Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session W16: Non-Equilibrium, Tunneling and Many-Body Properties of Quantum Dots |
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Sponsoring Units: DCMP Chair: Giovanni Vignale, University of Missouri Room: LACC 404A |
Thursday, March 24, 2005 2:30PM - 2:42PM |
W16.00001: Out-of-equilibrium Transport Phenomena through a Quantum Dot Tatsuya Fujii We investigate nonequilibrium transport through a dot in a finite magnetic field in a weak correlation regime by using the self-consistent perturbation theory in the Keldysh formalism. Separation of the density of states between the up and down spins becomes smaller gradually and ends up with the Zeeman energy as increasing the bias voltage. Concerning the differential conductance the zero-bias peak splits into two peaks when magnetic field is increased. The critical field for the splitting decreases as the Coulomb interaction is increased. [Preview Abstract] |
Thursday, March 24, 2005 2:42PM - 2:54PM |
W16.00002: The Bethe Ansatz Out of Equilibrium: Exact calculations of steady-state properties in quantum impurity models Pankaj Mehta, Natan Andrei We develop a scattering approach to the computation of steady state properties in quantum impurity models by generalizing the Bethe Ansatz approach to out of equilibrium situations. We present our results for the I-V charecteristics of the interacting resonant level model and compare with Keldysh where results are available. We also discuss calculations in progress to use this approach to describe quantum dots subject to a finite bias. [Preview Abstract] |
Thursday, March 24, 2005 2:54PM - 3:06PM |
W16.00003: Numerical Renormalization-Group Approach to the Non-Equilibrium Dynamics of Quantum Impurity Problems Frithjof Anders, Avraham Schiller We present a novel approach to time dependent non-equilibrium quantum impurity problems. It is based on a combination of Feynman's concept of a reduced density matrix and Wilson's numerical renormalization group. We discuss how dissipation and decoherence arises and benchmark our algorithm using the known exact solution of the resonant-level model. Depending on the cutoff scheme, all states are needed for tracking the full time evolution, for which we show a suitable resummation procedure. As a first application, we extract the two different time scales for spin- and charge-relaxation processes in the single impurity Anderson model. An outlook for pulse-driven quantum dot problems will be given. [Preview Abstract] |
Thursday, March 24, 2005 3:06PM - 3:18PM |
W16.00004: Shot noise in resonant tunneling through a two-level system Ivana Djuric, Bing Dong, Hong-Liang Cui We analyze the shot noise in electron tunneling through a two-level system connected to two leads taking account for the presence of coherent transitions between the two levels and Coulomb blockade effects. As particular implementations of such a system we study: a) a single quantum dot connected to two ferromagnetic leads with weak intradot spin-flip scattering, and b) two sequentially coupled quantum dots with coherent tunneling between them. In case a) we observe the shot noise enhancement with increasing the degree of polarization of the leads in both, parallel and antiparallel, lead configurations. The spin-flip scattering, on the other hand, causes the shot noise reduction. The frequency-dependent shot noise shows a peak in the parallel configuration but a dip in the antiparallel configuration at the Rabi frequency, reflecting different symmetries of states carrying current. In case b) we observe the appearance of the negative differential conductance in the current-voltage characteristic as a result of the enhanced decoherence rate induced by the presence of the second electron inside the system. The shot noise experiences an enhancement but remains sub-Poissonian. The frequency-dependent shot noise exhibits a dip at the tunneling frequency. [Preview Abstract] |
Thursday, March 24, 2005 3:18PM - 3:30PM |
