Electronics Guide

Material Systems

The first experimentally confirmed three-dimensional topological insulators were bismuth-based compounds, particularly Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃. These materials have relatively large bulk band gaps and well-defined surface states that can be studied using techniques such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM).

Two-dimensional topological insulators, also known as quantum spin Hall insulators, confine their conducting states to one-dimensional edges. HgTe/CdTe quantum wells provided the first experimental realization in 2007, following the 2006 theoretical proposal by Bernevig, Hughes, and Zhang, with InAs/GaSb quantum wells and the monolayer transition metal dichalcogenide WTe₂ offering additional platforms. Monolayer WTe₂ is notable for retaining its quantum spin Hall behavior to temperatures approaching 100 kelvin, far above the few-kelvin range of the semiconductor quantum wells. These systems exhibit edge conductance quantized near 2e²/h per pair of helical channels, making them attractive for applications requiring precise current control.

Device Applications

The robust surface conduction in topological insulators enables several device concepts. Spin-polarized current sources exploit spin-momentum locking to generate spin currents without external magnetic fields, potentially improving the efficiency of spintronic devices. Low-power interconnects could leverage the suppressed backscattering for energy-efficient signal transmission. Topological field-effect transistors aim to control the surface state conduction through electrostatic gating.

Challenges remain in realizing these applications, including achieving sufficiently insulating bulk behavior at room temperature and making reliable electrical contacts to the surface states. Research continues on improving material quality, developing suitable device architectures, and understanding the interplay between surface and bulk transport.

Weyl Semimetals

In Weyl semimetals, the conduction and valence bands touch at discrete points in momentum space called Weyl nodes. Near these points, electrons obey the Weyl equation, a massless version of the Dirac equation for particles with definite chirality. Weyl nodes come in pairs of opposite chirality and cannot be removed individually, making them topologically stable.

The chiral nature of Weyl fermions leads to unusual phenomena including the chiral anomaly, where parallel electric and magnetic fields pump electrons between nodes of opposite chirality, resulting in negative magnetoresistance. Weyl semimetals also exhibit Fermi arc surface states that connect the projections of bulk Weyl nodes onto the surface.

The first experimentally confirmed Weyl semimetals were the transition metal monopnictides TaAs, TaP, NbAs, and NbP, identified in 2015 through observation of their characteristic Fermi arcs. These are inversion-symmetry-breaking Weyl semimetals. Magnetic Weyl semimetals such as Co₃Sn₂S₂ and Mn₃Sn instead break time-reversal symmetry intrinsically, producing a large intrinsic anomalous Hall effect driven by the Berry curvature concentrated near the Weyl nodes.

Dirac Semimetals

Dirac semimetals possess band touching points where the conduction and valence bands meet at four-fold degenerate Dirac points. These can be viewed as overlapping Weyl nodes of opposite chirality protected by crystal symmetry. Breaking appropriate symmetries can split Dirac points into pairs of Weyl nodes.

Cd₃As₂ and Na₃Bi are prototypical three-dimensional Dirac semimetals, exhibiting extremely high electron mobilities and large, non-saturating magnetoresistance. Reported room-temperature mobilities in Cd₃As₂ exceed those of most conventional semiconductors. Their massless Dirac fermion behavior manifests in distinctive quantum oscillation patterns and optical responses that extend from terahertz to infrared frequencies.

Electronic Applications

The high mobility and unusual magnetotransport of Weyl and Dirac semimetals suggest applications in high-frequency electronics and magnetic field sensing. The chiral anomaly provides a mechanism for magnetoresistive devices, and the large Berry-curvature-driven response of magnetic Weyl semimetals is being explored for anomalous Hall and Nernst-effect sensors and for energy harvesting. Strong optical conductivity and large nonlinear responses, including a giant bulk photovoltaic effect, offer potential for broadband photodetectors and terahertz emitters and detectors. Most of these applications remain at the research stage, limited by the difficulty of isolating the topological surface or bulk contribution from ordinary conduction.

