Conductance Of Quantum Point Contact Research Articles

Calculation of conductance of quantum point contact in STM

The conductance of quantum point contact in scanning tunneling microscope is calculated by modal matching and scattering matrix method. The results show that the conductance of the nano-structure formed during quantum point contact in STM is quantized, which becomes more obvious as the radius and cone angle of the nano-structure decreases. The quantitative behavior could be observed more easily with semiconductors than with metals.

Electrostatic cross-talk between quantum dot and quantum point contact charge read-out in few-electron quantum dot circuits

We investigate by numerical simulation the effect of electrostatic coupling between a quantum point contact (QPC) detector of various geometries and a planar double quantum dot in a few-electron quantum dot circuit. Our simulation is based on solving coupled Kohn-Sham and Poisson equations self-consistently by the finite element method. We use the Slater formula to determine the first electron charging bias point of the plunger gate, and give the corresponding variation of the QPC conductance as a function of the QPC gate bias at that particular point, which we interpret as the detector sensitivity. For all QPC designs, we show that the charging bias point of the plunger gate decreases with increasing QPC gate bias. This effect is enhanced for designs wherein large QPC detection sensitivity is found.

Real-time detection of single-electron tunneling using a quantum point contact

We observe individual tunnel events of a single electron between a quantum dot and a reservoir, using a nearby quantum point contact (QPC) as a charge meter. The QPC is capacitively coupled to the dot, and the QPC conductance changes by about 1% if the number of electrons on the dot changes by one. The QPC is voltage biased and the current is monitored with a current–voltage (I–V) convertor at room temperature. We can resolve tunnel events separated by only 8μs, limited by noise from the I–V convertor. Shot noise in the QPC sets a 25ns lower bound on the accessible timescales.

Imaging electron waves

One can image the coherent flow of electron waves through a quantum point contact (QPC) into a two-dimensional electron gas by using scanning probe microscopy. A negatively charged tip depletes the electron gas below, backscatters electron waves, and reduces the QPC conductance. By raster scanning the tip over the sample, an image of electron flow is obtained. Images at liquid He temperatures show the individual quantum modes of the QPC. At greater distances, the electron flow forms narrow branches caused by small-angle scattering. Interference fringes in the images demonstrate the coherence of electron flow. An electron interferometer that acts as a quantum phase shifter was constructed by adding a gate to reflect electron waves back to the QPC, producing a V-shaped path for interfering electron waves with the apex at the QPC. When the length of one leg of the V is altered by changing the reflector gate voltage, the fringes at the other end of the V, under the tip, shift by the same distance. The interferometer is sensitive to transit time differences as small as ∼0.1 ps between the two electron paths. These observations are in good agreement with theoretical simulations of electron flow.

Electron-phonon scattering in quantum point contacts.

We study the negative correction to the quantized value 2e(2)/h of the conductance of a quantum point contact due to the backscattering of electrons by acoustic phonons. The correction shows activated temperature dependence and also gives rise to a zero-bias anomaly in conductance. Our results are in qualitative agreement with recent experiments studying the 0.7 feature in the conductance of quantum point contacts.

Experimental and theoretical investigation of quantumpoint contacts for the validation of models for surface states

We have performed an investigation of quantum pointcontacts (QPCs) defined by split gates on AlGaAs/GaAsheterostructures in order to understand the effects of surface stateson the transport characteristics of mesoscopic devices. We compareresults from transport measurements on a large number of QPCs withsimulations using a Poisson-Schrödinger solver in which theeffects of surface states are taken into account. We show thatsurface properties strongly affect the conductance of QPCs, and thata simple model for surface states allows us to reproduce withreasonable accuracy the pinch-off voltage of QPCs with different gatelayouts.

Fabrication of Si/SiGe quantum point contacts by electron-beam lithography and shallow wet-chemical etching

We present a low-damage processing technique for fabricating quantum point contacts (QPCs) in the two-dimensional electron gas (2DEG) of a strained Si/Si 0.7Ge 0.3 heterostructure. The result is a QPC conductance characteristic which at T=4.2 K exhibits a series of smeared step-like features. The QPCs were fabricated with a novel technique which combines electron-beam lithography with low-damage selective wet-chemical pattern transfer. The constriction of the QPC is formed by an etched groove with a break w positioned at the mesa center of a field-effect device perpendicular to the transistor channel. After subtracting a series resistance of 800 Ω five quantum steps can be observed in the differential conductance each of them contributing 4 e 2/ h. We attribute the steps to the quantum-ballistic 1D-transport through the constriction.

Analysis of the temperature-dependent quantum pointcontact conductance in relation to the metal-insulator transition intwo dimensions

The temperature dependence of the conductance of a quantum pointcontact has been measured. The conductance as a function of theFermi energy shows temperature-independent fixed points, located atroughly multiple integers of e2/h. Around the first fixedpoint at e2/h, the experimental data for different temperaturescan be scaled onto a single curve. For pure thermal smearing of theconductance steps, a scaling parameter of one is expected. Themeasured scaling parameter, however, is significantly larger than 1.The deviations are interpreted as a signature of the potentiallandscape of the quantum point contact, and of the source-drainbias voltage. We relate our results phenomenologically to themetal-insulator transition in two dimensions.

