What is Valleytronics?

Introduction to Valleytronics

In solid state electronics either classical or quantum, the information is carried by charge carriers such as electrons or holes. The information (0 or 1) is encoded with the presence or absence of electric charge. For the processing of information quickly, the charges must move around at high switching rates. For moving charges, it requires energy. But it produce heat and it will limit the high switching rate. This fundamental limit can be overcome by using spintronics. The semiconductor electronics uses the movement of electrons for encoding the bits of information. They didn’t use the magnetic properties or spin properties of electron. In spintronics, the magnetic spin properties of electrons are used for encoding the information instead of using charge of electrons. The spin of the electrons are used to carry the information. This reduces the fundamental limitation of today’s electronics.

Another way to overcome the fundamental limit of electronics is controlling the electric current by using valley degree of freedom (local maximum or minimum on the valence or conduction band) of electrons. It uses valence band or conduction band structure of semiconductors or insulators which possess multiple valleys such as diamond, graphene etc. This uses the wave quantum number of an electron in a crystalline material for encoding the information. The bits of information 0 and 1 are stored in different discrete values of crystal momentum. Valleytronics is the combination of two words such as valley and electronics. It is based on the quantum behavior of electrons. In terms of electronic band structure of materials, if one or more dips exists in the conduction band or peaks in the valence band, then the electronic band structure contains valleys. In valleytronics, the valley property of electrons is used to encode information without the physical movement of electrons. Some materials have different valleys. It is used for encoding information.

The electron travels through crystal as waves. These waves can be described by their different quantum numbers such as crystal momentum and spin. The electrons attain its minimum energy for zero momentum in vacuum. But the case of crystal material is different. Several theoretical and experiments are performed in different systems such as Graphene, Diamond, Molybdenumdisulphide etc.

Valleytronics-Diamond

In diamond, the electrons can attain minimum amount of energy at finite momentum along certain directions. It has 6 possible valleys of minimum energy. Figure shows the electronic band diagram of diamond. It shows the six valleys of minimum electron energy.

It has high symmetry in the crystal. At lower temperatures, the electrons stay at the valleys with minimum energy. Not only in diamond, but also in silicon and graphene have similar valleys. The valley polarized states have been created the 2D materials such as graphene, molybdenum disulphide. But they have very short life span. They stay for short time which is less than nanoseconds. But in the diamond, the electrons are relatively stable in their respective valley for a long time (300ns) at liquid nitrogen temperature, 77K .This is enough for utilizing this for information processing and experiments. Jan Isberg, Professor in the department of engineering sciences at Uppsala University says that this will prove to be the first step towards integrated valleytronic devices in the diamond. In the experiments the researchers shown that the polarized electrons can move across macroscopic distances about .7mm during the 300ns polarization relaxation. By using Hall effect, the polarization of electrons can be detected in magnetic field. As a consequence of different transport properties of different valleys, it is possible to detect the Hall angles of different polarization. The Hall angle detection of polarized electron beams is illustrated below. The polarized electrons created a line focus at the top surface which is shown in figure. The electron drifting occurs due to the applied bias between top and bottom surface. The resulting current can be measured from the strip contact. The Hall angle of polarized electrons can be measured by applying a magnetic field and moving the line focus.

Diamond is the hardest material and it is a good conductor of heat because of the strong covalent bonding and low phonon scattering. The thermal conductivity is six times than that of copper. It is also use as a semiconductor by doping to improve its electrical properties. Due to the long spin relaxation time, large band gap, valleytronic properties electrical properties, optical properties, the diamond is suggested as the material that can be used for future mechanics and quantum computer applications.

The recent paper in Nature Materials entitled “generation transport and detection of valley polarized electrons in diamond” ,Jan Isberg, Markus Gabrysch, Johan Hammersberg, Saman Majdi, Kiran Kumar Kovi, Daniel Twitchen show that the possibility of generate, transport, and detection of electrons with given valley quantum number in diamond at 77K temperature. It leads to the new opportunities of quantum control in electronic devices.

Valleytronics-Graphene

Figure below shows the band structure of graphene. Blue and red colour shows the two valleys.

Two researchers at the Naval Research Laboratory (NRL) have shown that valley degree of freedom in graphene can be polarized through scattering off a line defect. The electrons and holes could filter according to valley that they can occupy. The valley of degree of freedom gained attention in 2007. But it is difficult to fabricate the structure and valley filters. Still the valley filters are demonstrated experimentally. Figure below shows an extended line defect in graphene. The researchers from NRL say that extended line defect in graphene acts as a natural valley filter. In the near future, valley polarized currents can be generated. Valley means energy depressions in the band structure. It describes the energies of electron waves allowed by the symmetry of crystal. For graphene, these regions form two pairs of cones. The two valleys are separated by large crystal momentum. The valley degree of freedom is robust against slowly varying potentials which includes scattering due to low energy acoustic phonons that require low biased electronic devices operates at low temperature. Valley polarization can be achieved by carriers in one valley are separated spatially from carriers from the other. But it is difficult to do when the valleys have same energies. The graphene possess symmetry can achieve the spatial separation in connected graphene structure. The reflection symmetry only allows electron waves that are symmetric to pass through line defect. Anti-symmetric waves are reflected. The carrier (electron or hole) incident on line defect at high angle of incidence results in polarization approximately 100%.

Valleytronics - Molybdenumdisulphide

It consists of sulphide and molybdenum in staggered hexagonal structure.

The positions of atoms in conventional molybdenum disulphide are mirrored from one layer to the next is shown in figure (left). In the right figure, it shows the displacement of each layer from one below. It shows the great potential of valleytronics. The special energy valleys are created by the link between sulphur and molybdenum atoms. The channeling of charge carriers into valleys of set momentum in controlled way. The control of valleytronics using light is described in the papers of Nature nanotechnology. The experiments involve the semiconductor molybdenumdisulphide. The crystal structure of molybdenum disulphide creates two momentum valleys. They are not symmetric. The polarized light is used to manipulate the charge carriers. The researchers push carriers into one valley. The conduction band is the set of energy and momentum values, a charge carrier let this move freely throughout the material. Metals have electrons in the conduction band .At certain conditions; semiconductors have electrons in the conduction band such as external applied voltage etc. The charge carriers of molybdenumdisulphide (MoS2 ) are holes. Electrons are absent. The holes have mass, positive electric charge, spin etc.From the above figure, it is clear that molybdenumdisulphide has a hexagonal structure. But all atoms are not lie in same plane. i.e the lattice structure has two pieces. One is the mirror image of the other. Each contains two sulphur atom and one molybdenum atom. Each piece have conduction band and valley in the energy spectrum. The valley can trap the holes into particular momentum. They control the holes into particular way.

Researchers direct polarized light into single layer of molybdenumdisulphide. Polarized photon interact with spin of holes and nudged the holes into one of the valley. This is known as valley polarizations. The holes can stay in one valley for more than nanoseconds. The trapping of holes into the valley causes the transport of charge or electric current and spin at the same time. If two layes of molybdenum disulphide uses, then the effect will entirely vanished.

Advantages of Valleytronics

Processing speed is higher than conventional electronics.

Less power consumption.

Disadvantages of Valleytronics

Valley effect made to be practical.

Future Applications of Valleytronics