Table of contents

Transport properties of a new kind of ballistic electron billiards — two-dimensional (2D) lattice of Sinai billiards coupled through quantum point contacts — are experimentally studied. This lattice is peculiar by simultaneous existence of the effects inherent to single Sinai billiards or quantum dots, and the features reflecting lattice properties of system. Magnetotransport measurements give very pronounced commensurability peak even if the conductivity of the latticeG ≪ e²/h. Consequently it preserves the properties of ballistic regular structure at these conductivity states. On the other hand, the gate voltage dependencies of G show that the system behaves as percolation one. In weak magnetic fields negative magnetoresistance (NMR) is observed. It is described by theory of chaotic weak localization developed for case of single ballistic cavity. This NMR increases in going from G > e²/h to G ≪ e²/h. Thus, 2D lattice of coupled Sinai billiards is a unique system where coexistence of order, disorder and chaos are clearly demonstrated.

We report a new type of quantum chaotic system in which the classical Hamiltonian originates from the intrinsically quantum mechanical nature of the device. The system is a semiconductor superlattice in a magnetic field. The energy–momentum dispersion curves can be used to calculate semi- classical orbits for electrons confined to a single miniband. When a magnetic field is applied along the superlattice axis (x-direction), the electrons perform Bloch oscillations along the axis with cyclotron motion in the orthogonal plane. But when the magnetic field is tilted away from the x-direction, the orbits are chaotic, and have a spatial width along the superlattice axis, which is much larger than the amplitude of the Bloch oscillations. This is because the tilted field transfers momentum between the x- and z-directions, thereby delocalizing the electron path. This type of chaotic dynamics is fundamentally different to that identified in our previous studies of double–barrier resonant tunneling diodes. We investigate the relation between the orbits of the effective Hamiltonian, and the quantum states of the superlattice. In the regime of strong chaos, the wave functions have a highly diffuse structure which extends across many periods of the superlattice, just like the corresponding classical orbits. This chaos-induced delocalization increases the current flow through real devices. By contrast, in the stable domain the electron orbits remain localized along the paths of particular quasi-periodic orbits. We use theoretical and experimental current–voltage curves to show how the onset of chaos manifests itself in the transport properties of two- and three-terminal superlattice structures, and identify current oscillations associated with classical resonances. We also consider analogies with ultra-cold atoms in an optical lattice with a tilted harmonic trap.

We have studied the ac response and magnetoresistance of a two-dimensional electron gas in high-mobility samples in the presence of smooth disorder, with emphasis on the composite-fermion description of a half-filled Landau level. We have found that the low-ω behavior of the ac conductivity σ(ω) is governed by memory effects associated with return processes that are neglected in Boltzmann transport theory: the return-induced correction to Re σ exhibits a kink ∝ |ω|. It is shown that the non-Markovian quasiclassical kinetics leads to a strong magnetoresistance Δρ_xx. We argue that the quasiclassical memory effects account for the positive Δρ_xx observed at small deviations from half-filling. At a larger deviation, the positive magnetoresistance is followed by a sharp falloff of ρ_xx.

The calculation of the density of states for the Schrödinger equation with a Gaussian random potential is equivalent to the problem of a second-order transition with a `wrong' sign of the coefficient of the quartic term in the Ginzburg–Landau Hamiltonian. The special role of the dimension d = 4 for such Hamiltonian can be seen from different viewpoints but fundamentally is determined by the renormalizability of the theory. Construction of -expansion in direct analogy with the phase transitions theory gives rise to a problem of a `spurious' pole. To solve this problem, the proper treatment of the factorial divergency of the perturbation series is necessary. In (4 – )-dimensional theory, the terms of the leading order in 1/ should be retained for N ∼ 1 (N is an order of the perturbation theory) while all degrees of 1/ are essential for large N in view of the fast growth of their coefficients. The latter are calculated in the leading order in N from the Callan–Symanzik equation with results of Lipatov method using as boundary conditions. The qualitative effect consists in shifting of the phase transition point to the complex plane. This results in elimination of the `spurious' pole and in regularity of the density of states for all energies.

The Fermi energy and the Zeeman splitting of composite fermions are measured from the temperature dependence of the electron spin polarization at v = 1/2. We demonstrate that the Zeeman splitting of composite fermions is enhanced by a factor of 2.5 due to the interaction between CFs. The latter is very sensitive on the finite width of the 2D channel. The spin polarization at v = 1/3 and v = 2/3 displays an activated behavior and the derived spin-wave gaps are compared with simultaneously measured transport values.

