TraSPI: A numerically exact method for nonequilibrium quantum transport through nanostructures

TraSPI：一种通过纳米结构进行非平衡量子传输的数值精确方法

• 批准号: 523060084
• 负责人: Professor Dr. Alfred Hucht
• 金额: --
• 依托单位: Fakultät für Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/523060084?language=en
• 关键词: TraSPI; numerically; exact; method; nonequilibrium

The theoretical description of quantum transport through nanostructures is a challenging task. The complex interplay of nonequilibrium dynamics, Coulomb interaction, finite temperature and, if present, collective order does, in general, not allow for an exact analytical treatment. Therefore, a plethora of different theoretical methods have been developed to address various regimes of quantum transport in nanoscale devices. They all have their advantages and disadvantages. Some are restricted to the linear-response regime while others can cover strong nonequilibrium situations. In scenarios with a clear hierarchy of the involved parameters, a perturbation expansion in one of them can be used. However, in real experiments very often many of these parameters characterizing, e.g., temperature, tunnel coupling strength, Coulomb interaction as well as gate and bias voltage, are energetically of the same order of magnitude. Then, numerically exact methods are desirable. In a recent paper, we presented TraSPI ("Transfer-matrix Summation of Path Integrals") as such a numerically exact method [Mundinar et al., Phys. Rev. B 106, 165427 (2022)]. It is based on an iterative summation of path integrals, established as ISPI in the last decade. The virtue of ISPI (and thus also TraSPI) is that it naturally takes into account all orders in tunneling of electrons between quantum dot and leads, allows for arbitrary bias voltages that drive the system out of equilibrium, is not restricted to either low or high temperatures, and is able to include a finite Coulomb interaction. A major virtue of TraSPI is that the stationary limit is implemented by construction, and that certain derivatives can be calculated analytically. In addition, the use of transfer matrices allows for further improvements that enhance the efficiency and accuracy of the method. We will boost the performance of the TraSPI method by further development and through an efficient implementation, also on GPUs. Thereby, we will make use of similarities between the nonequilibrium TraSPI method and an effective long-range equilibrium Ising model. This will allow us to address several problems in quantum transport through nanostructures that are difficult or impossible to be tackled by other methods. This includes aspects of quantum-dot interferometry as well as the generation of superconducting correlations in quantum dots.

纳米结构中量子输运的理论描述是一项具有挑战性的任务。非平衡动力学、库仑相互作用、有限温度和集体秩序（如果存在的话）之间复杂的相互作用一般不允许进行精确的分析处理。因此，已经开发了过多的不同的理论方法来解决纳米器件中的量子输运的各种机制。它们都有其优点和缺点。有些被限制为线性响应制度，而其他人可以涵盖强非平衡的情况。在所涉及的参数具有清晰层次的场景中，可以使用其中一个参数的扰动展开。然而，在真实的实验中，这些参数中的许多参数表征，例如，温度、隧道耦合强度、库仑相互作用以及栅极和偏置电压在能量上具有相同的数量级。然后，需要数值精确的方法。在最近的一篇论文中，我们提出了TraSPI（“路径积分的转移矩阵求和”）作为这样一种数值精确方法[Mundinar等人，Phys. Rev. B 106，165427（2022）]。它是基于路径积分的迭代求和，在过去的十年中建立为ISPI。ISPI（以及TraSPI）的优点是它自然地考虑了量子点和引线之间电子隧穿的所有顺序，允许驱动系统脱离平衡的任意偏置电压，不限于低温或高温，并且能够包括有限的库仑相互作用。TraSPI的一个主要优点是静态极限是通过构造实现的，并且某些导数可以通过解析计算。此外，使用传递矩阵允许进一步改进，提高了该方法的效率和准确性。我们将通过进一步的开发和高效的实现来提高TraSPI方法的性能，也可以在GPU上实现。因此，我们将利用非平衡TraSPI方法和一个有效的长期平衡伊辛模型之间的相似之处。这将使我们能够解决通过纳米结构进行量子传输的几个问题，这些问题很难或不可能通过其他方法解决。这包括量子点干涉测量以及量子点中超导相关性的产生。