Coincidence double-tip scanning tunneling spectroscopy

TL;DR

This paper introduces a novel double-tip scanning tunneling spectroscopy technique that directly measures spatially resolved dynamical two-body electron correlations, advancing the study of strongly correlated electron systems.

Contribution

It proposes a new double-tip STS method with a theoretical framework linking measurements to two-body correlation functions, enabling direct probing of electron correlations.

Findings

Developed a nonequilibrium theory for coincidence dynamical conductance.

Demonstrated the method's ability to probe electron propagation in Fermi liquids.

Showed additional channels in superconducting states.

Abstract

The development of new experimental techniques for direct measurement of many-body correlations is crucial for unraveling the mysteries of strongly correlated electron systems. In this work, we propose a coincidence double-tip scanning tunneling spectroscopy (STS) that enables direct probing of spatially resolved dynamical two-body correlations of sample electrons. Unlike conventional single-tip scanning tunneling microscopy, the double-tip STS employs a double-tip scanning tunneling microscope (STM) equipped with two independently controlled tips, each biased at distinct voltages ($V_1$ and $V_2$). By simultaneously measuring the quantum tunneling currents $I_1(t)$ and $I_2(t)$ at locations $j_1$ and $j_2$, we obtain a coincidence tunneling current correlation $\overline{\langle I_1(t) I_2(t)\rangle}$. Differentiating this coincidence tunneling current correlation with respect to the two bias voltages yields a coincidence dynamical conductance. Through the development of a nonequilibrium theory, we demonstrate that this coincidence dynamical conductance is proportional to a contour-ordered second-order current correlation function. For the sample electrons in a nearly free Fermi liquid state, the coincidence dynamical conductance captures two correlated dynamical electron propagation processes: (i) from $j_1$ to $j_2$ (or vice versa) driven by $V_1$, and (ii) from $j_2$ to $j_1$ (or vice versa) driven by $V_2$. For the sample electrons in a superconducting state, additional propagation channels emerge from the superconducting condensate, coexisting with the above normal electron propagation processes. Thus, the coincidence double-tip STS provides direct access to spatially resolved dynamical two-body correlations, offering a powerful tool for investigating strongly correlated electron systems.