Localized plasmons in point contacts

Using a hydrodynamic model of the electron fluid in a point contact geometry we show that localized plasmons are likely to exist near the constriction. We attempt to relate these plasmons to the recent experimental observation of deviations of the quantum point contact conductance from ideal integer quantization. As a function of temperature, this deviation exhibits an activated behaviour, , with a density-dependent activation temperature of the order of 2 K. We suggest that can be identified with the energy needed to excite localized plasmons, and we discuss the conductance deviations in terms of a simple theoretical model involving quasiparticle lifetime broadening due to coupling to the localized plasmons.

On additional conductance quantization and related effects of an electric field in 2D quantum point contacts

Influence of the electric field on the quantum point contact (QPC) differential conductance is studied in two cases of well-developed transmission spectrum of (a) step-like and (b) resonance character. These are exemplified by a symmetric rectangular constriction and double-bend constriction in two-dimensional electron gas. It is shown that an additional structure in the constriction-conductance dependence on the Fermi energy (referred sometimes as half integer quantization) reflects the specific field distribution in the contact region at moderate fields and is washed out by nonlinear field effects produced by the potential variation inside the contact. To study field effects, we suggest an analytical expression for the transmission probability, which includes as particular cases two models used previously to confirm and to reject the possibility of the QPC conductance quantization by value e 2/ h. We also briefly discuss the case of resonance doubling accompanied by two-times decrease of the resonance intensity, representing another example of transformations in the QPC conductance, which have the same origin.

Analytic modeling of the conductance in quantum point contacts with large bias.

We have developed a model for calculating differential conductance that accounts for the effects observed at high source-drain voltage. The model uses a linear potential drop over a saddle-point potential. If the region of the potential drop is wide enough, only that region is contributing to the transmission and a simple expression is obtained. The temperature is assumed to increase linearly with the source-drain voltage and a model for an equipotential region in the saddle-point potential corresponding to the channel width is made. The result from the calculations of the conductance with this model is in good agreement with experimental results.

Noise in a quantum point contact due to a fluctuating impurity configuration

We propose a theoretical model for the low-frequency noise observed in a quantum point contact (QPC) electrostatically defined in the 2D electron gas at a GaAs-AlGaAs interface. In such contacts electron scattering by soft impurity or boundary potentials coherently splits an incoming wave function between different transverse modes. Interference between these modes has been suggested to explain observed non-linearities in the QPC conductance. In this study we invoke the same mechanism and the time-dependent current due to soft dynamical impurity scattering in order to analyse the low-frequency (telegraph-like) noise which has been observed along with a non-linear conductance. For the simplified case of a channel with two extended (current carrying) modes, a simple analytical formula for the noise intensity is derived. Generally we have found qualitative similarities between the noise and the square of the transconductance. In comparison with the more traditional d.c. transport measurements we believe that noise measurements can provide additional information about the dynamical properties of QPCs.

Fractional Quantum Point Contact Conductance Quantization Produced by an Electric Field

Fractional Quantum Point Contact Conductance Quantization Produced by an Electric Field

THEORY OF ELECTRON TRANSPORT THROUGH QUANTUM CONSTRICTIONS IN SEMICONDUCTOR NANOSTRUCTURES

Detailed numerical results are presented for the calculated conductance of quantum point contacts, or, narrow constrictions between high mobility two-dimensional electron systems fabricated on semiconductor nanostructures. The conductance is calculated from the two-terminal multichannel transmission matrix formalism using the recursive single-particle Green’s function technique. The Green’s functions are obtained recursively for a tight-binding two-dimensional disordered Anderson lattice model representing the constriction. The conductance is calculated as a function of the shape and the size of the constriction (i.e., its geometry), the temperature, and, the elastic disorder in the system. Our main results, which are consistent with experimental findings, are: (1) increase of elastic scattering destroys the quantization; (2) for a fixed amount of disorder (i.e., for a given value of the elastic mean free path), the conductance quantization is poorer for longer constrictions; (3) in general, the quantization is poorer for higher quantum numbers or subbands; (4) constrictions with sharper geometry have sharper quantization, but may have quantum resonances associated with their sharp corners; (5) the quantum resonances (in sharp constrictions) are suppressed for shorter constriction lengths and at higher temperatures; (6) in general, higher temperatures lower the quantization quality by smoothening out the conductance except for sharp constrictions where at the lowest temperatures the quantum resonances show up, adversely affecting the quantization; (7) in smooth or adiabatic constrictions, the conductance quantization is smooth (but not extremely accurate) but, adiabaticity is not a necessary requirement for conductance quantization; (8) in general, geometry, finite temperature, and finite disorder effects do not allow better than 1% type accuracy in the quantization (compared with integral multiples of 2e2/h) even in the best of circumstances; (9) increase of elastic disorder smoothly takes the system from a conductance quantized regime to the regime of universal conductance fluctuations; and, (10) inelastic scattering, which we treat only in a very crude phenomenological model, behaves similar to thermal effects in broadening and smearing the sharpness of the conductance quantization. We also discuss the effect of an external magnetic field on the conductance quantization phenomenon. Some results are given for the conductance of two constrictions in series.

