Electronics uses charge. Spintronics uses spin. Valleytronics proposes a third label: the valley. In certain crystals, electrons can live in one of two distinct momentum-space pockets — valleys — that are energetically equivalent but distinguishable. If those valleys can be selectively populated, manipulated, and read out, they can encode information. In monolayer transition metal dichalcogenides, the valley is coupled to light, to spin, and to Berry curvature in ways that make it optically addressable. That coupling is what makes valleytronics more than a theoretical curiosity.
What a valley is
In a crystal, the energy of an electron depends on its crystal momentum, described by a wavevector in the Brillouin zone. The band structure — energy as a function of momentum — has minima and maxima at particular points. A valley is a local minimum in the conduction band, or a local maximum in the valence band, around which carriers can accumulate.
In many semiconductors, there are multiple equivalent valleys related by symmetry. Silicon, for example, has six equivalent conduction-band valleys. In most contexts, those valleys are not used as an information degree of freedom, because scattering between them is fast and there is no easy way to address one valley without addressing the others.
Monolayer transition metal dichalcogenides — molybdenum disulfide, tungsten diselenide, and their relatives — are different. Their band structure has two inequivalent valleys at the corners of the hexagonal Brillouin zone, labeled K and K’. The two valleys are related by time-reversal symmetry, so they have the same energy, but they have opposite spin-orbit splitting, opposite Berry curvature, and opposite optical selection rules for circularly polarized light. Those opposites are the resource.
The reason the two valleys are special is symmetry. A monolayer transition metal dichalcogenide lacks inversion symmetry — the crystal does not look the same when flipped through its center. That broken inversion symmetry, combined with strong spin-orbit coupling from the heavy transition metal atoms, produces valley-contrasting physics. In a bilayer with inversion symmetry restored, the valley contrast is suppressed, which is why monolayer and odd-layer samples are the primary valleytronic platform, and why stacking and symmetry matter.
Valley selection by light
The most celebrated property of valley physics in monolayers is valley-selective optical excitation. Circularly polarized light with one handedness couples preferentially to one valley, and light with the opposite handedness couples to the other. Right-circularly polarized light excites excitons in the K valley; left-circularly polarized light excites excitons in the K’ valley, or vice versa depending on convention. Linearly polarized light, which is a superposition of the two circular polarizations, excites both valleys coherently.
This selection rule is not approximate. It follows from the angular momentum of the Bloch states at K and K’, and from the conservation of angular momentum when a photon is absorbed. In an ideal monolayer, the valley polarization of the emitted light — the degree to which photoluminescence retains the circular polarization of the excitation — can be high, approaching unity in some experiments at low temperature. In practice, intervalley scattering, disorder, and exchange interactions depolarize the valley population, and the measured polarization depends on temperature, sample quality, excitation energy, and whether the emission is from neutral excitons, trions, or other species.
Valley coherence is a related but distinct concept. If linearly polarized light creates a coherent superposition of K and K’ excitons, the phase between them is preserved for a time set by dephasing. That coherence can be read out as linearly polarized emission whose polarization angle tracks the excitation. Valley coherence is more fragile than valley polarization, because it requires not just that population stays in one valley, but that the phase relationship between valleys is maintained. Measuring both polarization and coherence, and their different lifetimes, is a standard part of valley experiments.
Spin-valley locking
In monolayer transition metal dichalcogenides, spin and valley are locked. The strong spin-orbit coupling splits the valence band by a large amount — on the order of hundreds of milli-electron-volts in tungsten-based materials — with opposite spin ordering in the two valleys. The conduction band is also split, though by a smaller amount, and the sign of the splitting differs between molybdenum- and tungsten-based materials.
Spin-valley locking means that the spin of a carrier is tied to its valley. A hole in the K valley has one spin; a hole in the K’ valley has the opposite spin. Flipping the valley requires flipping the spin, which requires a spin-flip scattering process. That suppression of intervalley scattering is part of why valley polarization can be long-lived in these materials, especially for holes, where the spin-orbit splitting is large.
For electrons, the story is more nuanced, because the conduction-band splitting is smaller and the ordering differs by material. In tungsten-based monolayers, the lowest conduction band in a given valley has opposite spin to the highest valence band in the same valley, which makes the lowest-energy exciton dark — a spin-forbidden transition. In molybdenum-based monolayers, the lowest exciton is bright. This bright-dark ordering, and its consequences for lifetimes and valley dynamics, is a key difference between the two families, and it is why papers specify whether they are working with a molybdenum or tungsten compound.
Valley Hall effect and Berry curvature
Valleys are not just labels; they have dynamics. The Berry curvature — a geometric property of the Bloch wavefunctions — has opposite sign in the two valleys. Berry curvature acts like a magnetic field in momentum space, deflecting carriers transverse to an applied electric field. Because the sign is opposite in K and K’, carriers in the two valleys deflect in opposite directions. The result is a valley Hall effect: a transverse valley current, with K carriers going one way and K’ carriers going the other, even though the net charge current is zero.
The valley Hall effect can be detected optically, by imaging the valley polarization that accumulates at opposite edges of a sample, or electrically, by nonlocal measurements that sense the valley imbalance. It is a hallmark of valley-contrasting Berry curvature, and it connects valleytronics to the broader field of topological and geometric transport.