We report on magnetocapacitance study of the quantum Hall effect (QHE) states. Capacitance minima width was found to be independent of magnetic field and to be the same for even, odd and fractional QHE states when measured as a function of the average electron density. This result indicates that the width of capacitance minima in the samples investigated are governed by long-range carrier density fluctuations. At low temperatures, the amplitudes of the minima decrease linearly with the temperature increase. All our experimental results for the integer QHE states are quantitatively explained by introducing unbroadened magnetic levels and dispersion of the electron density along the sample. The energy gaps at even filling factors obtained from fitting the experimental data are found to be close to the known cyclotron gaps. At odd fillingsv = 1, 3, and 5, the energy gaps appear to be enhanced in comparison with the Zeeman splitting, with the enhancement decreasing with filling factor.

The capacitance minima are argued to originate from the motion of incompressible regions along a sample caused by the gate voltage variation. We derive the condition for the appearance and motion of such regions for the case of gated samples with long-range fluctuations of density of charged donors.

The appearance of narrow magnetocapacitance peaks when a dc current is passed through the sample is reported. We hypothesize that these peaks are due to the current percolation along incompressible regions.

We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkel'stein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as Chern–Simons gauge theory. We elaborate on the meaning of a new symmetry ( invariance) for systems with an infinitely ranged interaction potential. We address the renormalization of the theory and present the main results in terms of a scaling diagram of the conductances.

Phase diagram of a bilayer quantum well at integer filling factors is established using the hidden symmetry method. Three phases: ferromagnetic, canted antiferromagnetic (CAP) and spin-singlet, have been found. We confirm early results of Das Sarma et al. Each phase violates the SU(4) hidden symmetry and is stabilized by the anisotropy interactions.

The interaction between quantum well excitons and cavity photons in semiconductor microcavities in the strong coupling regime results in mixed 2D exciton–photon states, called exciton polaritons. The behavior of a dense polariton system is of particular interest due to the fact that these particles have integer spin and, hence, obey Bose–Einstein statistics. Drastic nonlinearities have been observed both in the low polariton (LP) emission intensity and polarization in the case of the resonant excitation into the LP branch under condition that 2ℏω(k_ex) = ℏω(k = 0) + ℏω(2k_ex). The experiments have shown a very strong final state stimulation of a two polariton scattering due to the bosonic nature of the polaritons. The filling of k = 0 LP state significantly exceeding 1 has been realized under continuous excitation at T = 1:8 K. The dependence of the effect on the polarization of photoexcited light and temperature is discussed.

Experimentally electron-beam injection and detection via quantum point-contacts is used to investigate the scattering of a non-equilibrium electron distribution in a two-dimensional electron gas (2DEG) of a GaAs/(Ga,Al)As heterostructure. The energy dependence of electron–electron scattering processes has been studied in a weak magnetic field by investigating the detector signal. Assuming electron beams with a narrow opening angle a magnetic field B perpendicular to the 2DEG plane causes only electrons which are scattered in a point O at an angle α to reach the detector. Thus, it is possible to measure directly the energy dependence of the angular electron distribution after scattering. The experimental data give a clear evidence for the importance of small angle scattering processes in two-dimensional systems, as predicted theoretically.

We review our fabrication methods to produce submicron charge-density-wave (CDW) structures and present measurements of CDW dynamics on a microscopic scale. Our data show that mesoscopic CDW dynamics is different from bulk behavior. We have studied current-conversion and found a size-effect that can not be accounted for by existing models. An explanation might be that the removal and addition of wave fronts becomes correlated in time when probe spacing is reduced below a few µm. On small segments we occasionally observe negative differential resistance in the I(V) characteristics and sometimes the resistance may even become negative. We believe that the interplay between CDW deformations (strain) and quasi-particles may yield non-equilibrium effects that play a crucial role in this new phenomenon. No detailed theoretical calculations are available. Our measurements clearly show the need of a microscopic model for CDW dynamics.

This report is a summary of recent work on the properties of phase coherent diffusive conductors, especially in the geometry of networks — also called graphs — made of quasi-1D diffusive wires. These properties are written as a function of the spectral determinant of the diffusion equation (the product of its eigenvalues). For a network with N nodes, this spectral determinant is related to the determinant of anN × N matrix which describes the connectivity of the network. I also consider the transmission through networks made of 1D ballistic wires and show how the transmission coefficient can be written in terms of an N × N matrix very similar to the above one. Finally I present a few considerations on the relation between the magnetism of noninteracting systems and the magnetism of interacting diffusive systems.

We show experimental evidence of a proximity-induced superconducting transition in individual single-walled carbon nanotubes with normal state resistance much large than the quantum of resistance. The critical current of samples is extensively studied as a function of temperature and magnetic field. We also studied an influence of electron and ion beams radiation on the superconducting properties of carbon nanotubes.

