Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moore's law. Nevertheless, their dispersion has never been probed and is often assumed to be simply linear, without any rigorous justification. Here we determine the non-linear electrical response of topological edge states in the ballistic regime and demonstrate the way this response ascertains the presence of symmetry breaking terms in the edge dispersion, such as deviations from non-linearity and tilted spin quantization axes. The non-linear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of topological materials and discuss experimental measurement.
Ballistic transport of hot electrons in a quantum Hall edge channel is attractive for studying electronic analog of quantum optics, where the edge potential profile is an important parameter that governs the charge velocity and scattering by longitudinal-optical (LO) phonons. Here we use a parallel double gate to control the electric field of the edge potential, and investigate the ballistic length of the channel by using hot-electron spectroscopy. The ballistic length is significantly enhanced by reducing the LO phonon scattering rate in the tailored potential.
We study the linear Hall response of 2D ballistic system on inhomogeneous magnetic field. We establish that in classical limit the Hall conductivity response on local magnetic field is quantized in units of $α_H \equiv \frac{e^3}{2 π^2 \hbar c}$. The quantized value depends on the point where the field is applied, this dependence being irregular in chaotic billiards. The phenomenon allows for direct tracing of special electron trajectories that belong to fractal repellor. We discuss how quantum effects smooth the quantization.
We demonstrate theoretically how a two-dimensional electron gas can be used to probe local potential profiles using the Hall effect. For small magnetic fields, the Hall resistance is inversely proportional to the average potential profile in the Hall cross and is independent of the shape and the position of this profile in the junction. The bend resistance, on the other hand, is much more sensitive on the exact details of the local potential profile in the cross junction.
The quantum spin Hall (QSH) state, observed in a zero magnetic field in HgTe quantum wells, respects the time-reversal symmetry and is distinct from quantum Hall (QH) states. We show that the QSH state persists in strong quantizing fields and is identified by counter-propagating (helical) edge channels with nonlinear dispersion inside the band gap. If the Fermi level is shifted into the Landau-quantized conduction or valence band, we find a transition between the QSH and QH regimes. Near the transition the longitudinal conductance of the helical channels is strongly suppressed due to the combi…
The spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction is studied numerically. We find that the spin Hall conductance is very sensitive to the transverse measuring location, the shape and size of the device, and the strength of the spin-orbit interaction. Not only the amplitude of spin Hall conductance but also its sign can change. This non-universal behavior of the spin Hall effect is essentially different from that of the charge Hall effect, in which the Hall voltage is almost invariant with the transverse measuring site and is a …
We report an experimental study of the quantum corrections to the longitudinal conductivity and the Hall coefficient of a low mobility, high density two-dimensional two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5 K - 110 K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It was therefore possible to study the crossover region for the longitudinal conductivity and the Hall effect.
In graphene superlattices, bulk topological currents can lead to long-range charge-neutral flow and non-local resistance near Dirac points. A ballistic version of these phenomena has never been explored. Here, we report transport properties of ballistic graphene superlattices. This allows us to study and exploit giant non-local resistances with a large valley Hall angle without a magnetic field. In the low-temperature regime, a crossover occurs toward a new state of matter, referred to as a quantum valley Hall state (qVHS), which is an analog of the quantum Hall state without a magnetic field.…
We investigate the ballistic electron transport in a two dimensional Quantum Wire under the action of an electric field ($E_y$). We demonstrate how the presence of a Spin Orbit coupling, due to the uniform electric confinement field gives a non-commutative effect as in the presence of a transverse magnetic field. We discuss how the non commutation implies an edge localization of the currents depending on the electron spins also giving a semi-classical spin dependent Hall current. We also discuss how it is possible obtain a quantized Spin Hall conductance in the ballistic transport regime by de…
We demonstrate that flow of longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce nonequilibrium spin accumulation which has opposite sign for the two lateral edges and it is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation…
We show that a nanometric four-probe ballistic junction can be used to check the presence of a transverse spin Hall current in a system with a Spin Orbit coupling not of the Rashba type, but rather due to the in-plane electric field. Indeed, the spin Hall effect is due to the presence of an effective small transverse magnetic field corresponding to the Spin Orbit coupling generated by the confining potential. The strength of the field and the junction shape characterize the quenching Hall regime, usually studied by applying semi-classical approaches. We discuss how a quantum mechanical relativ…
