Short time dynamics of molecular junctions after projective measurement

In this work, we study the short time dynamics of a molecular junction described by Anderson-Holstein model using full-counting statistics after projective measurement. The coupling between the central quantum dot (QD) and two leads was turned on at remote past and the system is evolved to steady state at time $t=0$, when we perform the projective measurement in one of the lead. Generating function for the charge transfer is expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. It is found that the current is not constant at short times indicating that the measurement does perturb the system. We numerically compare the current behaviors after the projective measurement with those in the transient regime where the subsystems are connected at $t=0$. The universal scaling for high-order cumulants is observed for the case with zero QD occupation due to the unidirectional transport at short times. The influences of electron-phonon interaction on short time dynamics of electric current, shot noise and differential conductance are analyzed

The focusing of electron flow in a bipolar Graphene ribbon with different chiralities

The focusing of electron flow in a symmetric p-n junction (PNJ) of graphene ribbon with different chiralities is studied. Considering the PNJ with the sharp interface, in a armchair ribbon, the electron flow emitting from $(-L,0)$ in n-region can always be focused perfectly at $(L,0)$ in p-region in the whole Dirac fermion regime, i.e. in whole regime $E_0<t$ where $E_0$ is the distance between Dirac-point energy and Fermi energy and $t$ is the nearest hopping energy. For the bipolar ribbon with zigzag edge, however, the incoming electron flow in n-region is perfectly converged in p-region only in a very low energy regime with $E_0<0.05t$. Moreover, for a smooth PNJ, electrons are backscattered near PNJ, which weakens the focusing effect. But the focusing pattern still remains the same as that of the sharp PNJ. In addition, quantum oscillation in charge density occurs due to the interference between forward and backward scattering. Finally, in the presence of weak perpendicular magnetic field, charge carriers are deflected in opposite directions in the p-region and n-region. As a result, the focusing effect is smeared. The lower energy $E_0$, the easier the focusing effect is destroyed. For the high energy $E_0$ (e.g. $E_0=0.9t$), however, the focusing effect can still survive in a moderate magnetic field on order of one Tesla.Comment: 29 pages, 16 figure

Symmetry and transport property of spin current induced spin-Hall effect

We study the spin current induced spin-Hall effect that a longitudinal spin dependent chemical potential $qV_{s=x,y,z}$ induces a transverse spin conductances $G^{ss'}$. A four terminal system with Rashba and Dresselhaus spin-orbit interaction (SOI) in the scattering region is considered. By using Landauer-B$\ddot u$ttiker formula with the aid of the Green function, various spin current induced spin-Hall conductances $G^{ss'}$ are calculated. With the charge chemical potential $qV_c$ or spin chemical potential $qV_{s=x,y,z}$, there are 16 elements for the transverse conductances $G^{\mu \nu}_p=J_{p,\mu}/V_{\nu}$ where $\mu,\nu=x,y,z,c$. Due to the symmetry of our system these elements are not independent. For the system with $C_2$ symmetry half of elements are zero, when the center region only exists the Rashba SOI or Dresselhaus SOI. The numerical results show that of all the conductance elements, the spin current induced spin-Hall conductances $G^{ss'}$ are usually much greater (about one or two orders of magnitude) than the spin Hall conductances $G^{sc}$ and the reciprocal spin Hall conductances $G^{cs}$. So the spin current induced spin-Hall effect is dominating in the present device.Comment: 7 pages, 6 figure

Transient dynamics of molecular devices under step-like pulse bias

We report first principles investigation of time-dependent current of molecular devices under a step-like pulse.Our results show that although the switch-on time of the molecular device is comparable to the transit time, much longer time is needed to reach the steady state. In reaching the steady state the current is dominated by resonant states below Fermi level. The contribution of each resonant state to the current shows the damped oscillatory behavior with frequency equal to the bias of the step-like pulse and decay rate determined by the life time of the corresponding resonant state. We found that all the resonant states below Fermi level have to be included for accurate results. This indicates that going beyond wideband limit is essential for a quantitative analysis of transient dynamics of molecular devices

First-principles investigation of dynamical properties of molecular devices under a steplike pulse

We report a computationally tractable approach to first principles investigation of time-dependent current of molecular devices under a step-like pulse. For molecular devices, all the resonant states below Fermi level contribute to the time-dependent current. Hence calculation beyond wideband limit must be carried out for a quantitative analysis of transient dynamics of molecules devices. Based on the exact non-equilibrium Green's function (NEGF) formalism of calculating the transient current in Ref.\onlinecite{Maciejko}, we develop two approximate schemes going beyond the wideband limit, they are all suitable for first principles calculation using the NEGF combined with density functional theory. Benchmark test has been done by comparing with the exact solution of a single level quantum dot system. Good agreement has been reached for two approximate schemes. As an application, we calculate the transient current using the first approximated formula with opposite voltage $V_L(t)=-V_R(t)$ in two molecular structures: Al-${\rm C}_{5}$-Al and Al-${\rm C}_{60}$-Al. As illustrated in these examples, our formalism can be easily implemented for real molecular devices. Importantly, our new formula has captured the essential physics of dynamical properties of molecular devices and gives the correct steady state current at $t=0$ and $t\rightarrow \infty$.Comment: 15 pages, 8 figure

Crossed Andreev effects in two-dimensional quantum Hall systems

We study the crossed Andreev effects in two-dimensional conductor/superconductor hybrid systems under a perpendicular magnetic field. Both a graphene/superconductor hybrid system and an electron gas/superconductor one are considered. It is shown that an exclusive crossed Andreev reflection, with other Andreev reflections being completely suppressed, is obtained in a high magnetic field because of the chiral edge states in the quantum Hall regime. Importantly, the exclusive crossed Andreev reflection not only holds for a wide range of system parameters, e.g., the size of system, the width of central superconductor, and the quality of coupling between the graphene and the superconductor, but also is very robust against disorder. When the applied bias is within the superconductor gap, a robust Cooper-pair splitting process with high-efficiency can be realized in this system.Comment: 10 pages, 10 figure

The parity of specular Andreev reflection under mirror operation in zigzag graphene ribbon

It is known that the parity of reflection amplitude can either be even or odd under the mirror operation. Up to now, all the parities of reflection amplitude in the one-mode energy region are even under the mirror operation. In this paper, we give an example of odd parity for Andreev reflection (AR) in a three-terminal graphene-supercondutor hybrid systems. We found that the parity is even for the Andreev retroreflection (ARR) and odd for specular Andreev reflection (SAR). We attribute this remarkable phenomenon to the distinct topology of the band structure of graphene and the specular Andreev reflection involving two energy bands with different parity symmetry. As a result of odd parity of SAR, the SAR probability of a four-terminal system with two superconducting leads (two reflection interfaces) can be zero even when the system is asymmetric due to the quantum interference of two ARs.Comment: 11 pages, 3 figure