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A theoretical condensed matter physicist who coauthored a quantitative description of quantum Hall edge states. The theory combines charge screening with confinement in a two-dimensional electron gas, predicting alternating compressible and incompressible regions. It helps explain why edge transport depends on electrostatics as well as the bulk filling.^[ref]

An experimental condensed matter physicist who coauthored images of coherent electron flow from a quantum point contact. A charged scanning tip locally depleted a two-dimensional electron gas and backscattered carriers; recording the resulting electrical conductance change as the tip moved produced a spatial response map. The experiment revealed mode-dependent angular patterns and branching while probing inelastic scattering.^[ref]

An experimental physicist who coauthored the 1988 observation of quantized electrical conductance in quantum point contacts. A gate narrowed a constriction in a two-dimensional electron gas. The conductance changed in steps as transverse conducting modes became available, making a controllable semiconductor device a direct demonstration that a narrow channel carries current through discrete quantum modes.^[ref]

An injector and collector aligned across an open two-dimensional electron gas. A direction-sensitive signal between them probes ballistic electron transport. Contact resistance and diffuse current backgrounds must be separated from the direct beam contribution.

David Thouless coauthored a theory connecting the Hall conductivity of a two-dimensional electron gas to a topological invariant. In a uniform magnetic field and periodic potential, the Kubo formula can be written so that quantization becomes explicit when the Fermi energy lies in a gap. The integer character of the response explains why continuous changes of microscopic parameters need not continuously change the Hall plateau. A transition between distinct plateaus requires leaving the conditions that protect that quantization.^[ref]

A physicist who researched superfluidity and superconductivity in thin systems.^[ref]

A theoretical condensed matter physicist who coauthored a theory of quantum Hall edge states with B. I. Shklovskii and L. I. Glazman. Their electrostatic treatment predicts strip widths and positions, providing a spatial model for how the edge of a confined two-dimensional electron gas carries current.^[ref]

A small electron island confined laterally by depletion gates in an already vertically confined two-dimensional electron gas. Tunnel barriers couple it to reservoirs, and a plunger gate tunes charge occupation. Coulomb blockade and orbital confinement resolve individual electron additions.

For a two-dimensional electron gas in a perpendicular magnetic field of magnitude $B>0$, the filling factor is the electron number per unit area $n_s$ divided by the orbital degeneracy per unit area $eB/h$ of one spin branch of a Landau level. Here $e$ is the positive elementary charge and $h$ the Planck constant. The nominal filling factor varies continuously with $n_s/B$; it need not be an integer.

An experimental physicist who coauthored the 1980 report of quantized Hall resistance. A two-dimensional electron gas in a silicon transistor exhibited reproducible Hall-resistance values, enabling comparison with fundamental constants. The result showed why the microscopic quality and confinement of a semiconductor device could matter to precision electrical measurement.^[ref]

An experimental physicist who coauthored electron-focusing measurements using two quantum point contacts. One contact injected electrons into a two-dimensional electron gas, and the other collected them after a magnetic field bent their trajectories. Focusing peaks and additional interference structure connected the device geometry with ballistic motion and the quantum coherence of electronic edge states.^[ref]

An experimental physicist who studied composite fermions using patterned antidot arrays in a two-dimensional electron gas. Near half filling of a Landau level, periodic arrays produced geometric resonances when the effective orbits matched the array spacing; random arrays did not. This comparison tested the orbital picture through a deliberately controlled scattering geometry.^[ref]

Klaus von Klitzing coauthored the discovery of precisely quantized Hall resistance in a silicon device containing a two-dimensional electron gas. In a strong magnetic field, resistance plateaus followed values set by $h/e^2$ and an integer filling index, rather than changing smoothly with every microscopic device parameter. The 1980 work used the reproducibility for a precision-constants measurement. The integer quantum Hall effect thus connects a collective electronic state with a robust electrical reference.^[ref]

A physicist.^[ref]

Konstantin Novoselov coauthored experiments showing that atomically thin graphene can operate as an electrically controlled conducting sheet. A gate changes its carrier population, making a single carbon layer an accessible two-dimensional electron gas. The 2004 work demonstrated a field effect and ballistic transport over submicrometre distances even at room temperature. It turned an isolated atomic layer into a device for testing transport in two dimensions.^[ref]