The spin-Hall effect has recently attracted a lot of attention and a central question is whether the effect is due to the intrinsic spin-orbit interaction or due to spin-asymmetric scattering by extrinsic impurities. The objective of this paper is to shed light on this question using a new approach based on the non-equilibrium Green function (NEGF) formalism, which allows us to go continuously from the ballistic to the diffusive limit and we present approximate analytical expressions that describe our results fairly well. Our model suggests that a spin accumulation proportional to the current …
Geometric oscillations of local Hall and Nernst effects in ballistic graphene at weak magnetic fields
Abrikosov Center for Theoretical Physics, MIPT（莫斯科物理技术学院阿布里科索夫理论物理中心）；Institute of Physics of DFRS of the RAS（俄罗斯科学院达吉斯坦共和国科学中心物理研究所）；School of Science, Westlake University（西湖大学理学院）
We show that a 3-port interferometer, defined by quantum point contacts in a two-dimensional electron gas, and working in the quantum Hall regime, can implement different logic gates at each port depending on the energy of charge carriers and the operating conditions. In all cases the input logic states are encoded in the potentials applied on the quantum point contacts, while the output logic states are encoded in the values of the overall transmission coefficients at each port. In addition, the output of such compact configurations can be reprogrammed by combining two 3-port interferometers.
We propose a new scheme of spin filtering based on nanometric crossjunctions in the presence of Spin Orbit interaction, employing ballistic nanojunctions patterned in a two-dimensional electron gas. We demonstrate that the flow of a longitudinal unpolarized current through a ballistic X junction patterned in a two-dimensional electron gas with Spin Orbit coupling (SOC) induces a spin accumulation which has opposite signs for the two lateral probes. This spin accumulation, corresponding to a transverse pure spin current flowing in the junction, is the main observable signature of the spin Hall …
In high-quality solid-state systems at low temperatures, the hydrodynamic or the ballistic regimes of heat and charge transport are realized in the electron and the phonon systems. In these regimes, the thermal and the electric conductance of the sample can reach abnormally large magnitudes. In this paper, we study the Hall effect in a system of interacting two-dimensional charged particles in a ballistic regime. We demonstrated that the Hall electric field is caused by a change in the densities of particles due to the effect of external fields on their free motions between the sample edges. I…
Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels
Université Paris-Saclay, CEA, CNRS, SPEC（巴黎萨克雷大学、法国原子能和替代能源委员会、法国国家科学研究中心、物理谱与现象实验室）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究所材料纳米架构研究中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室、巴黎高等师范学院、巴黎文理研究大学、法国国家科学研究中心、索邦大学、巴黎西岱大学）
Universal properties of spin-Hall effect in ballistic 2D electron systems are addressed. The net spin polarization across the edge of the conductor is second order, ~λ^2, in spin-orbit coupling constant independent of the form of the boundary potential, with the contributions of normal and evanescent modes each being ~ \sqrtλ but of opposite signs. This general result is confirmed by the analytical solution for a hard-wall boundary, which also yields the detailed distribution of the local spin polarization. The latter shows fast (Friedel) oscillations with the spin-orbit coupling entering via …
We have studied magnetotransport of a degenerate two-dimensional electron gas in a Hall sample in the Knudsen regime, when the mean free paths of electrons with respect to their collisions with each other and with impurities are much larger than the width of the sample. In contrast to the usually considered symmetric sample, whose both its edges reflect electrons diffusely, we considered an asymmetric sample, one edge of which reflects them diffusely, while the other specularly. It is shown that in such structure in low magnetic fields the Hall coefficient is parametrically large in comparison…
We report an experimental study of quantum conductivity corrections in a low mobility, high density two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5K - 110K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It has been therefore possible to study the crossover between these regimes for both the longitudinal conductivity and the Hall effect. We perform a parameter free comparison of our experimental data for the longitudinal conductivity at zero magnetic field, the Hall coefficient, and the…
Recent quantum Hall experiments conducted on disordered graphene pn junction provide evidence that the junction resistance could be described by a simple Ohmic sum of the n and p mediums' resistances. However in the ballistic limit, theory predicts the existence of chirality-dependent quantum Hall plateaus in a pn junction. We show that two distinctively separate processes are required for this ballistic-Ohmic plateau transition, namely (i) hole/electron Landau states equilibration and (ii) valley iso-spin dilution of the incident Landau edge state. These conclusions are obtained by a simple s…