Quantum electron transport through narrow constrictions in semiconductor nanostructures.

Detailed numerical results, with emphasis on the role of disorder and constriction geometry, are presented for the calculated conductance of quantum point contacts between high-mobility two-dimensional electron systems fabricated on semiconductor nanostructures. The conductance is calculated from the two-terminal multichannel transmission matrix formalism using the recursive single-particle Green's-function technique. The Green's functions are obtained recursively for a tight-binding two-dimensional disordered Anderson lattice model representing the constriction. The conductance is calculated as a function of the shape and the size of the constriction (i.e., its geometry) and the elastic disorder in the system.

Conductance of quantum point contacts in the presence of disorder.

We have calculated the conductance of a two-dimensional electron gas through single and double constrictions using a mode-matching technique. In order to take into account the smooth variation of the confinement potential, and the presence of disorder, the calculation is made within a lattice model. We find that the conductance at plateaus is reduced below the quantized values if short-range scatterers are introduced in the channel. However, the conductance remains well quantized even in the presence of long-range impurities. These observations explain the suppression of conductance time-dependent fluctuations at plateaus experimentally observed by Timp et al. [Phys. Rev. B 42, 9259 (1990)]. We also examine the effects of impurities on the resonant transmission properties through a single quantum dot. As the disorder is introduced, the resonances are broadened in energy and can appear as either peaks or dips depending on the strength of the disorder.

Nonlinear conductance of quantum point contacts in a magnetic field

The conductance of geometrically asymmetric quantum point contacts formed in 2D electron gas (2 DEGs) in GaAs/(AlGa)As heterojunctions has been studied as a function of the applied bias and magnetic field. The nonlinear conductance is found to be independent of bias direction in zero magnetic field in agreement with other workers but at higher magnetic fields the I(V) curves are highly asymmetric in terms of both the onset and the type of nonlinearity observed. The curves are described using simple theory. The same experimental arrangement is also used to study nonlinearity in the quantum Hall regime when the device acts as an adjustable, narrow channel. The nonlinearity is qualitatively different to the first case and there are discontinuous changes in the dissipation which the authors identify with scattering between magneto-electric subbands.

Quantum ballistic and adiabatic electron transport studied with quantum point contacts.

We present an experimental and theoretical study of quantum ballistic transport in single quantum point contacts (QPC's), defined in the two-dimensional electron gas (2DEG) of a high-mobility GaAs/${\mathrm{Al}}_{0.33}$${\mathrm{Ga}}_{0.67}$As heterojunction. In zero magnetic field the conductance of quantum point contacts shows the formation of quantized plateaus at multiples of 2${\mathit{e}}^{2}$/h. The experimental results are explained with a simple model. Deviations from ideal quantization are discussed. The experimental results are compared with model calculations. Energy averaging of the conductance has been studied, both as a function of temperature and voltage across the device. The application of a magnetic field leads to the magnetic depopulation of the one-dimensional subbands in the QPC. It is shown that the zero-field quantization and quantization in high magnetic fields are two limiting cases of a more general quantization phenomenon. We use quantum point contacts to study the high-magnetic-field transport in a 2DEG. Quantum point contacts are used to selectively populate and detect edge channels. The experiments show that scattering between adjacent edge channels can be very weak, under certain circumstances even on length scales longer than 200 \ensuremath{\mu}m. This adiabatic transport has resulted in the observation of an anomalous integer quantum Hall effect, in which the quantization of the Hall conductance is not determined by the number of Landau levels in the bulk 2DEG, but by the number of Landau levels in the QPC's instead. Related effects are the anomalous quantization of the longitudinal resistance and the adiabatic transport through QPC's in series. A theoretical description for transport in the presence of Shubnikov--de Haas (SdH) backscattering is given. This model explains the experimentally observed suppression of the SdH oscillations due to the selective population or detection of edge channels. Finally, we demonstrate that the combination of a QPC and a bulk Ohmic contact can act as a controllable edge-channel mixer.

Conductance of quantum point contacts calculated using realistic potentials

The quantized conductance of ballistic electrons in narrow constrictions requires the low scattering rates of a high mobility 2-dimensional electron gas(2DEG). Despite the spectacular mobilities of 2DEGs, quantization breaks down for constrictions longer than about 500 nm, whereas the mean free path in the ungated 2DEG may exceed 10 μm. We show that potential fluctuations from a random distribution of ionised donors modify the guiding potential from the gate in an unpredictable way. The fluctuations are responsible for the variability among nominally identical devices. For a short constriction (200 nm) the conductance can be well quantized. The accuracy of quantization in a longer constriction (600 nm) is reduced by scattering from the random potential of the donors. This occurs when the length scale of the constriction is greater than that of the fluctuations. The conductance characteristics depend strongly on the exact configuration of impurities. In some cases the random potential causes a resonance in the channel.