Spinless Electrons Research Articles

Quenching of compressible edge states around antidots

We provide a systematic quantitative description of the edge state structure around a quantum antidot in the integer quantum Hall regime. The calculations for spinless electrons within the Hartree approximation reveal that the widely used Chklovskii et al. electrostatic description [Phys. Rev. B 46, 4026 (1992)] greatly overestimates the widths of the compressible strips; the difference between these approaches diminishes as the size of the antidot increases. By including spin effects within density functional theory in the local spin-density approximation, we demonstrate that the exchange interaction can suppress the formation of compressible strips and lead to a spatial separation between the spin-up and spin-down states. As the magnetic field increases, the outermost compressible strip related to spin-down states starts to form. However, in striking contrast to quantum wires, the innermost compressible strip (due to spin-up states) never develops for antidots.

Electron lifetime in Luttinger liquids

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp(-t/\tau_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys $\tau_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T\tau_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.

Tunneling of interacting one-dimensional electrons through a single scatterer: Luttinger liquid behavior in the Hartree–Fock model

We study tunneling of weakly interacting spinless electrons at zero temperature through a single δ barrier in one-dimensional wires and rings of finite lengths. Our numerical calculations are based on the self-consistent Hartree–Fock approximation, nevertheless, our results exhibit features known from correlated many-body models. In particular, the transmission in a wire of length L at the Fermi level is proportional to L - 2 α with the universal power α (depending on the electron–electron interaction only, not on the strength of the δ barrier). Similarly, the persistent current in a ring of the circumference L obeys the rule I ∝ L - 1 - α known from the Luttinger liquid and Hubbard models. We show that the transmission at the Fermi level in the wire is related to the persistent current in the ring at the magnetic flux h / 4 e .

Spatial spin polarization and suppression of compressible edge channels in the integer quantum Hall regime

We perform systematic numerical studies of the structure of spin-resolved compressible strips in split-gate quantum wires taking into account the exchange and correlation interactions within the density functional theory in the local spin-density approximation. We find that for realistic parameters of the wire the exchange interaction can completely suppress the formation of the compressible strips. As the depletion length or magnetic field are increased, the compressible strips starts to form first for the spin-down and then for spin-up edge channels. We demonstrate that the widths of these strips plus the spatial separation between them caused by the exchange interaction are equal to the width of the compressible strip calculated in the Hartree approximation for spinless electrons. We also discuss the effect of electron density on the suppression of the compressible strips in quantum wires.

Coherent transport of interacting electrons through a single scatterer

Using the self-consistent Hartree–Fock method, we calculate the persistent current of weakly interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We find that the persistent current decays with the system length ( L) asymptotically like I ∝ L - 1 - α , where α > 0 is the power depending only on the electron–electron interaction. We also simulate tunneling of the weakly interacting one-dimensional electron gas through a single δ barrier in a finite wire biased by contacts. We find that the Landauer conductance decays with the system length asymptotically like L - 2 α . The power laws L - 1 - α and L - 2 α have so far been observed only in correlated models. Their existence in the Hartree–Fock model is thus surprising.

Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I ∝ L - 1 - α , where L is the ring length and α > 0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.

One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.

Exchange coupling in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. The asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons is derived. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach.

Exchange interaction in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is valid in several independent asymptotic regimes, including low electron density case, under the general condition of a strong spin-charge separation. Explicit formulas for the exchange constant are obtained for thin quantum rings and wires with realistic Coulomb interactions by calculating the pair-correlation function via a many-body instanton approach. A remarkably smooth interpolation between high and low electron density results is shown to be possible. These results are applicable to the case of one-dimensional wires of intermediate width as well. Our method can be easily generalized to other interaction laws, such as the inverse distance squared one of the Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the known exact results for the latter model and show that they are relevant for a realistic experimental setup in which the bare Coulomb interaction is screened by an edge of a two-dimensional electron gas.

Hartree-Fock Simulation of Persistent Current in Rings with Single Scatterer

Using the self-consistent Hartree–Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier. Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction. The persistent current is a sine-like function of magnetic flux. It decays with the ring length (L) faster than L−1 and eventually like L−α−1, where α > 0 is universal.