We report observation of intrinsic inverse spin Hall effect in un-doped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time-resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well befo…
We report the first electrical manipulation and detection of the mesoscopic intrinsic spin-Hall effect (ISHE) in semiconductors through non-local electrical measurement in nano-scale H-shaped structures built on high mobility HgTe/HgCdTe quantum wells. By controlling the strength of the spin-orbit splittings and the n-type to p-type transition by a top-gate, we observe a large non-local resistance signal due to the ISHE in the p-regime, of the order of kOhms, which is several orders of magnitude larger than in metals. In the n-regime, as predicted by theory, the signal is at least an order of …
We report the temperature($T$) and perpendicular magnetic field($B$) dependence of the Hall resistivity $ρ_{xy}(B)$ of dilute metallic two-dimensional(2D) holes in GaAs over a broad range of temperature(0.02-1.25K). The low $B$ Hall coefficient, $R_H$, is found to be enhanced when $T$ decreases. Strong magnetic fields further enhance the slope of $ρ_{xy}(B)$ at all temperatures studied. Coulomb interaction corrections of a Fermi liquid(FL) in the ballistic regime can not explain the enhancement of $ρ_{xy}$ which occurs in the same regime as the anomalous metallic longitudinal conductivity. In …
We report on the fabrication and room temperature measurements of a high frequency electrical signal detector. The device is based on the ballistic transport in graphene to detect a high frequency signal. The observed response is linear in the considered power range (-40dBm - 0dBm) and exhibits a sensitivity as high as 10 Volts/Watt. Finally the device detected signals up to 50GHz with a maximum response at 10GHz. This device outperforms any previously reported carbon based detectors in frequency response and compares to current state of the art Schottky based detectors in dynamic range.
Spin Hall and Edelstein effects in a ballistic quantum dot with Rashba spin-orbit coupling
CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Università di Salerno（萨莱诺大学）；Dipartimento di Fisica ”E.R. Caianiello”, Università di Salerno（萨莱诺大学埃·R·卡亚涅洛物理系）；INFN, Sezione di Napoli, Gruppo collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Dipartimento di Fisica, Università della Calabria（卡拉布里亚大学物理系）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；AGH University of Krakow, Faculty of Physics and Applied Computer Science（克拉科夫AGH科技大学物理与应用计算机科学系）
We study spin conductance in a ballistic and quasi-ballistic two dimensional electron system with Rasbha spin-orbit coupling. The system has a four-terminal geometry with round corners at the connection to the leads. It is found that by going from sharp corners to more round corners in the ballistic system the energy depended spin conductance goes from being relatively flat to a curve showing a series of minima and maxima. It is also found that when changing the size of the terminal area by modifying the roundness of the terminal corners the maxima and minima in the transverse spin conductance…
We report on the observation of quantum transport and interference in a graphene device that is attached with a pair of split gates to form an electrostatically-defined quantum point contact (QPC). In the low magnetic field regime, the resistance exhibited Fabry-Pérot (FP) resonances due to np'n (pn'p) cavities formed by the top gate. In the quantum Hall (QH) regime with a high magnetic field, the edge states governed the phenomena, presenting a unique condition where the edge channels of electrons and holes along a p-n junction acted as a solid-state analogue of a monochromatic light beam. We…
The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field E using the tight binding model. While for small ballistic flight times the current is linear in E and independent of time, for larger ballistic times the current increases and finally at yet larger times Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate only o…
It is demonstrated how the correction factor alpha used in Hall magnetometry of localized magnetic field profiles depends on the sample geometry and on the electron mean free path, in the quasi-ballistic and ballistic regimes, for weak and strong magnetic field regimes. The frequently used approximation of a constant correction factor close to 1 is generally not justified, especially in the case of bipolar magnetic field profiles and may lead to large errors in the determination of the magnitude of the magnetic fields. Rather, alpha depends in a nontrivial way on the parameters of both the mag…
We predict that unpolarized charge current driven through the longitudinal leads attached to ballistic quantum-coherent two-dimensional electron gas (2DEG) in semiconductor heterostructure will induce a {\em pure} spin current, which is not accompanied by any net charge flow, in the transverse voltage probes. Its magnitude can be tuned by the Rashba spin-orbit (SO) interaction and, moreover, it is resilient to weak spin-independent scattering off impurities within the metallic diffusive regime. While the polarization vector of the spin transported through the transverse leads is not orthogonal…