Physical Principles

In conventional superconductors, electrons form Cooper pairs with opposite momentum and spin. Topological superconductors involve pairing configurations that lead to zero-energy bound states at surfaces, vortices, or other defects. These Majorana bound states are protected by a combination of particle-hole symmetry inherent to superconductors and the topological nature of the bulk pairing.

The gap protecting Majorana states from excitations is related to the induced superconducting gap, which in candidate systems is small, on the order of a few hundred microelectronvolts or less. This places stringent requirements on temperature and disorder for observing and manipulating these states, typically demanding dilution-refrigerator temperatures in the tens of millikelvin.

Material Platforms

Several approaches exist for realizing topological superconductivity. Intrinsic topological superconductors such as Sr₂RuO₄ have been studied, though the precise nature of their pairing remains debated. Iron-based superconductors in certain configurations may host topological surface states.

Engineered systems offer more control. Semiconductor nanowires with strong spin-orbit coupling, such as InAs or InSb, proximity-coupled to conventional superconductors and subjected to magnetic fields can realize the Kitaev chain model supporting end Majorana states. Magnetic atom chains on superconducting substrates provide an alternative one-dimensional platform.

Two-dimensional topological superconductivity can emerge at surfaces of topological insulators proximity-coupled to superconductors or in hybrid structures combining quantum anomalous Hall insulators with superconductors.

Integer Quantum Hall Effect

The integer quantum Hall effect arises from the formation of Landau levels, discrete energy levels for electrons in a magnetic field. When the Fermi level lies between Landau levels, the bulk becomes insulating while chiral edge states carry current without dissipation. The number of current-carrying edge channels equals the number of filled Landau levels, directly determining the quantized Hall conductance.

Quantum Hall resistance quantization is reproducible to about one part in 10⁹ and is independent of material and sample details, which is why it underpins the practical realization of the ohm. Since the 2019 revision of the International System of Units fixed the numerical values of h and e exactly, the von Klitzing constant is likewise an exact quantity, and quantum Hall resistance standards provide a primary realization of the ohm rather than a conventional reference value. Graphene devices now allow these standards to operate at higher temperatures and lower magnetic fields than the traditional gallium arsenide heterostructures. Quantum Hall arrays also serve as precise current-to-voltage converters in electrical metrology.

Fractional Quantum Hall Effect

At very high magnetic fields and low temperatures, electron-electron interactions lead to the fractional quantum Hall effect, where the Hall resistance is quantized at fractional values of h/e². The electronic ground states in this regime are strongly correlated and can be described by exotic quantum fluids.

The fractional quantum Hall effect was discovered by Tsui, Stormer, and Gossard in 1982 and explained by Laughlin, work recognized by the 1998 Nobel Prize in Physics. Its quasiparticles carry fractional electric charge, such as e/3 at filling factor 1/3, a striking consequence of the strongly correlated ground state. Certain states, particularly the one at filling factor 5/2, are candidates to host non-Abelian anyons. These quasiparticles have exchange statistics more complex than those of bosons or fermions and could in principle serve as the basis for topological quantum computing.

Quantum Anomalous Hall Effect

The quantum anomalous Hall effect produces quantized Hall conductance without an external magnetic field, instead relying on magnetic ordering within the material. It was first observed in 2013 in chromium-doped (Bi,Sb)₂Te₃ films at temperatures around 30 millikelvin. Intrinsic magnetic topological insulators such as MnBi₂Te₄ have since raised the quantization temperature into the low single-digit kelvin range (a zero-field effect near 1.4 kelvin, extended to a few kelvin under an applied field in thin flakes), though these temperatures remain well below ambient.

The quantum anomalous Hall effect offers a pathway to dissipationless edge transport without large external magnets, and it provides the magnetic ingredient sought for engineering chiral topological superconductivity. Raising the operating temperature toward practical levels remains an active research challenge.

Photonic Topological Insulators

Photonic topological insulators are structured optical materials that support unidirectional edge modes immune to backscattering from defects and sharp bends. These can be implemented using magneto-optical materials, time-modulated systems, or synthetic gauge fields created through careful structural design.