Berry curvature also gives rise to an orbital magnetic moment associated with valley states, which means valley polarization can be controlled by magnetic fields and can be detected by magnetic responses. The valley Zeeman effect — the splitting of K and K’ exciton energies in a magnetic field — is a standard measurement, and its magnitude, often expressed as a g-factor, is a fingerprint of valley physics.
How valley information is lost
Valley polarization does not last forever. Several mechanisms depolarize it.
Intervalley scattering moves carriers from one valley to the other. For excitons, the electron-hole exchange interaction is a particularly efficient depolarization mechanism: the electron and hole can exchange, flipping the valley of the exciton without requiring a single carrier to scatter. This exchange-driven depolarization is fast for bright excitons in many monolayers, and it is one reason valley polarization decays on picosecond timescales in some experiments, even though single-carrier valley lifetimes can be longer.
Phonon scattering, disorder scattering, and scattering at defects also contribute. At higher temperature, phonon-assisted intervalley scattering increases, and valley polarization drops. At higher excitation density, exciton-exciton scattering adds another channel. Encapsulation, clean samples, and resonant excitation — exciting at the exciton energy rather than well above it — all help preserve valley polarization, because they reduce the excess energy and scattering that drive depolarization.
Dark excitons, because they have different exchange interactions and different scattering, can have longer valley lifetimes than bright excitons. That has motivated interest in using dark states, or resident carriers rather than excitons, as valley memories, with optical initialization and readout but longer storage.
Valleytronic devices: what would they do?
The valleytronic vision is a device that writes, stores, manipulates, and reads valley information. The components have been demonstrated in various forms, but a complete, practical valleytronic processor does not yet exist, and honest accounts distinguish demonstrations from devices.
Writing can be done optically, with circularly polarized light, or electrically, by valley-selective injection or by the valley Hall effect. Storage requires a valley lifetime long enough to be useful — ideally microseconds or longer for a memory, though shorter times may suffice for a switch or modulator if the operation is fast. Manipulation requires a way to rotate the valley pseudospin — the two-level system formed by K and K’ — using electric fields, magnetic fields, strain, or optical pulses. Readout can be optical, via the polarization of emitted light, or electrical, via the valley Hall effect or valley-selective transport.
Several proof-of-concept devices have been reported: valley Hall transistors, valley filters that preferentially transmit one valley, valley valves that block or pass valley current, and electrically tunable valley polarization in gated devices. Each demonstrates a piece of the vision. The challenges are integration, room-temperature operation, and readout. Optical readout is convenient in the lab but not ideal for a compact electronic device. Electrical readout of valley polarization is harder, because valley is not charge, and converting valley imbalance to a voltage requires a valley-sensitive mechanism.
Room temperature is a particular hurdle. Valley polarization is strongest at low temperature, where phonon scattering is suppressed. At room temperature, depolarization is faster, though monolayer materials with large spin-orbit splitting and strong excitonic effects retain measurable valley polarization in favorable conditions. Whether valleytronic devices can operate at room temperature with sufficient fidelity for applications remains an open question, and the field does not claim otherwise.
Valley physics beyond monolayers
Valley physics is not limited to monolayer transition metal dichalcogenides. Bilayer graphene, with its tunable band gap and valley-contrasting Berry curvature, is a valleytronic platform with electrical control. Moiré superlattices add a spatial dimension to valley physics, with valley-dependent moiré potentials and valley-polarized correlated states. Other hexagonal materials, including hexagonal boron nitride and some oxides, have valley degrees of freedom that are being explored.
The common thread is symmetry: valley-contrasting physics requires broken inversion symmetry, or a way to break it with a field, and a mechanism to address valleys selectively. The specific material determines the energy scales, the optical rules, and the practical trade-offs.
Where valleytronics stands
Valleytronics is best understood as a physics-rich research program with device aspirations, not as a mature technology. The fundamental physics — valley selection rules, spin-valley locking, Berry curvature, valley Hall effect — is well established in monolayer transition metal dichalcogenides. The device demonstrations are real but early. The path to a valleytronic technology that competes with charge-based electronics on speed, energy, or density is not yet clear, and it may be that valleytronics finds its first applications not as a replacement for electronics, but as a complement: in optoelectronics, where light and valley are naturally coupled, in quantum information, where valley can be an additional qubit degree of freedom, or in sensing, where valley polarization is a sensitive probe of fields and symmetry.
That is a reasonable place for a young field to be. The valley degree of freedom was, until recently, ignored. Now it is addressable, measurable, and manipulable. What it becomes next depends on whether the lifetimes can be extended, the readout can be made electrical and compact, and the integration can be made compatible with existing platforms.
Sources and further reading
For valley physics, valley selection rules, spin-valley locking, and valley Hall effect in monolayer transition metal dichalcogenides, see review articles in Nature Physics, Nature Reviews Materials, Reviews of Modern Physics, and Nature Photonics on valleytronics and on excitons in two-dimensional semiconductors. For valley polarization, coherence, and depolarization mechanisms, see review and primary literature on valley dynamics in monolayer semiconductors. For valley Hall effect and Berry curvature, see reviews on Berry phase and topological transport in two-dimensional materials. For valleytronic device concepts, see reviews on valleytronic devices and on van der Waals heterostructure devices. Where this article gives orders of magnitude for spin-orbit splitting or valley lifetimes, that reflects the spread across materials and conditions reported in that review literature.