The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream'' modes, moving against the direction of charge current flow, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here we report on noise measurements at the edges of fractional QH (FQH) phases realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of…
We propose an analytic model to study intrinsic spin polarization effect in a ballistic Rashba bar with two semi-infinite leads. The wave functions expanded with plane waves in Rashba bar are required to satisfy boundary conditions at both longitudinal and transverse interfaces. We find out-of-plane spin Hall accumulation effect can be induced in the Rashba bar even with large dimensions by injecting unpolarized current from the lead. The longitudinal in-plane spin Hall effect, however, becomes obscure in large-size sample. An interesting direction-flipping of the out-of-plane spin accumulatio…
An electric field that builds in the direction against current, known as negative nonlocal resistance, arises naturally in viscous flows and is thus often taken as a telltale of this regime. Here we predict negative resistance for the ballistic regime, wherein the ee collision mean free path is greater than the length scale at which the system is being probed. Therefore, negative resistance alone does not provide strong evidence for the occurrence of the hydrodynamic regime; it must thus be demoted from the rank of a smoking gun to that of a mere forerunner. Furthermore, we find that negative …
We introduce the spin and momentum dependent {\em force operator} which is defined by the Hamiltonian of a {\em clean} semiconductor quantum wire with homogeneous Rashba spin-orbit (SO) coupling attached to two ideal (i.e., free of spin and charge interactions) leads. Its expectation value in the spin-polarized electronic wave packet injected through the leads explains why the center of the packet gets deflected in the transverse direction. Moreover, the corresponding {\em spin density} will be dragged along the transverse direction to generate an out-of-plane spin accumulation of opposite sig…
Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited from the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "antiballistic". Co…
The phenomenon of mesoscopic Spin-Hall effect reveals in a nonequilibrium spin accumulation (driven by electric current) at the edges of a ballistic conductor or, more generally, in the regions with varying electron density. In this paper we review our recent results on spin accumulation in ballistic two-dimensional semiconductor heterostructures with Rashba/Dresselhaus spin orbit interactions, and extend the method developed previously to predict the existince of spin-Hall effect on the surface of three-dimensional topological insulators. The major difference of the new Spin-Hall effect is it…
The response of electric devices to an applied thermal gradient has, so far, been studied almost exclusively in two-terminal devices. Here we present measurements of the response to a thermal bias of a four-terminal, quasi-ballistic junction with a central scattering site. We find a novel transverse thermovoltage measured across isothermal contacts. Using a multi-terminal scattering model extended to the weakly non-linear voltage regime, we show that the device's response to a thermal bias can be predicted from its nonlinear response to an electric bias. Our approach forms a foundation for the…
It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes which breaks the $ω\rightarrow-ω$ symmetry (where $ω$ is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a non-zero thermoelectric response when the junction length is of the order of coherence length of the superconductor and the corresponding thermoelectric coefficient confirms to the universal sinusoidal dependence on $ϕ_{12}$, where $ϕ_{1…
Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with…
We show that engineering of tunnel barriers forming at the interfaces of a one-dimensional spin valve provides a viable path to a strong gate-voltage tunability of the magnetoresistance effect. In particular, we investigate theoretically a carbon nanotube (CNT) spin valve in terms of the influence of the CNT-contact interface on the performance of the device. The focus is on the strength and the spin selectivity of the tunnel barriers that are modelled as Dirac-delta potentials. The scattering matrix approach is used to derive the transmission coefficient that yields the tunneling magnetoresis…
A theory of the valley and spin Hall effects and resulting accumulation of the valley and spin polarization is developed for ultraclean channels made of two-dimensional semiconductors where the electron mean free path due to the residual disorder or phonons exceeds the channel width. Both ballistic and hydrodynamic regimes of the electron transport are studied. The polarization accumulation is determined by interplay of the anomalous velocity, side-jump and skew scattering effects. In the hydrodynamic regime, where the electron-electron scattering is dominant, the valley and spin current gener…
A new type of linear response Hall effect is predicted in time-reversal-invariant systems with built-in electric field at zero magnetic field. The Hall response results from a quantum Magnus effect where a self-rotating Bloch electron wavepacket moving under electric field develops an anomalous velocity in the transverse direction. We show that in the ballistic limit the Magnus Hall conductance measures the distribution of Berry curvature on the Fermi surface.