Coupled resonator arrays, photonic crystals with designed symmetry breaking, and arrays of helical waveguides have all demonstrated topological photonic behavior, including the first observation of photonic Floquet topological insulator edge states in 2013. The helical edge states in these systems can guide light around sharp corners with strongly suppressed reflection.

Applications and Devices

Topological protection in photonics enables robust optical delay lines, filters, and interconnects that maintain performance despite fabrication imperfections. Topological lasers use edge modes to achieve single-mode operation with enhanced stability. The concept extends to nonlinear optics, where topological protection can enhance frequency conversion and soliton propagation.

Quantum photonics benefits from topological protection by preserving quantum states of light during propagation. Topological photonic circuits could serve as reliable platforms for quantum information processing with photons.

Acoustic Topological Insulators

Acoustic topological insulators confine sound to edges or interfaces while the bulk remains silent for frequencies within a band gap. These can be constructed from arrays of resonators, structured plates, or three-dimensional phononic crystals with appropriately designed geometry.

Because sound has no intrinsic spin, alternative mechanisms are required to create topological behavior. Approaches include circulating airflow to break time-reversal symmetry, coupled resonators with designed phase relationships that emulate a pseudo-spin, and structures exploiting crystalline (valley) symmetries.

Applications

Robust sound guiding through complex geometries benefits acoustic device design, enabling compact waveguides that route signals around obstacles with low loss. Topological acoustic concepts extend to vibration isolation, where protected modes can channel mechanical energy away from sensitive regions, and to one-way sound transport for acoustic isolators. Ultrasonic and sonar systems could leverage topological robustness for reliable operation in scattering environments.

Physical Mechanism

Higher-order topology arises when a material has a gapped bulk and gapped surfaces, with protected states emerging only at the intersections of surfaces. This can occur when the surface of a material is itself a topological phase, requiring its own boundary to host conducting states.

The symmetries protecting higher-order phases often involve spatial (crystalline) symmetries such as rotation or mirror operations, in addition to or instead of time-reversal symmetry. This leads to a rich variety of possible higher-order topological phases with different symmetry classifications.

Material Realizations

Higher-order topological phases have been predicted in bismuth, which may support one-dimensional hinge states on its three-dimensional crystals. Engineered systems including photonic, acoustic, and electrical circuit networks provide platforms for demonstrating higher-order topological physics with precise control.

The corner and hinge states of higher-order topological insulators could enable novel device architectures, though practical applications remain largely unexplored as the field is still developing.

Non-Abelian Anyons

The most developed topological quantum computing scheme relies on non-Abelian anyons, quasiparticles that exist only in two dimensions and have exchange statistics different from bosons and fermions. When non-Abelian anyons are exchanged, the quantum state of the system transforms in a way that depends on the order and topology of the exchange paths, not just on which particles were exchanged.

Quantum gates are implemented by braiding anyons around one another, with the resulting unitary transformation determined by the topology of the braiding pattern. Because this topology is robust against smooth deformations of the paths, the gates inherit protection against certain classes of error. The Majorana-based scheme is not by itself computationally universal; it must be supplemented by additional, non-protected operations (so-called magic states) to achieve universal quantum computation.

Majorana-Based Qubits

Majorana zero modes in topological superconductors provide one route to non-Abelian anyons suitable for quantum computing. A pair of Majorana bound states, localized at opposite ends of a topological superconductor nanowire, together form a single fermionic mode that can be either occupied or empty. The quantum information is stored in this shared occupation, which is nonlocal and therefore insensitive to local perturbations.

Major research programs at companies and universities are pursuing Majorana-based qubits. In February 2025, Microsoft announced Majorana 1, a chip built on indium arsenide and aluminum nanowire structures (which the company calls topoconductors) and a measurement-based qubit architecture. The announcement drew significant skepticism from parts of the physics community over whether the underlying Majorana states had been conclusively demonstrated, illustrating both the rapid progress and the unresolved verification challenges in the field. Broader progress includes improved materials and fabrication for semiconductor-superconductor nanowires, development of measurement and control protocols, and theoretical work on error correction and fault tolerance.

