Spectral properties of interacting helical channels driven by Lorentzian pulses

Abstract

Precise shaping of coherent electron sources allows the controlled creation of wavepackets into a one dimensional (1D) quantum conductor. Periodic trains of Lorentzian pulses have been shown to induce minimal excitations without creating additional electron-hole pairs in a single non-interacting 1D electron channel. The presence of electron-electron (e-e) interactions dramatically affects the non-equilibrium dynamics of a 1D system. Here, we consider the intrinsic spectral properties of a helical liquid, with a pair of counterpropagating interacting channels, in the presence of timedependent Lorentzian voltage pulses. We show that peculiar asymmetries in the behavior of the spectral function are induced by interactions, depending on the sign of the injected charges. Moreover, we discuss the robustness of the concept of minimal excitations in the presence of interactions, where the link with excess noise is no more straightforward. Finally, we propose a scanning tunneling microscope setup to spectroscopically access and probe the non-equilibrium behavior induced by the voltage drive and e-e interactions. This allows a diagnosis of fractional charges in a correlated quantum spin Hall liquid in the presence of time-dependent drives.

Spectral features of voltage pulses in interacting helical channels

“…In the non-interacting case K = 1 and Φ ± = Φ ↑/↓ , while K < 1 describes repulsive interactions. By solving the equations of motion associated to the Hamiltonian H edge + H gate , one can show that the voltage pulse V(t) simply modifies the time evolution of bosonic chiral fields as [56,87]…”

“…As far as the particle density is concerned, the voltage pulse generates excitations propagating both to the right (x > 0) and to the left (x < 0) with respect to the injection point x = 0. These excitations retain the temporal profile V(t) of the drive, apart from interaction-dependent prefactors which renormalize the charge they carry with them [87]. Explicitly, the electron density variation (with respect to its equilibrium value) ∆n(x, t) reads…”

“…By exploiting Eqs. (4), (6), (8) and 9, the variation of the lesser Green function can be expressed as [87]…”

“…stems from the point splitting procedure and ensures that the diagonal limit lim τ→0 ∆G < σ (t, τ, x) correctly reproduces the variation of the electron density [87,93]. The function Υ σ (t, τ, x) encodes all the effect of the voltage pulse and reads…”

Time-dependent spectral properties of a photoexcited one-dimensional ionic Hubbard model: an exact diagonalization study

“…In photoemission experiments, the central quantity of interest is the probability to detect an electron kicked out by photons. Assuming a uniform strength of probing laser pulses for duration of 2T, the probability of detecting an ejected electron after the probe pulse is expressed by lesser and greater Green's functions as [46,47,[61][62][63][64]]…”