## Publications

126 results found

Ridley M, MacKinnon A, Kantorovich L, 2017, Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias, *Physical Review. B*, Vol: 95, ISSN: 0163-1829

Working within the nonequilibrium Green’s function formalism, a formula for the two-time current correlationfunction is derived for the case of transport through a nanojunction in response to an arbitrary time-dependentbias. The one-particle Hamiltonian and the wide-band limit approximation are assumed, enabling us to extract allnecessary Green’s functions and self-energies for the system, extending the analytic work presented previously[Ridleyet al.,Phys. Rev. B91,125433(2015)]. We show that our expression for the two-time correlationfunction generalizes the Büttiker theory of shot and thermal noise on the current through a nanojunction to thetime-dependent bias case including the transient regime following the switch-on. Transient terms in the correlationfunction arise from an initial state that does not assume (as is usually done) that the system is initially uncoupled,i.e., our approach is partition free. We show that when the bias loses its time dependence, the long-time limit ofthe current correlation function depends on the time difference only, as in this case an ideal steady state is reached.This enables derivation of known results for the single-frequency power spectrum and for the zero-frequencylimit of this power spectrum. In addition, we present a technique which facilitates fast calculations of the transientquantum noise, valid for arbitrary temperature, time, and voltage scales. We apply this formalism to a molecularwire system for both dc and ac biases, and find a signature of the traversal time for electrons crossing the wire inthe time-dependent cross-lead current correlations.

Ridley M, MacKinnon A, Kantorovich L, 2016, Fluctuating-bias controlled electron transport in molecular junctions, *Physical Review B*, Vol: 93, ISSN: 1550-235X

We consider the problem of transport through a multiterminal molecular junction in the presence of a stochastic bias, which can also be used to describe transport through fluctuating molecular energy levels. To describe these effects, we first make a simple extension of our previous work [Phys. Rev. B 91, 125433 (2015)] to show that the problem of tunneling through noisy energy levels can be mapped onto the problem of a noisy driving bias, which appears in the Kadanoff-Baym equations for this system in an analogous manner to the driving term in the Langevin equation for a classical circuit. This formalism uses the nonequilibrium Green's function method to obtain analytically closed formulas for transport quantities within the wide-band limit approximation for an arbitrary time-dependent bias and it is automatically partition free. We obtain exact closed formulas for both the colored and white noise-averaged current at all times. In the long-time limit, these formulas possess a Landauer-Büttiker–type structure which enables the extraction of an effective transmission coefficient for the transport. Expanding the Fermi function into a series of simple poles, we find an exact formal relation between the parameters which characterize the bias fluctuations and the poles of the Fermi function. This enables us to describe the effect of the temperature and the strength of the fluctuations on the averaged current which we interpret as a quantum analog to the classical fluctuation-dissipation theorem. We use these results to convincingly refute some recent results on the multistability of the current through a fluctuating level, simultaneously verifying that our formalism satisfies some well-known theorems on the asymptotic current. Finally, we present numerical results for the current through a molecular chain which demonstrate a transition from nonlinear to linear I−V characteristics as the strength of fluctuations is increased, as well as a stochastic reson

Ridley M, MacKinnon A, Kantorovich L, 2016, Calculation of the current response in a nanojunction for an arbitrary time-dependent bias:application to the molecular wire, Progress in Non-equilibrium Green’s Functions (PNGF VI), Publisher: IOP Publishing: Conference Series, ISSN: 1742-6588

PAPER • OPEN ACCESSCalculation of the current response in a nanojunction for an arbitrary time-dependent bias: application to the molecular wireMichael Ridley1,2, Angus MacKinnon2 and Lev Kantorovich1Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 696, Number 1 Article PDF12 Total downloadsExport citation and abstractBibTeX RISShare this articleArticle informationAbstractRecently [Phys. Rev. B 91, 125433 (2015)] we derived a general formula for the time-dependent quantum electron current through a molecular junction subject to an arbitrary time-dependent bias within the Wide Band Limit Approximation (WBLA) and assuming a single particle Hamiltonian. Here we present an efficient numerical scheme for calculating the current and particle number. Using the Padé expansion of the Fermi function, it is shown that all frequency integrals occurring in the general formula for the current can be removed analytically. When the bias in the reservoirs is assumed to be sinusoidal it is possible to manipulate the general formula into a form containing only summations over special functions. To illustrate the method, we consider electron transport through a one-dimensional molecular wire coupled to two leads subject to out-of-phase biases. We also investigate finite size effects in the current response and particle number that result from the switch-on of this bias.

