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

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.