Coulomb Drag Effect In Capacitively Coupled Double Quantum-dot System

The Coulomb interaction between electrons plays an extremely important role in condensed matter physics,and its existence leads to extremely rich physical phenomena,such as high temperature superconductivity and fractional quantum hall effect,and Coulomb drag effect,which have attracted extensive attention and research.This paper mainly focuses on the Coulomb drag effect,which is is an interesting transport phenomenon caused by Coulomb interaction in mesoscopic systems.It refers to two conductors that are adjacent but not in contact,when a potential difference(or temperature difference)is applied to one of the conductors and generate an electric current,a current or potential difference is induced in another conductor,the mechanism is the energy or momentum transfer of electrons between conductors caused by Coulomb interactions.Coulomb drag effect was first observed in AlGaAs / GaAs electron gas experiments in 1987,then widely studied in low-dimensional mesoscopic systems such as quantum dots and nanowires.In recent years,due to the rapid development of two-dimensional materials such as graphene,research on the new mechanisms of the Coulomb drag effect has set off a new wave.Inspired by recent experimental and theoretical research advances of the Coulomb drag effect in a capacitively coupled double quantum-dot systems,we use the T-matrix based master equation and hierarchical equation of motion to theoretically study the rich electron transport caused by Coulomb drag effect in different parameter regions of the double quantum-dot systems.At present,international research on the Coulomb drag effect in quantum dot systems mainly uses the T-matrix based master equation,the essence of this method is based on treating quantum dots and the tunneling coupling strength between the electrode ? as perturbation.The T-matrix based master equation has been widely used to studying the electron transport phenomenon caused by voltage or temperature differences in quantum dot systems,and its reliability in high temperature regions has been confirmed by other methods(i.e.,the thermal fluctuation is greater than the perturbation term ?).By comparing the Coulomb drag current calculated in the high temperature region with the T-matrix based master equation and the numerically exact hierarchical equation of motion,we find that the T-matrix based master equation can give a qualitative and reliable results,but inaccurate when the quantum point charge fluctuation is large and the fourth-order tunneling process is dominant.We point out that this unexpected result is caused by the unique transport mechanism of the Coulomb drag and the T-matrix based master equation overlooking the fourth-order single electron tunnelings.Our findings provide a warning for future attempts to quantitatively study the Coulomb drag effect in quantum dot systems using the T-matrix based master equation,and provide a method for judging the reliability of quantitative results.Due to the perturbation properties of the T-matrix based master equation,it will inevitably fail in the low temperature region(i.e.the thermal fluctuation is less than the perturbation term ?).We use hierarchical equation of motion to study the Coulomb drag effect in the low temperature region of double quantum-dot systems,and give the relationship between the quantum dot energy level and the current when U is positive or negative.By calculating the systems' currents as a function of temperature,we find that the current change is obvious due to the large electronic thermal fluctuations at high temperature.However,at low temperature,the current is entirely caused by the inherent electronic structure of the quantum dot systems,The influence of the electron tunneling process by thermal fluctuations almost disappears,the current tend to stable.We also find that the broadening of the Hubbard peak in the density of states of the two quantum dots affects each other,not only regulated by the coupling strength of adjacent electrodes.Through analytical approximations,we conclude that the non-local broadening effect of the density of quantum dot states is caused by the self-energy correction of Coulomb interactions.Finally we studied the orbital Kondo effect in the double quantum dot systems at low temperature and the influence of the systems parameters on the effect.The hierarchical equation of motion provides a powerful tool for studying the Coulomb drag effect in double quantum dot systems.Our theoretical calculation is of great significance for further quantitative research and experimental detection of Coulomb drag effect.In addition to the current characteristics and the state density broadening effect at low temperature,the Coulomb drag effect under the conditions of multi-level quantum dots,interdot Coulomb interaction,alternating voltage,microwave field etc.requires our further exploration.