Order O(1) algorithm for first-principles transient current through open quantum systems

TL;DR

This paper introduces an order O(1) algorithm that significantly accelerates first-principles transient current calculations in nanoelectronics, enabling efficient analysis of large-scale systems like graphene nanoribbons.

Contribution

The authors develop a novel order O(1) algorithm that reduces computational complexity from TN^3 to T^0 N^3, allowing fast simulations of large nanoelectronic devices.

Findings

Benchmark on graphene nanoribbons confirms O(1) scaling.

Algorithm enables analysis of large-scale magnetic and ferroelectric tunneling junctions.

Significantly reduces computation time for transient current calculations.

Abstract

In the study the response time of ultrafast transistor and peak transient current to prevent melt down of nano-chips, the first principles transient current calculation plays an essential role in nanoelectronics. The first principles calculation of transient current through nano-devices for a period of time T is known to be extremely time consuming with the best scaling TN^3 where N is the dimension of the device. In this work, we provide an order O(1) algorithm that reduces the computational complexity to T^0 N^3 for large systems. Benchmark calculation has been done on graphene nanoribbons with N = 10^4 confirming the O(1) scaling. This breakthrough allows us to tackle many large scale transient problems including magnetic tunneling junctions and ferroelectric tunneling junctions that cannot be touched before.