We investigated the local density of states (LDOS) of a normal metal (N) in good electrical contact with a superconductor (S) as a function of the distance x to the NS interface. The sample consists of a pattern of alternate L = 1 mm wide strips of Au and Nb made by UV lithography. We used a low temperature scanning tunneling microscope and a lock-in detection technique to record simultaneously dI/dV(V,x) curves and the topographic profile z(x) at 1.5 K. We scanned along lines perpendicular to the strips. All the spectra show a dip near the Fermi energy, which spectral extension decreases from the superconducting gap Δ at the NS interface to zero at distances x ≫ ξ_N where ξ_N ≃ √ℏD_N/2Δ ≃ 53nm is the coherence length in the normal metal. Our measurements are correctly described in the framework of the quasi-classical Green's function formalism. We numerically solved the 1D Usadel equation and extracted a decoherence time in gold of 4 ps. We also investigated the LDOS of small ridges of Au deposited on the top of the Nb lines. In this case, L ⩽ ξ_N and the spatial variations of the spectra depend on the exact shape of the Au ridge. However, our results are consistent with a predicted minigap related to the Thouless energy.

The paper deals with entangled electron states arising in a normal conductor located near a superconductor. Such paired entangled states can be treated as decomposed Cooper pairs. Some general problems of the theory of measurements are also considered.

We review a novel approach to the superconductive proximity effect in disordered normal–superconducting (N-S) structures. The method is based on the multicharge Keldysh action and is suitable for the treatment of interaction and fluctuation effects. As an application of the formalism, we study the subgap conductance and noise in two-dimensional N-S systems in the presence of the electron–electron interaction in the Cooper channel. It is shown that singular nature of the interaction correction at large scales leads to a nonmonotonuos temperature, voltage and magnetic field dependence of the Andreev conductance.

Reentrant superconducting behavior of the critical supercurrent temperature dependencies has been observed for the Nb–Cu/Ni–Nb Josephson SFS (superconductor–ferromagnet–superconductor) junctions. The I_c(T) oscillations detected are associated with a crossover of the SFS junctions from '0'- to 'π'-state that is related to a special feature of superconducting pair flow through a ferromagnet (spatial oscillations of induced superconducting order parameter in presence of the exchange field). A triangular array of the junctions in the π-state shows evidence for a phase shift of π on the I_c(H) dependence. We have argued advantages of the SFS π-junction use for the quantum bit implementation based on the superconducting loop with quantum Josephson junctions. While designs proposed previously are based on magnetically frustrated superconducting loops, we discuss the advantages offered by the π-junctions in obtaining naturally degenerate two-level systems.

The Anderson theory of dirty superconductivity was established a few years after the discovery of the BCS wave function. Disregarding the rich properties in the one-particle energy spectrum in dirty limit, the theory claimed that the ground state condensate is translationally invariant and free from Toulouse type of frustrations. This theory also set down the foundation of dirty superconductivity in the presence of external fields.

In this talk, I demonstrate the failure of the Anderson theory in amorphous superconducting films in general and its connection with Wigner–Dyson surmise. I will discuss the Chandrasekar–Glogston limit in which the nodes in one-particle wave functions are shown to result in a novel superconducting glass phase. I will also discuss why nature has tolerated the failure.

We present low-temperature transport measurements on single and multiply connected SNS systems fabricated on the basis of superconducting polycrystalline PtSi film. Zero bias anomaly (ZBA) and subharmonic energy gap structure (SGS) originating from the proximity effects and the multiple Andreev reflections were observed and carefully studied. It was found that the ZBA is not described by any theories developed for SNS junctions with high-transparent NS interface. The value of excess conductance and the width of ZBA for single SNS junction far exceed values predicted by up-to-date theories.

The NS interfaces of our SNS junctions are really high-transparent, for superconducting and normal metal parts are made of the same material. On the other hand, as we have to deal with long diffusive SNS junctions one might expect that impurities could provide the conditions for incoherent multiple Andreev reflections.

In comparison with single SNS junctions we observe significant narrowing of the ZBA in multiply connected SNS systems: one-dimensional (1D) and two-dimensional arrays (2D) of SNS junctions. In 2D arrays an appreciable SGS appears, with up to n = 16(eV = ±2Δ/n) and some numbers being lost. One of the most interesting results obtained on 1D arrays consists in the appearance of symmetrical dips on the dependences dV/dI - V at dc voltage corresponding to some multiples of Δ/e. Presented results show that coherent phenomena governed by Andreev reflection are not self-averaging and are maintained over a macroscopic scale.

The theory of fluctuation conductivity for an arbitrary impurity concentration including ultra-clean limit (Tτ ≫ √T_c/T – T_c) is developed. It is demonstrated that the formal divergency of the fluctuation density of states contribution obtained previously for the clean case is removed by the correct treatment of the nonlocal ballistic electron scattering. We show that in the ultra-clean limit the density-of-states quantum corrections are canceled by the Maki–Thompson term and only classical paraconductivity remains.

