Probing the intrinsic state of a one-dimensional quantum well with a photon-assisted tunneling

TL;DR

This paper proposes using photon-assisted tunneling spectroscopy on a carbon nanotube quantum well to probe the Tomonaga Luttinger liquid state, enabling identification of charge and spin excitations and extraction of fundamental parameters.

Contribution

It introduces a novel PAT spectroscopy method to identify TLL excitations and determine parameters in a quantum well setup, specifically targeting charge and spin bosonic modes.

Findings

Identification of $ ho_{+}$ boson energy levels via PAT.

Detection of spin boson levels through Zeeman splitting.

Extraction of TLL parameters from differential conductivity measurements.

Abstract

The photon-assisted tunneling (PAT) through a single wall carbon nanotube quantum well (QW) under influence an external electromagnetic field for probing of the Tomonaga Luttinger liquid (TLL) state is suggested. The elementary TLL excitations inside the quantum well are density ($\rho_{\pm}$) and spin ($\sigma_{\pm} $) bosons. The bosons populate the quantized energy levels $\epsilon^{\rho +}_n =\Delta n/ g$ and $\epsilon^{\rho -(\sigma \pm)}_n = \Delta n$ where $\Delta = h v_F /L $ is the interlevel spacing, $n$ is an integer number, $L$ is the tube length, $g$ is the TLL parameter. Since the electromagnetic field acts on the $\rho_{+}$ bosons only while the neutral $\rho_{-}$ and $\sigma_{\pm} $ bosons remain unaffected, the PAT spectroscopy is able of identifying the $\rho_{+}$ levels in the QW setup. The spin $\epsilon_n^{\sigma+} $ boson levels in the same QW are recognized from Zeeman splitting when applying a d.c. magnetic field $H \neq 0$ field. Basic TLL parameters are readily extracted from the differential conductivity curves.