Quantum Transport in Mesoscopic Systems

Physical Review B

We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage V dc , and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series. 1 The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on V dc can reduce the current compared to its dc value, at the same V dc , questioning the terminology "photo-assisted". Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.

Physical Review Letters, 2008

We study the conductance through a ring described by the Hubbard model (such as an array of quantum dots), threaded by a magnetic flux and subject to Rashba spin-orbit coupling (SOC). We develop a formalism that is able to describe the interference effects as well as the Kondo effect when the number of electrons in the ring is odd. In the Kondo regime, the SOC reduces the conductance from the unitary limit, and in combination with the magnetic flux, the device acts as a spin polarizer. 71.70.Ej, 75.10.Jm, Advances in semiconductor technology have provided useful tools to test fundamental concepts of quantum physics, such as the superposition principle and the existence of topological phases . Beautiful demonstrations of these are studies of the Aharonov-Bohm (AB) effect in mesoscopic rings, particularly with embedded quantum dots (QDs) . The effect of interactions in these systems is still a matter of debate . Despite the enormous effort to describe transport through interacting regions [6], at present we do not have a unified procedure to extend the results of the single particle case to manybody cases. A serious shortcoming of the calculation of the conductance G through an interacting ring is that even knowing the exact eigenstates of the ring, there is no simple procedure to calculate G. When the coupling V of the ring to the conducting leads is small, Jagla and Balseiro (JB) used a perturbative expression in V for G that is exact for any V in the non-interacting limit . Similar equations were used recently, assuming that a Zeeman term destroys the Kondo effect in the system . Another expression in order V 2 was proposed last year . Unfortunately these expressions are not valid in the Kondo regime, in which the number of electrons in the ring is odd, because the resulting Kondo physics cannot be described by perturbation theory in V . The ideal conductance in the Kondo regime was recovered by mapping the model into an impurity Anderson model, but in this formulation interference effects were lost .

2015

Physical Review B, 2011

It was recently shown that a spatially modulated Rashba spin-orbit coupling in a quantum wire drives a transition from a metallic to an insulating state when the wave number of the modulation becomes commensurate with the Fermi wave length of the electrons in the wire [G. I. Japaridze et al., Phys. Rev. B 80 041308(R) (2009)]. On basis of experimental data from a gated InAs heterostructure it was suggested that the effect may be put to practical use in a future spin transistor design. In the present article we revisit the problem and present a detailed analysis of the underlying physics. First, we explore how the build-up of charge density wave correlations in the quantum wire due to the periodic gate configuration that produces the Rashba modulation influences the transition to the insulating state. The interplay between the modulations of the charge density and that of the spin-orbit coupling turns out to be quite subtle: Depending on the relative phase between the two modulations, the joint action of the Rashba interaction and charge density wave correlations may either enhance or reduce the Rashba current blockade effect. Secondly, we inquire about the role of the Dresselhaus spin-orbit coupling that is generically present in a quantum wire embedded in semiconductor heterostructure. While the Dresselhaus coupling is found to work against the current blockade of the insulating state, the effect is small in most materials. Using an effective field theory approach, we also carry out an analysis of effects from electron-electron interactions, and show how the single-particle gap in the insulating state can be extracted from the more easily accessible collective charge and spin excitation thresholds. The smallness of the single-particle gap together with the anti-phase relation between the Rashba and chemical potential modulations pose serious difficulties for realizing a Rashba-controlled current switch in an InAs-based device. Some alternative designs are discussed.

Solid State Communications, 2021

We study the behavior of a quantum dot attached to two electrodes with localized spin-orbit (Rashba) interactions. Using the Anderson model we report the occupation number, specific heat, susceptibility and conductance in the zero-band width limit. We compare our results with those in the absence of the Rashba interactions. The symmetry and regime of various phases demonstrate a strong dependence on the above interactions.

Phys Rev B, 2005

The quantum magnetic oscillations of electrical (Shubnikov-de Haas effect) and thermal conductivities are studied for graphene which represents a distinctive example of planar systems with a linear, Dirac-like spectrum of quasiparticle excitations. We show that if utmost care is taken to separate electron and phonon contributions in the thermal conductivity, the oscillations of electron thermal conductivity κ(B) and Lorenz number, L(B) would be observable in the low-field (less than a few teslas) regime.

Les Houches, 2005

Photo: width 7.5cm height 11cm 4 Dmitrii L. Maslov 7.3. Conductance of a wire attached to reservoirs 7.3.1. Inhomogeneous Luttinger-liquid model 7.3.2. Elastic-string analogy 7.3.3. Kubo formula for a wire attached to reservoirs 7.3.4. Experiment 7.4. Spin component of the conductance 7.5. Thermal conductance: Fabry-Perrot resonances of plasmons 8. Acknowledgments Appendix A. Polarization bubble for small q in arbitrary dimensionality Appendix B. Polarization bubble in 1D Appendix B.1. Small q Appendix B.2. q near 2k F Appendix C. Some details of bosonization procedure Appendix C.1. Anomalous commutators Appendix C.2. Bosonic operators Appendix C.2.1. Commutation relations for bosonic fields ϕ and ϑ Appendix C.3. Problem with backscattering References

Physica A-statistical Mechanics and Its Applications, 2002

After a brief historical survey and summary of previous work involving the linear response theory (LRT) Hamiltonian, H =H (system)−AF(t), where the latter part refers to the e ect of an applied ÿeld F(t) as in Kubo's theory, we deal with the nonlinear problem in which the applied electric ÿeld of arbitrary strength, as well as a possible magnetic ÿeld, are included in the system Hamiltonian, H = H [system(E; B)]. In Part A of this study we deal with the general formalism on the many-body level. Projection operators are applied to the Von Neumann equation in the interaction picture, H (system) = H 0 + V , which after the Van Hove limit, → 0; t → ∞; 2 t ÿnite, leads to the master equation for @ =@t, containing both the Pauli-Van Hove diagonal part involving the transitions W , and a nondiagonal quantum-interference part, as obtained by us previously. Likewise, the full many-body current operator JA is obtained by manipulation of the Heisenberg equation of motion for dA=dt in the interaction picture.

Physical Review B, 2000

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are reexamined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters, a fine-tuning which is possible even with bandwidth mismatch between superconductor and normal metal. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E << ∆, the superconducting gap) can be obtained by "integrating out" the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior. We calculate the critical exponents, which are different at these two different fixed points.