A theory of the zero-temperature superconductor-metal transition is developed for an array of superconductive islands (of size d) coupled via a disordered two-dimensional conductor with the dimensionless conductance g = ℏ/e²R_□ ≫ 1. At T = 0 macroscopically superconductive state of the array with lattice spacing b ≫ d is destroyed at g < g_c ≈ 0.1 ln² (b/d). At high temperatures the normal-state resistance between neighboring islands at b = b_c is much smaller than R_Q = h/4e².

As the normal-state sheet resistance, R_n, of a thin- film superconductor increases, its superconducting properties degrade. For R_n ≃ h/4e² superconductivity disappears and a transition to a nonsuperconducting state occurs. We present electron tunneling and transport measurements on ultrathin, homogeneously disordered superconducting films in the vicinity of this transition. The data provide strong evidence that fluctuations in the amplitude of the superconducting order parameter dominate the tunneling density of states and the resistive transitions in this regime. We briefly discuss possible sources of these amplitude fluctuation effects. We also describe how the data suggest a novel picture of the superconductor-to-nonsuperconductor transition in homogeneous 2D systems.

We have measured the ac complex resistivity in the linear regime, as well as dc resistivity, for thick (100, 300 nm) amorphous (a-)Mo_xSi_1–x films at low temperatures (T > 0.04 K) in constant fields B. The critical behavior associated with the second-order transition has been observed for both dc and ac resistivities, which is similar to that observed for granular indium films. This is the first convincing evidence for the vortex glass transition (VGT) in the homogeneously disordered low-T_C superconductors containing microscopic pinning centers. We have found that the VGT persists down toT ∼ 0.1T_C0 up to B ∼ 0.9B_C2(0), where T_C0 and B_C2(0) are the mean-field transition temperature and upper critical field atT = 0, respectively. At T → 0 the VGT line B_g(T) extrapolates to a field below B_C2(0), indicative of the presence of a T = 0 quantum-vortex-liquid phase in the region B_g(0) <B < B_C2(0).

For thin (4 nm) films the (T = 0) field-driven superconductor–insulator transition takes place at B_C. We have not obtained evidence of the metallic quantum liquid phase belowB_C, while in B > B_C an anomalous negative magnetoresistance (MR) suggesting the presence of the localized Cooper pairs has been observed. The negative MRis commonly observed for thin films; however, for thick films the MR is always positive. This means that the two-dimensionality plays an important role in the appearance of the negative MR (or localized Cooper pairs). The negative MR is no longer visible as the field is applied parallel to the film surface, consistent with the view that mobile vortices, as well as localized Cooper pairs, are present inB > B_C.

We report a new type of single-electron transistor (SET) comprising two highly resistive Cr thin-film strips (∼ 1 µm long) connecting a 1 µm-long Al island to two Al outer electrodes. These resistors replace small-area oxide tunnel junctions of traditional SETs. Our transistor with a total asymptotic resistance of 110 kΩ showed a very sharp Coulomb blockade and reproducible, deep and strictly e-periodic gate modulation in wide ranges of bias currents I and gate voltages Vg. In the Coulomb blockade region (|V| ⩽ about 0.5 mV), we observed a strong suppression of the co-tunneling current allowing appreciable modulation curves V(Vg) to be measured at currents I as low as 100 fA. The noise figure of our SET was found to be similar to that of typical Al/AlO_x/Al single-electron transistors, viz. δQ ≈ 5 × 10^-4e/√Hz at 10 Hz.

Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantum-mechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1/2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwave-spectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.

The influence of a noisy environment on coherent transport in Andreev states through a point contact between two superconductors is considered. The amount of dephasing is estimated for a microwave-activated quantum interferometer. Possibilities of experimentally investigating the coupling between a superconducting quantum point contact and its electromagnetic environment are discussed.

Entanglement acts as a fundamental resource for many applications in quantum communication. We propose and theoretically analyze methods for preparing and detecting entanglement between the spins of electrons in a mesoscopic environment. The entanglement production mechanism which we present is based on two quantum dots coupled to a superconductor from which paired electrons are injected via Andreev tunneling. The spin-correlated electrons can then hop from the quantum dots into normal leads. For detection we propose to measure the shot noise which is produced by the entangled electrons after they have passed a beam splitter. The enhancement of the noise by a factor of two turns out to be a unique signature for the spin singlet, a maximally entangled state. In a different setting, the entangled ground state in two tunnel-coupled quantum dots is detected via the Aharonov–Bohm oscillations in the co-tunneling current.

Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses two ground states with an energy difference proportional to exp(-L/l₀) and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron spectrum. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a three-dimensional p-wave superconductor, provided that the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone (each spin component counts separately).