We generalize Landauer's theory of ballistic transport in a one-dimensional (1D) conductor to situations where charge carrier injection and extraction are not any more confined to electrodes at either end of the channel, but may occur along its whole length. This type of distributed injection is expected to occur from the two-dimensional (2D) bulk of, e.g., a quantum spin (or anomalous) Hall insulator to its topologically protected edge states. We apply our conceptual solution to the case of two metal electrodes contacting the 2D bulk, enabling us to derive criteria that discriminate ballistic…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
Similar to the Landauer electric dipole created around an impurity by the electric current, a spin polarized cloud of electrons can be induced by the intrinsic spin-Hall effect near a spin independent elastic scatterer. It is shown that in the ballistic range around the impurity, such a cloud appears in the case of Rashba spin-orbit interaction, even though the bulk spin-Hall current is absent.
At high magnetic fields the conductance of graphene is governed by the half-integer quantum Hall effect. By local electrostatic gating a \textit{p-n} junction perpendicular to the graphene edges can be formed, along which quantum Hall channels co-propagate. It has been predicted by Tworzidło and co-workers that if only the lowest Landau level is filled on both sides of the junction, the conductance is determined by the valley (isospin) polarization at the edges and by the width of the flake. This effect remained hidden so far due to scattering between the channels co-propagating along the \tex…
We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $σ^z_{xy}$ is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field $B$ and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated $σ^z_{xy}$ exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density $n_{2D}$) is varied between the subb…
We discuss the transport properties of a quantum spin-Hall insulator with sizable Rashba spin-orbit coupling in a disk geometry. The presence of topologically protected helical edge states allows for the control and manipulation of spin polarized currents: when ferromagnetic leads are coupled to the quantum spin-Hall device, the ballistic conductance is modulated by the Rashba strength. Therefore, by tuning the Rashba interaction via an all-electric gating, it is possible to control the spin polarization of injected electrons.
We present results for time-dependent electron transport in a ballistic graphene field-effect transistor with an ac-driven gate. Nonlinear response to the ac drive is derived utilizing Floquet theory for scattering states in combination with Landauer-Büttiker theory for transport. We identify two regimes that can be useful for applications: (i) low and (ii) high doping of graphene under source and drain contacts, relative to the doping level in the graphene channel, which in an experiment can be varied by a back gate. In both regimes, inelastic scattering induced by the ac drive can excite qua…
We show that the spin Hall conductivity in insulators is related with a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin Hall effect. As a result, we theoretically predict that bismuth will show the quantum spin Hall effect, both by calculating the helical edge states, and by showing the non-triviality of the Z_2 topological number, and propose possible experiments.
We study mesoscopic spin Hall effect on the surface of topological insulator with a step-function potential. The giant spin polarization induced by a transverse electric current is derived analytically by using McMillan method in the ballistic transport limit, which oscillates across the potential boundary with no confinement from the potential barrier due to the Klein paradox, and should be observable in spin resolved scanning tunneling microscope.
I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and De…