A physicist researching experimental condensed matter physics.^[ref]

A theoretical condensed matter physicist who coauthored a self-consistent electrostatic theory of quantum Hall edge states. The confined two-dimensional electron gas separates into alternating compressible and incompressible strips. Their positions and widths connect an applied gate potential to the actual conducting edge structure.^[ref]

An experimental physicist who, with collaborators, used scanning tunnelling microscopy to image standing waves in the electronic surface states of copper. Steps and defects scattered the two-dimensional electron gas, producing spatial oscillations in the local density of states. Measuring those patterns gave access to the electrons' dispersion relation, making a quantum-wave property visible in a real-space experiment.^[ref]

An experimental condensed matter physicist who coauthored the observation of quantized Hall resistance in a two-dimensional electron gas. A silicon transistor supplied the confined carriers; Hall-voltage measurements revealed plateaus insensitive to device geometry. The integer quantum Hall effect therefore connected an electronic transport experiment to precision determination of fundamental constants.^[ref]

A two-dimensional electron gas supplied by remote donors in aluminium gallium arsenide and confined on the gallium arsenide side of a heterojunction. An undoped spacer separates ionized donors from mobile carriers, reducing impurity scattering. A conduction-band band offset and self-consistent band bending create the confinement well.

Modulation doping places ionized dopants away from the region in which their supplied charge carriers move. In a semiconductor heterostructure, band alignment can transfer electrons from a doped layer into a nearby lower-energy channel.

This separation reduces scattering from nearby charged impurities while maintaining a substantial mobile-carrier population. It supports a two-dimensional electron gas and the channel of a high-electron-mobility transistor. Separation is not complete decoupling: the donors still set electrostatics, and remote impurities, interfaces and other scattering mechanisms can still limit charge carrier mobility.

A metal-oxide-semiconductor field-effect transistor, with an insulating layer separating the gate from the semiconductor. Its gate electric field controls the channel's mobile charge carriers; a semiconductor inversion layer can form a two-dimensional electron gas.

A GaAs–AlGaAs semiconductor heterostructure confines electrons normal to the interface in a semiconductor quantum well. Remote modulation doping supplies a high-mobility two-dimensional electron gas. Negative split gates deplete it laterally, leaving a narrow quantum point contact with discrete transverse subbands and continuous longitudinal momentum. A single occupied subband requires transverse excitation gaps larger than thermal and applied-bias energies.

Take $e>0$ and count one spin-resolved channel. In a length $L$, right-moving states have density $Ldk/(2\pi )$; each contributes charge current $-e{v}_k/L$. ThusThe second expression is the right reservoir's left-moving contribution expressed in the same left-to-right conventional-current sign. Since $v_{k}dk=dE/\hslash$,The limit needs $k_{B}T,|eV|\ll \mu -E_0$ and ballistic transport. Velocity cancels the one-dimensional state density. Two degenerate spin channels give $2e^2/h$, not an extra factor hidden in the quoted single-channel result.

For elastic phase-coherent scattering, expand each incident flux-normalized mode in outgoing lead modes. Its transmitted fraction is $|(t_E{)}_{nm}{|}^2$; sum over all open outgoing $n$ and occupied incident $m$. Linearizing the reservoir occupations gives the Landauer formulaThe source's $T_E^{+}$ denotes this amplitude matrix, not temperature or a probability matrix. Flux normalization is essential: ordinary wave-amplitude ratios need a velocity factor. Reservoirs equilibrate, contacts supply incoming Fermi distributions, and inelastic processes within the channel are neglected. Spin is included among channel labels. At $T\to 0$, only transmissions at $\mu$ contribute; perfect channels each add one quantum. This is a two-terminal conductance including contact resistance, even with no internal backscattering.

Trace I has steps near integer $2e^2/h$ as less-negative gate voltage opens successive spin-degenerate subbands. At the printed parallel field $11\mathrm{T}$, Zeeman splitting separates the two spin thresholds, allowing approximately half-sized steps in the plotted units; the onset also shifts. Thermal broadening, imperfect transmission and unresolved thresholds round the plateaux. A parallel field primarily resolves spin in the ideal thin-interface model; finite layer thickness can also shift subband energies. The plot alone does not determine a unique effective $g$ factor or microscopic disorder model.