W16.00005: Shot noise induced switching of current in one-dimensional bistable resonant tunneling devices Oleg Tretiakov, Konstantin Matveev Current switching in a double-barrier resonant tunneling structure is studied in the regime where the current-voltage characteristic exhibits intrinsic bistability. In the bistable region of the $I$-$V$ curve two different steady states of current are possible at each value of bias. Close to the upper boundary $V_{th}$ of the bistable region the upper current state is metastable. The current decays from this metastable to the lower stable state due to shot noise. We find the time of this switching process in one-dimensional structures. The latter are devices whose cross-section has a shape of a strip with the width small compared to its length. As the bias $V$ is tuned away from the boundary value $V_{th}$ of the bistable region, the mean switching time $\tau$ increases exponentially. We show that in long strips $\ln\tau \propto (V_{th} -V)^{5/4}$, whereas in short strips $\ln\tau \propto (V_{th}-V)^{3/2}$. The fact that the problem is one-dimensional enables us to obtain analytically exact expressions for both the exponential factor and the prefactor of $\tau$ as functions of bias, in-plane conductivity, and length of the strip. Furthermore, we show that, depending on the parameters of the system, the switching can be initiated either in the middle of the strip, or at its end. Work supported by U.S. DOE, Office of Science, Contract No. W-31-109-ENG-38. [Preview Abstract] |
Thursday, March 24, 2005 3:30PM - 3:42PM |
W16.00006: Non equilibrium noise peak in magnetically doped mesoscopic wires Eran Lebanon, Piers Coleman We study the non-equilibrium noise in mesoscopic diffusive wires hosting magnetic impurities. We find that the noise develops a peak at intermediate source-drain biases of the order of the Kondo temperature. The enhanced impurity contribution at intermediate biases is also manifested in the effective distribution. The predicted peak represents increased inelastic scattering rate at the non-equilibrium Kondo crossover. [Preview Abstract] |
Thursday, March 24, 2005 3:42PM - 3:54PM |
W16.00007: A Numerical Parameter Study of Electronic Transport through a Resonant Tunneling Structure Greg Recine, Bernard Rosen, Hong-Liang Cui The standard Resonant Tunneling Structure (RTS) studied by lattice Weyl-Wigner methods is a layered active region confined in a 'simulation box'. Centered in this n-doped box is an undoped double barrier region consisting of a spacer layers (GaAs), barriers (AlGaAs) \& wells (GaAs). We examine the RTS dependency on simulation box parameters by observing the emitter quantum well's (EQW) effect on I-V curve features (hysteresis \& plateau) and intrinsic high frequency current oscillations. For small boxes ($<$70nm) the hysteresis size, oscillation strength and the I-V curve shape vary noticeably with box size. For boxes $>$90nm the I-V curve is insensitive to box size. Mid-size box ranges ($\sim$70-90nm) are unstable. For small boxes the space between the boundary and the active region is small enough to be a quantum well itself. This results in large amplitude damped standing carrier density waves in the emitter region which accounts for the EQW formation (through electron depletion). As the box grows, the density wave amplitude at the boundary tends towards the background density and the EQW disappears. Only when the simulation box is bigger than the interference length of the density wave does the I-V curve becomes insensitive to the box length. [Preview Abstract] |
Thursday, March 24, 2005 3:54PM - 4:06PM |
W16.00008: Shot noise of a quantum displacement detector Aashish Clerk, Steve Girvin Several recent experiments \footnote{Knobel {\it et al.}, Nature {\bf 424}, 291 (2003).} \footnote{M. D. LaHaye {\it et al.}, Science {\bf 304}, 74, (2004).} have demonstrated that a mesoscopic conductor (such as a single-electron transistor) can act as a near quantum-limited detector of the position of a nanomechanical oscillator; such experiments directly probe the output noise of the detector. Here, we study theoretically the frequency-dependent current noise of a quantum tunnel junction coupled to a nano-mechanical oscillator, focusing on the quantum versus classical aspects of the noise. We treat both the cases of dc and ac voltage bias. The dynamics of the oscillator can lead to large signatures in the shot noise, even if the oscillator-tunnel junction coupling is too weak to yield an appreciable signature in the average current. Moreover, the modification of the shot noise by the oscillator cannot be fully explained by a simple picture of a fluctuating conductance. [Preview Abstract] |
