Absolute measurement of the exchange interaction in an InSb quantum well using Landau-level tunnelling spectroscopy

TL;DR

This study measures the exchange interaction energy in an InSb quantum well using Landau-level tunneling spectroscopy, providing an absolute value and a new empirical formula linking exchange shift to magnetic field and electron filling.

Contribution

It introduces a stationary contact tunneling spectroscopy method to directly measure the absolute exchange energy in Landau levels, improving upon prior relative and oscillatory g-factor measurements.

Findings

Identified clear Landau level peaks up to 15 T magnetic field.

Derived an empirical formula for exchange shift as a function of magnetic field and filling.

Found that exchange shift occurs only in the ground state Landau level.

Abstract

We studied InSb quantum well devices using Landau level tunneling spectroscopy through a three-terminal differential conductance technique. This method is similar to filled state scanning tunneling microscopy but uses a stationary contact instead of a mobile tip to analyze the two-dimensional electron system. Applying magnetic fields up to 15 T, we identified clear peaks in the differential current-voltage profiles, indicative of Landau level formation. By examining deviations from the expected Landau fan diagram, we extract an absolute value for the exchange-induced energy shift. Through an empirical analysis, we derive a formula describing the exchange shift as a function of both magnetic field strength and electron filling. Our findings indicate that the emptying of the $\nu=2$ and $\nu=3$ Landau levels causes an exchange interaction energy shift in the $\nu=1$ level. Unlike prior studies that infer level energies relative to one another and report oscillatory g-factor behavior, our method references the energy of the Landau levels above the filled states of the contact under a bias voltage, revealing that only the ground state Landau level experiences a measurable exchange shift.