Challenges and Progress

Creating and conclusively demonstrating non-Abelian anyons remains experimentally challenging. A prominent 2018 report of quantized Majorana conductance was retracted in 2021 after independent reanalysis, underscoring how readily trivial Andreev bound states can mimic Majorana signatures. The small energy scales involved demand millikelvin temperatures and very high material quality, and performing braiding or measurement-based operations requires sophisticated device geometries and control.

Despite these challenges, topological quantum computing remains attractive because even partial hardware-level protection could substantially reduce the overhead required for quantum error correction compared with approaches that rely entirely on error-correcting codes implemented in software.

Detection and Signatures

Majorana bound states are expected to manifest in tunneling spectroscopy as a zero-bias conductance peak whose height is predicted to approach the quantized value 2e²/h at zero temperature. In practice this signature is difficult to establish unambiguously: trivial Andreev bound states and disorder effects can reproduce zero-bias peaks of similar height, so a single conductance measurement is not considered conclusive.

More definitive signatures include the 4π-periodic Josephson effect, in which the supercurrent through a topological Josephson junction has twice the period of a conventional junction in the fermion-parity-conserving regime. Interferometric measurements that probe the non-Abelian statistics directly, or correlated measurements at both ends of a wire, would provide the most compelling evidence.

Device Concepts

Majorana devices could enable new functionality in superconducting electronics. Topological Josephson junctions may exhibit unusual current-phase relationships useful for superconducting circuits. The nonlocal encoding of Majorana states suggests applications in sensing and in protocols where information is inherently distributed across spatially separated modes. These concepts remain largely theoretical, contingent on first establishing well-controlled Majorana modes.

Fabry-Perot and Mach-Zehnder Geometries

Fabry-Perot interferometers in the quantum Hall regime confine quasiparticles within a cavity defined by quantum point contacts. The resonant tunneling through the cavity depends on the number and type of anyons inside, enabling detection of fractional statistics.

Mach-Zehnder interferometers split and recombine edge-state paths, with the interference depending on the enclosed anyons. These geometries have been implemented in integer and fractional quantum Hall systems, providing evidence for fractional charge and statistics.

Non-Abelian Interferometry

Detecting non-Abelian statistics requires interferometers where the outcome depends on the order of braiding operations. This is more challenging than Abelian interferometry but is essential for verifying the non-Abelian nature of candidate particles and for implementing topological quantum computing.

Proposals exist for non-Abelian interferometry in fractional quantum Hall systems and topological superconductor networks. Realizing these experiments requires precise control over anyon positions and trajectories, as well as fast, sensitive detection.

Temperature Requirements

Many topological phenomena require cryogenic temperatures to observe, though the threshold varies widely by effect. The topological surface states of Bi₂Se₃ persist to room temperature but compete with residual bulk conduction; the integer quantum Hall effect typically needs liquid-helium temperatures of a few kelvin; the quantum anomalous Hall and Majorana experiments operate in the millikelvin range. This spread, rather than a single cutoff, shapes which applications are near-term and which are distant.

Raising operating temperatures is a key goal for practical topological electronics. Approaches include finding materials with larger bulk band gaps, engineering heterostructures to enhance topological protection, and developing more robust topological phases.

Material Quality

Topological protection does not make materials immune to all defects. While certain types of disorder are suppressed, others can degrade or destroy topological behavior. High-quality single crystals, epitaxial films, and carefully controlled interfaces are typically required for clean observation of topological phenomena.

Progress in molecular beam epitaxy, chemical vapor deposition, and other growth techniques continues to improve the quality of topological materials, expanding the range of observable phenomena and potential applications.

Integration with Existing Technology

For topological electronics to achieve practical impact, integration with conventional semiconductor technology is important. This includes developing compatible fabrication processes, establishing reliable low-resistance electrical contacts to surface or edge states, and creating scalable device architectures.

Hybrid approaches that combine topological materials with silicon or III-V semiconductors may provide pathways to practical devices while leveraging the extensive infrastructure of the semiconductor industry.