Thursday, March 24, 2005 4:06PM - 4:18PM |
W16.00009: Out-of-phase plasmons in double-layer electron systems B. Tanatar, G. Vignale It is well known that a double-layer electron system supports an out-of-phase plasmon in which the densities of the two layers oscillate out of phase with each other. In RPA this mode exhibits acoustic behavior (i.e., a linear dispersion in $q$ at small $q$). It has been suggested that at low density it may acquire an ``optical'' character , i.e., a gap at $q=0$$^1$. Here we investigate the long-wavelength dispersion relation of out-of-phase plasmons using dynamic exchange-correlation (xc) kernels within the density-density response function for a double-layer system. Starting from the recently formulated exact expression for the dynamic xc-kernel at long-wavelengths $ f_{{\rm xc},\alpha\beta}(q,\omega)= [2\delta_{\alpha\beta}-1]{n^2\over n_\alpha n_\beta}\,{A(\omega) \over q^2} +B_{\alpha\beta}(\omega)+{\cal O}(q^2) $ where $\alpha,\,\beta$ are the layer indices, $n_\alpha+n_\beta=2n$, we obtain a workable formula for the frequency dependent function $A (\omega)$. A mode-decoupling form for $\hbox{Im}[A(\omega)]$ together with the Kramers-Kronig relation and exact high and low frequency limits allows us to construct $A(\omega)$. Solving for the zeros of the dielectric function of the double- layer system we obtain the long-wavelength form of the out-of- phase plasmon dispersion and discuss the possibility of a gap developing at low density.\\ $^1$G. Kalman, V. Valtchinov, and K. I. Golden, Phys. Rev. Lett. {\bf 82}, 3124 (1999) [Preview Abstract] |
Thursday, March 24, 2005 4:18PM - 4:30PM |
W16.00010: The effect of electron-phonon interaction in artificial atoms within nanoscale Yiming Mi, Shuichi Iwata A model artificial atom containing two electronic states and several optical phonon modes is considered. The physical properties are studied by calculating the electronic Green's function and dielectric function of the artificial atom within non-perturbative approach. The calculated partial spectral densities of states , optical absorption and emission spectra of the artifical atoms under consideration are given explicitly for different physical parameters. It is shown that the inter-, intra-level interactions and multi-phonon processes are important in artificial atoms within nanoscale. [Preview Abstract] |
Thursday, March 24, 2005 4:30PM - 4:42PM |
W16.00011: Tuning the quantum critical crossover in quantum dots Ganpathy Murthy Quantum dots with large Thouless number g embody a regime where both disorder and interactions can be treated nonperturbatively using large-N techniques (with N=g) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a new, tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at the new energy scale. The nonperturbative physics of this regime can only be described by the large-N approach, as we illustrate with two experimentally relevant examples. G. Murthy, PRB 70, 153304 (2004). G. Murthy, R. Shankar, D. Herman, and H. Mathur, PRB 69, 075321 (2004) [Preview Abstract] |
Thursday, March 24, 2005 4:42PM - 4:54PM |
W16.00012: QMC Study of Quantum Dots with Strong Interactions Amit Ghosal, Cyrus Umrigar, Denis Ullmo, Harold Baranger We study the interplay of Coulomb repulsion and shell effects for electrons confined in a circular parabolic quantum dot. We use variational and diffusion Monte Carlo methods to calculate the ground state, excitation energies, and addition energy. We focus on the dependence of these quantities on both the total electron number, N up to 20, and the electron gas parameter (which measures interaction strength), $r_s$ up to about 10. For strong interaction our results show violations of Hund's second rule, which is expected. Strong interaction drives an electron gas toward Wigner crystallization; it is thought that nanoscale confinement may affect significantly this process, leading perhaps to ``incipient" crystallization. With regard to the latter, we present results for the pair correlation function and discuss implications.\\ This work was supported by the NSF (DMR-0103003 and DMR- 0205328). [Preview Abstract] |
