state, they use plasmonic antennae. These are nanostructures that can enhance the interaction of light with materials. In valley transistors, they are chiral and have circular dichroism properties. Circular dichroism refers to the absorption of left-right-handed circularly polarized light by a material. Chiral plasmonic antennae with circular dichroism properties selectively inject charge carriers into the MoS2 channel based on the polarization of incoming light. Meaning they interact differently with left-right-handed circularly polarized light. This property has achieved valley-selective charge in the MoS2 channel.

Optoelectronics
Conversely, the complementary effect is possible, where electrical information converts into optical polarization. One application of this concept is the development of valley LEDs. A valley LED is a light-emitting diode where the emission polarization can be controlled by external factors, for example gate voltage. A valley LED provides a means to manipulate the emission polarization of the emitted light. In the design of valley LEDs, the structure of the p–n junction plays a pivotal role in influencing the emitted light's characteristics. When the p–n junction aligns with a particular axis of the material's structure, forward-bias results in a valley current flowing parallel to the bias direction. The current induces the injections valley-polarized electrons and holes into the junction, culminating in a circularly polarized light emission.