Coincidence double-tip scanning tunneling spectroscopy

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. 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.