Although the unit of charge in nature is a fundamental constant, the charge of individual quasiparticles in some low-dimensional systems may be fractionalized. Quantum one-dimensional (1D) systems, for instance, are theoretically predicted to carry charge in units smaller than the electron charge e. Unlike 2D systems, the charge of these excitations is not quantized and depends directly on the strength of the Coulomb interactions. For example, in a 1D system with momentum conservation, it is predicted that the charge of a unidirectional electron that is injected into the wire decomposes into right-and left-moving charge excitations carrying fractional charges f 0 e and (1 − f 0 )e respectively 1,2 . f 0 approaches unity for non-interacting electrons and is less than one for repulsive interactions. Here, we provide the first experimental evidence for charge fractionalization in one dimension. Unidirectional electrons are injected at the bulk of a wire and the imbalance in the currents detected at two drains on opposite sides of the injection region is used to determine f 0 . Our results elucidate further 3,4 the collective nature of electrons in one dimension.Charge fractionalization in one dimension is already predicted for the spinless Luttinger model 1,2 . The charge fraction f 0 is given bywhere g c is the Luttinger-liquid interaction parameter. For a galilean invariant system, g c = v F /v c , where v F is the bare Fermi velocity and v c is the velocity of charge excitations. Roughly,where U is the Coulomb interaction energy and ε F is the Fermi energy. In spinfull one-dimensional (1D) systems, charge fractionalization occurs in addition to spin-charge separation, which has been recently confirmed by spectroscopy and tunnelling experiments [4][5][6] .Observing interaction effects in 1D systems using transport experiments is a considerable challenge. For example, the d.c. twoterminal conductance with ideal contacts is universal and given by G = G 0 ≡ 2e 2 /h, independent of interactions 7-11 . Shot-noise measurements have been useful in detecting fractional charge in 2D systems [12][13][14] . However, low-frequency shot-noise measurements in an ideal wire would only reveal the physics of the Fermi-liquid contacts, remaining insensitive to fractionalization 15 . Although both noise and conductance should reveal interaction effects at frequencies exceeding v F /g c L ∼ 10 10 Hz, where the excitation wavelength is shorter than the wire segment [16][17][18] , these frequencies are difficult to explore experimentally at low temperatures.Initial experimental indication of electron fractionalization in one dimension is provided by angle-resolved photo-emission spectroscopy measurements on stripe-ordered cuprate materials 5 . Recent theoretical studies have proposed transport experiments aimed at detecting the same physics in quantum wires. Generally, these involve the realization of multi-terminal geometries, including: (1) local injection of electrons into a wire, where high-frequency noise correlations are expecte...

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We present transport measurements of cleaved edge overgrowth GaAs quantum wires. The conductance of the first mode reaches 2 e 2 /h at high temperatures T > ∼ 10 K, as expected. As T is lowered, the conductance is gradually reduced to 1 e 2 /h, becoming T -independent at T < ∼ 0.1 K, while the device cools far below 0.1 K. This behavior is seen in several wires, is independent of density, and not altered by moderate magnetic fields B. The conductance reduction by a factor of two suggests lifting of the electron spin degeneracy in absence of B. Our results are consistent with theoretical predictions for helical nuclear magnetism in the Luttinger liquid regime.Conductance quantization is a hallmark effect of ballistic one-dimensional (1D) non-interacting electrons [1][2][3][4]. One mode of conductance e 2 /h opens for each spin, giving conductance steps of 2 e 2 /h for spin degenerate electrons. In presence of electron-electron (e-e) interactions, strongly correlated electron behavior arises, described by Luttinger liquid (LL) theory [5][6][7]. Salient LL signatures include ubiquitous power-law scaling [8][9][10][11][12], separation of spin and charge modes, and charge fractionalizationall recently observed [13][14][15][16] in cleaved edge overgrowth (CEO) GaAs quantum wires [17], thus establishing CEO wires as a leading realization of a LL. Interestingly, the conductance of a clean 1D channel is not affected by interactions, since it is given by the contact resistance in the Fermi liquid leads [18][19][20][21][22]. In presence of disorder, however, the conductance is reduced with LL powerlaws [23,24]. While short constrictions display universal quantization [2,3], the ballistic CEO wires exhibit steps reduced below 2 e 2 /h at temperatures T ≥ 0.3 K [25,26], presenting an unresolved mystery [11,13,25,27].In this Letter, we revisit the conductance quantization in CEO wires, investigating for the first time low temperatures down to T ∼ 10 mK. We find that the conductance of the first wire mode drops to 1 e 2 /h at T ∼ 100 mK and remains fixed at this value for lower T , while the electron temperature cools far below 100 mK. At high T > ∼ 10 K, the conductance approaches the expected universal value 2 e 2 /h [25]. This behaviour suggests a lifting of the electron spin degeneracy at low T , in absence of an external magnetic field B. The observed quantization values are quite robust, appearing in several devices, unaffected by moderate magnetic fields, and independent of the overall carrier density. A recent theory [28][29][30] predicts a drop of the conductance by a factor of two in presence of a nuclear spin helix -a novel quantum state of matter. Our data agree well with this model, while other available theories are inconsistent with the experiments, thus offering a resolution of the non-universal conductance quantization mystery.Ultra-clean GaAs CEO double wires (DWs) were measured (inset, Fig. 1), similar to Refs. [13][14][15][16], offering Arrows indicate VG above which modes start to contribute to g, as label...

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment—thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.

It has been found experimentally that if a mixture of hydrogen and argon is pinched, a separation between the two components occurs very early during the implosion phase; the light ions move faster to the center, leaving the heavier ions behind. A model is presented which describes the dynamics of the pinch and explains the separation. The collisional electron gas is treated as a fluid and the ions are treated as free particles accelerated by the collective electrostatic field set up by the flow. The set of equations describing such a flow is presented and some simple problems are worked out in order to show that a separation is possible. These problems include the ion sound wave, the general flow with impurities, and the shock wave structure.