Ridley M, MacKinnon A, Kantorovich L, 2015, Current through a multilead nanojunction in response to an arbitrary time-dependent bias, *Physical Review B*, Vol: 91, ISSN: 1550-235X

We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide-band-limit approximation, it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et al. [Phys. Rev. B 50, 5528 (1994)] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et al. [Phys. Rev. B 89, 085131 (2014)] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally varying bias. At certain frequencies of the driving bias, we observe “ringing” oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude, and temperature is also investigated.

Tahir M, MacKinnon A, Schwingenschlogl U, 2014, Novel spectral features of nanoelectromechanical systems, *Scientific Reports*, Vol: 4, ISSN: 2045-2322

Tahir M, Sabeeh K, MacKinnon A, 2011, Temperature effects on the magnetoplasmon spectrum of a weakly modulated graphene monolayer, *JOURNAL OF PHYSICS-CONDENSED MATTER*, Vol: 23, ISSN: 0953-8984

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- Citations: 5

Tahir M, MacKinnon A, 2010, Time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator, *PHYSICAL REVIEW B*, Vol: 81, ISSN: 1098-0121

We present a theoretical study of time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator within the nonequilibrium Green’s function technique. An arbitrary voltage is applied to the tunnel junction and electrons in the leads are considered to be at zero temperature. The transient and the steady-state behavior of the system are considered here in order to explore the quantum dynamics of the oscillator as a function of time. The properties of the phonon distribution of the nanomechanical oscillator strongly coupled to the electrons on the dot are investigated using a nonperturbative approach. We consider both the energy transferred from the electrons to the oscillator and the Fano factor as a function of time. We discuss the quantum dynamics of the nanomechanical oscillator in terms of pure and mixed states. We have found a significant difference between a quantum and a classical oscillator. In particular, the energy of a classical oscillator will always be dissipated by the electrons whereas the quantum oscillator remains in an excited state. This will provide useful insight for the design of experiments aimed at studying the quantum behavior of an oscillator.

Kramer B, MacKinnon A, Ohtsuki T,
et al., 2010, FINITE SIZE SCALING ANALYSIS OF THE ANDERSON TRANSITION, *INTERNATIONAL JOURNAL OF MODERN PHYSICS B*, Vol: 24, Pages: 1841-1854, ISSN: 0217-9792

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- Citations: 22

Tahir M, Sabeeh K, MacKinnon A, 2010, The magnetoplasmon spectrum of a weakly modulated two-dimensional electron gas system, *JOURNAL OF PHYSICS-CONDENSED MATTER*, Vol: 22, ISSN: 0953-8984

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- Citations: 1

Kramer B, MacKinnon A, Ohtsuki T, et al., 2010, Finite size scaling analysis of the Anderson transition, 50 Years of Anderson Localization, Pages: 347-360, ISBN: 9789814299060

This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localization and the Anderson model of localization are briey sketched. The finite size scaling method is described. Recent results for the critical exponents of the di_erent symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.

MacKinnon A, 2008, Towards a simulation of disordered systems with interactions, *JOURNAL OF PHYSICS-CONDENSED MATTER*, Vol: 20, ISSN: 0953-8984

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- Citations: 2

Tahir M, MacKinnon A, 2008, Quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator, *Physical Review B*, Vol: 77, ISSN: 2469-9950

We discuss the quantum transport of electrons through a resonant tunnel junction coupled to a nanomechanical oscillator at zero temperature. By using the Green’s-function technique, we calculate the transport properties of electrons through a single dot strongly coupled to a single oscillator. We consider a finite chemical-potential difference between the right and left leads. In addition to the main resonant peak of electrons on the dot, we find satellite peaks due to the creation of phonons. These satellite peaks become sharper and more significant with increasing coupling strength between the electrons and the oscillator. We also consider the energy transferred from the electrons to the oscillator.

Mackinnon A, 2008, Localization in disordered systems with interactions, International Workshop on the Physics of Mesoscopic and Disordered Materials (MESODIS 2006), Publisher: INDIAN ACAD SCIENCES, Pages: 211-220, ISSN: 0304-4289

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- Citations: 1

Tahir M, Sabeeh K, MacKinnon A, 2007, Weiss oscillations in the electronic structure of modulated graphene, *JOURNAL OF PHYSICS-CONDENSED MATTER*, Vol: 19, ISSN: 0953-8984

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- Citations: 10

MacKinnon A, 2005, Theory of some nano-electro-mechanical systems, *Physica E-Low-Dimensional Systems & Nanostructures*, Vol: 29, Pages: 399-410, ISSN: 1386-9477

Carter JM, MacKinnon A, 2005, Disorder and interactions in one-dimensional systems, *PHYSICAL REVIEW B*, Vol: 72, ISSN: 1098-0121