Thursday, March 24, 2005 4:54PM - 5:06PM |
W16.00013: Beyond the maximum density droplet: From few-electron to many-electron quantum dots in strong magnetic fields Yuesong Li, Constantine Yannouleas, Uzi Landman Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of $N$-electron parabolic quantum dots in strong magnetic fields in the medium-size range $10 \leq N \leq 30$. The physical picture suggested by our calculations is that of non-rigid rotating Wigner molecules (RWM's) comprising multiple rings, with the rings rotating independently of each other. A quasi-classical expression for the energetics of such non-rigid multi-ring RWM's is derived; it is applicable to arbitrary sizes given the corresponding equilibrium configuration of classical point charges. [Preview Abstract] |
Thursday, March 24, 2005 5:06PM - 5:18PM |
W16.00014: Singlet-triplet splitting and electron localization in elliptic quantum dots Constantine Yannouleas, Uzi Landman Experimental control of the singlet-triplet splitting in a two- electron $(2e)$ quantum dot molecule (QDM) as a function of the magnetic field is an important step in the implementation of quantum logic gates.\footnote{D.M. Zumb\"{u}hl {\it et al.\/}, cond-mat/0408276} Using symmetry breaking at the unrestricted Hartree-Fock level and subsequent symmetry restoration via projection techniques, we show that the two electrons localize and form a molecule (in the sense of Heitler- London) even when the interdot barrier {\it vanishes\/}.$^3$ This $2e$ molecule is characterized by a singlet-triplet curve similar to that of a QDM with a {\it finite\/} interdot barrier.\footnote{C. Yannouleas and U. Landman, Int. J. Quantum Chem. {\bf 90}, 699 (2002)} Most importantly, we find that a $2e$ molecule exhibiting a similar singlet-triplet curve is also formed in the case of a {\it single}, but {\it elliptic\/} QD; this is in agreement with experimental observations.$^2$ [Preview Abstract] |
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W16.00015: Interaction effects in the thermodynamic properties of quantum-dots: a Hartree-Fock study. Nelson Studart, Luis Dias da Silva We study electron-electron interaction effects in the thermodynamic properties of quantum-dot systems. Using a finite-temperature self-consistent Hartree-Fock method, [1,2,3] we obtain the direct and exchange contributions to the specific heat $C_{v}$ of square quantum dots of size $L$ with up to $N=20$ electrons. An exchange-induced phase transition [2] is observed at a finite transition temperature $T^*$. Our analysis shows that $T^*$ scales with $L^{-1}$ and is on the range of a few Kelvin for dots tens of nanometers across. The exchange contribution to $C_{v}$ dominates over the direct and kinetic contributions in the intermediate regime of interaction strength ($r_{s}\sim 1$), similarly to results obtained for the magnetic susceptibility [3]. Furthermore, the specific oscillates as function of an applied magnetic field and both oscillation amplitude and period are modified by the electron-electron interaction. Supported by FAPESP-Brazil. \newline [1] H. Tamura and M. Ueda, Phys. Rev. Lett. 79 1345 (1997). \newline [2] D.~J. Dean, M.~R. Strayer, and J.~C. Wells, Phys. Rev. B 64, 125305 (2001). \newline [3] L.~G.~G.~V. Dias da Silva, C. Lewenkopf, and Nelson Studart, Phys. Rev. B 69, 075311 (2004). [Preview Abstract] |
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W16.00016: Charge Oscillations in Quantum Dots Alessandro Silva, Michael Sindel, Yuval Oreg, Jan von Delft We analyze the local level occupation of a spinless, interacting two-level quantum dot coupled to two leads by means of Wilson's numerical renormalization group. A gate voltage sweep, causing a rearrangement of the charge such that the system's energy is minimized, leads to oscillations, and sometimes even inversions, in the level occupations. We find that these oscillations, qualitatively understandable by a simple Hartree analysis, are generic and occur in a wide range of system parameters. By allowing a relative sign in one tunnelling matrix element between dot and leads, we extend our findings to more generic models. [Preview Abstract] |
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