Tunneling of Interacting Fermions in 1D Systems

Using the self-consistent Hartree{Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single ‐ barrier in a flnite one-dimensional wire connected to contacts. Our results exhibit features known from correlated many-body models. In particular, the conductance decays with the wire length as / L i2fi , where the power fi is universal. We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the ‐ barrier in a one-dimensional ring, where it is known that I / L i1ifi . PACS numbers: 73.23.{b, 73.61.Ey

Quantum manipulation and simulation using Josephson junction arrays

We discuss the prospect of using quantum properties of large scale Josephson junction arrays for quantum manipulation and simulation. We study the collective vibrational quantum modes of a Josephson junction array and show that they provide a natural and practical method for realizing a high quality cavity for superconducting qubit based QED. We further demonstrate that by using Josephson junction arrays we can simulate a family of problems concerning spinless electron–phonon and electron–electron interactions. These protocols require no or few controls over the Josephson junction array and are thus relatively easy to realize given currently available technology.

Fermionic quasiparticle representation of Tomonaga-Luttinger Hamiltonian

We find a unitary operator which asymptotically diagonalizes the Tomonaga-Luttinger Hamiltonian of one-dimensional spinless electrons. The operator performs a Bogoliubov rotation in the space of electron-hole pairs. If bare interaction of the physical electrons is sufficiently small this transformation maps the original Tomonaga-Luttinger system on a system of free fermionic quasiparticles. Our representation is useful when the electron dispersion deviates from linear form. For such situation we obtain non-perturbative results for the electron gas free energy and the density-density propagator.

Dephasing and Weak Localization in Disordered Luttinger Liquid

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.

Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach

We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced two-body ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.

Nonmonotonic charge occupation in double dots

We study the occupation of two electrostatically-coupled single-level quantum dots with spinless electrons as a function of gate voltage. While the total occupation of the double-dot system varies monotonically with gate voltage, we predict that the competition between tunneling and Coulomb interaction can give rise to a nonmonotonic filling of the individual quantum dots. This non-monotonicity is a signature of the correlated nature of the many-body wavefunction in the reduced Hilbert space of the dots. We identify two mechanisms for this nonmonotonic behavior, which are associated with changes in the spectral weights and the positions, respectively, of the excitation spectra of the individual quantum dots. An experimental setup to test these predictions is proposed.

Mass renormalization in nonrelativistic quantum electrodynamics

In nonrelativistic quantum electrodynamics the charge of an electron equals its bare value, whereas the self-energy and the mass must be renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine structure constant α, in the case of a single, spinless electron. As is well known, if m denotes the bare mass and meff the mass computed from the theory, to order α one has meff∕m=1+(8α∕3π)log(1+12(Λ∕m))+O(α2) which suggests that meff∕m=(Λ∕m)8α∕3π for small α. If correct, in order α2 the leading term should be 12((8α∕3π)log(Λ∕m))2. To check this point we expand meff∕m to order α2. The result is Λ∕m as leading term, suggesting a more complicated dependence of meff on m.

Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes

We present a theoretical study of degeneracy breaking due to short-ranged impurities in finite, single-wall, metallic carbon nanotubes. The effective mass model is used to describe the slowly varying spatial envelope wave functions of spinless electrons near the Fermi level at two inequivalent valleys ($K$-points) in terms of the four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wave function on the sublattice atoms (``$A$'' and ``$B$''). Using boundary conditions at the ends of the tube that neither break valley degeneracy nor mix pseudospin eigenvectors, we use degenerate perturbation theory to show that the presence of impurities has two effects. First, the position of the impurity with respect to the spatial variation of the envelope standing waves results in a sinusoidal oscillation of energy level shift as a function of energy. Second, the position of the impurity within the hexagonal graphite unit cell produces a particular $4\ifmmode\times\else\texttimes\fi{}4$ matrix structure of the corresponding effective Hamiltonian. The symmetry of this Hamiltonian with respect to pseudospin flip is related to degeneracy breaking and, for an armchair tube, the symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing.

Fisher information, Wehrl entropy, and Landau diamagnetism

Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. We reveal a new Fisher-uncertainty relation, derived via the Cramer-Rao inequality, that involves phase space localization and energy fluctuations.

COULOMB BLOCKADE OSCILLATIONS OF CONDUCTANCE AT FINITE ENERGY LEVEL SPACING IN A QUANTUM DOT

We find an analytical expression for the conductance of a single electron transistor in the regime when temperature, level spacing and charging energy of a grain are all of the same order. We consider the model of equidistant energy levels in a grain in the sequential tunneling approximation. In the case of spinless electrons, our theory describes transport through a dot in the quantum Hall regime. In the case of spin-½ electrons, we analyze the line shape of a peak, shift in the position of the peak's maximum as a function of temperature and the values of the conductance in the odd and even valleys.