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- Citations: 18

Mackinnon A, Pendry J, 2004, Elizabeth Ann Johnson - Obituaries, *PHYSICS TODAY*, Vol: 57, Pages: 105-106, ISSN: 0031-9228

MacKinnon A, Armour AD, 2003, Transport via a quantum shuttle, 23rd International Conference on Low Temperature Physics (LT23), Publisher: ELSEVIER SCIENCE BV, Pages: 95-96, ISSN: 1386-9477

We investigate the effect of quantisation of vibrational modes on a system in which the transport path is through a quantum dot mounted on a cantilever or spring such that tunnelling to and from the dot is modulated by the oscillation. We consider here the implications of quantum aspects of the motion. Peaks in the current–voltage characteristic are observed which correspond to avoided level crossings in the eigenvalue spectrum. Transport occurs through processes in which phonons are created. This provides a path for dissipation of energy as well as a mechanism for driving the oscillator, thus making it easier for electrons to tunnel onto and off the dot and be ferried across the device.

MacKinnon A, Armour AD, 2003, Quantum interference and inelastic scattering in a which-way device, 23rd International Conference on Low Temperature Physics (LT23), Publisher: Elsevier, Pages: 235-236, ISSN: 1386-9477

A which-way device is one which is designed to detect which of two paths is taken by a quantum particle. One such device is represented by an Aharonov–Bohm ring with a quantum dot on one branch. A charged cantilever or spring is brought close to the dot as a detector of the presence of an electron. In this paper we show that, contrary to popular belief, it is in fact possible to change the state of the oscillator while preserving the quantum interference phenomenon, but that this tells us little about the path traversed by the particle.

Carter JM, MacKinnon A, 2003, Disorder and interactions on a 1D chain, *Journal of the Physical Society of Japan*, Vol: 72, Pages: 163-164, ISSN: 0031-9015

MacKinnon A, Armour AD, 2003, Quantum interference and inelastic scattering in a model which-way device, Pages: 118-122, ISSN: 0031-9015

A which-way device is one which is designed to detect which of 2 paths is taken by a quantum particle, whether Schrodinger's cat is dead or alive. One possible such device is represented by an Aharonov-Bohm ring with a quantum dot on one branch. A charged cantilever or spring is brought close to the dot as a detector of the presence of an electron. The conventional view of such a device is that any change in the state of the cantilever implies a change in the electron state which will in turn destroy the interference effects. In this paper we show that it is in fact possible to change the state of the oscillator while preserving the quantum interference phenomenon. © 2003 The Physical Society of Japan.

Römer RA, MacKinnon A, Villagonzalo C, 2003, Thermoelectric properties of disordered systems, Pages: 167-168, ISSN: 0031-9015

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- Citations: 7

Carter JM, MacKinnon A, 2003, Disorder and interactions on a 1D chain, Pages: 163-164, ISSN: 0031-9015

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- Citations: 1

MacKinnon A, 2003, Bernhard Kramer and his contributions to physics, Anderson localization and its ramifications: disorder, phase coherence and electron correlations, Editors: Brandes, Kettemann, Berlin, Publisher: Springer, Pages: VII-X, ISBN: 9783540407850

MacKinnon A, Armour AD, 2003, Quantum interference and inelastic scattering in a model which-way device, *Journal of the Physical Society of Japan*, Vol: 72, Pages: 118-122, ISSN: 0031-9015

Romer RA, MacKinnon A, Villagonzalo C, 2003, Thermoelectric properties of disordered systems, *Journal of the Physical Society of Japan*, Vol: 72, Pages: 167-168, ISSN: 0031-9015

MacKinnon A, 2003, Transfer matrices and disordered systems, Berlin, 283rd international WE Heraeus seminar on localization, quantum coherence and interactions, Hamburg, Germany, 4 - 6 September 2002, Publisher: Springer-Verlag, Pages: 21-30

MacKinnon A, 2002, Quantum gears: a simple mechanical system in the quantum regime, *NANOTECHNOLOGY*, Vol: 13, Pages: 678-681, ISSN: 0957-4484

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- Citations: 10

Taylor AP, MacKinnon A, 2002, The metal-insulator transition in disordered systems: a new approach to the critical behaviour, *JOURNAL OF PHYSICS-CONDENSED MATTER*, Vol: 14, Pages: 8663-8675, ISSN: 0953-8984

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- Citations: 5

Armour AD, MacKinnon A, 2002, Transport via a quantum shuttle, *PHYSICAL REVIEW B*, Vol: 66, ISSN: 2469-9950

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- Citations: 86

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