The excitation operator method and its application to spin dynamics in the one-dimensional XXZ model

Wang, Pei

doi:10.1016/j.physe.2012.10.032

Cited by 5 publications

(6 citation statements)

References 58 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We employ the numerical excitation operator method [29] to calculate the tunneling current I(t) and its stationary value I = lim t→∞ I(t). The numerical method is described as follows.…”

Section: Methodsmentioning

confidence: 99%

“…Due to the presence of a time-dependent potential, it is impossible to solve it analytically. We solve it numerically by the excitation operator method [29], which is accurate and efficient in obtaining both the transient and stationary currents with a time-dependent Hamiltonian (See the details of the method in the supplementary materials). The current depends on the potential V g (t), a stochastic time series, in which the noise term W t is created by a random number generator.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Randomly fluctuating potential-controlled multistable resonant tunneling current through a quantum dot

Wang¹,

Xianlong²,

Xu³

2014

EPL

Self Cite

View full text Add to dashboard Cite

We study the transport through a quantum dot subject to a randomly fluctuating potential, generated by a sequence of pulses in the gate voltage with the help of the autoregressive model. We find that the tunneling current is multistable when the fluctuating potential with a finite correlation time is applied before the non-equilibrium steady state is built up. The non-equilibrium stationary current is heavily dependent on the history of the fluctuating potential during the transient period if the potential has a finite correlation time. Furthermore, the averaged current over the path of the fluctuating potential is a function of its strength and correlation time. Our work therefore provides a robust theoretical proposal for the controlling of the non-equilibrium stationary current through a quantum dot in a randomly fluctuating potential.Introduction.-The study of the electronic transport in mesoscopic systems is one of today's most active research areas in condensed matter physics. A typical currentcarrying system comprises of two electron reservoirs of different temperatures or chemical potentials, between which the electrons continuously flow [1]. Whether the stationary current is uniquely determined by the temperatures and chemical potentials of the reservoirs is a fundamental problem in the quantum transport [2][3][4][5][6][7][8].One of the simplest models that can carry a nonequilibrium stationary current is the resonant level model, typically describing the coherent transport through a nanostructure [9], e.g., a quantum dot made from the semiconductor heterostructure. In the wide band limit, the tunneling current I as a function of the voltage bias V is well known to be I = (Γ/π) arctan[V /(2Γ)] at zero temperature [10], independent of the initial conditions, where Γ denotes the level broadening. In recent years, the transport through nanostructures subject to time-dependent potentials, called the driven quantum transport, attracted much attention [11][12][13][14][15][16][17][18][19][20][21]. In these studies, a deterministic driving, especially a time-periodic one, is used, in which the Keldysh formalism, the Floquet approach, or the transfer matrix approach can be applied (see Ref. [12] for a review of methods). However, little is known about the non-equilibrium stationary current when the level position of a quantum dot fluctuates randomly in time, which can be caused by the interactions between the electrons in the dot and the phonons in the environment [22] or by a manually generated fluctuating potential.The effect of the electron-phonon interaction on the electron transport has been discussed recently by several authors [6][7][8]23], while there is still controversy on the existence of the multistability of the stationary currents.

show abstract

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Randomly fluctuating potential-controlled multistable resonant tunneling current through a quantum dot

Wang¹,

Xianlong²,

Xu³

2014

EPL

Self Cite

View full text Add to dashboard Cite

show abstract

“…, which is solved by the numerical operator method, first developed in Ref [18]. The procedure is summarized as follows.…”

Section: The Numerical Operator Methodsmentioning

confidence: 99%

“…It is obliged to improve a new numerical method for finite two dimensional structures. In this paper, we will introduce the numerical operator method, which is first developed in Ref [18]. In this method, the current is calculated by solving the Heisenberg equation iteratively.…”

Section: Introductionmentioning

confidence: 99%

The numerical operator method to the real time dynamics of currents through the nanostructures with different topologies

2014

Self Cite

View full text Add to dashboard Cite

We present the numerical operator method designed for the real time dynamics of currents through nanostructures beyond the linear response regime. We apply this method to the transient and stationary currents through nanostructures with different topologies, e.g., the flakes of square and honeycomb lattices. We find a quasi-stationary stage with a life proportional to the flake size in the transient currents through the square flakes, but this quasistationary stage is destroyed in the presence of disorder. However, there is no quasi-stationary stage in the transient currents through the honeycomb flakes, showing that the transient current depends strongly upon the topologies of the nanostructures. We also study the stationary current by taking the limit of the current at long times. We find that the stationary current through a square flake increases smoothly as the voltage bias increasing. In contrast, we find a threshold voltage in the current-voltage curve through a honeycomb flake, indicating a gap at the Fermi energy of a honeycomb flake.

show abstract

“…However, the study of the transport through a junction containing the Kitaev chain with incommensurate potentials is still lack. In this paper, we employ the numerical operator method 36 to study this problem. Our results clarify the effect of incommensurate disorder on the transport through topological superconductors, and provide information of distinguishing the different phases by the feature of the current-voltage curves.…”

Section: Introductionmentioning

confidence: 99%

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

2014

Self Cite

View full text Add to dashboard Cite

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e 2 /h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the I − V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2gs + 2∆ with ∆ the p-wave pairing amplitude and gs the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I − V curve exhibits an exponential shape.

show abstract

The excitation operator method and its application to spin dynamics in the one-dimensional XXZ model

Cited by 5 publications

References 58 publications

Randomly fluctuating potential-controlled multistable resonant tunneling current through a quantum dot

Randomly fluctuating potential-controlled multistable resonant tunneling current through a quantum dot

The numerical operator method to the real time dynamics of currents through the nanostructures with different topologies

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

Contact Info

Product

Resources

About