Enhancing the Energy Resolution in Scanning Tunneling Microscopy: from dynamical Coulomb blockade to cavity quantum electrodynamics

Abstract

Scanning tunneling microscopy and spectroscopy have become indispensable tools for probing condensed matter at atomic length scales, yet achieving ultimate energy resolution remains a persistent challenge. At mK temperatures, the dynamical Coulomb blockade regime fundamentally limits spectroscopic precision through energy exchange between tunneling electrons and the electromagnetic environment. Here, we demonstrate that combining local electromagnetic shielding with low-pass filtering directly at the cryogenic scan head improves the energy resolution by nearly an order of magnitude, reaching benchmark values as low as 3.7$μ$eV at 10mK. We attribute this enhancement to efficient suppression of high-frequency radiation and capacitive shunting of the tunnel junction. Remarkably, this improved sensitivity reveals that the Josephson current couples to electromagnetic cavity modes of the centimeter-scale scan head, establishing a direct connection between atomic-scale tunneling processes and macroscopic cavity quantum electrodynamics. These advances open pathways for exploring ultra-low-energy phenomena with unprecedented precision.

Figures (4)

• Figure 1: (a) Schematic of the STM scan head (golden trapezoid) inside the cryostat (black rectangle) along with the positions of the low-pass filters. Every line that goes into the cryostat as well as into the scan head is filtered. (b) Three-dimensional drawing of the scan head (golden) along with the guidance cone (gray) on the bottom for tip and sample transfer and the electrical connections on the top along with the filters. (c) Cross sectional view of the three-dimensional drawing of the scan head. The coarse motor (attocube) is shown in blue with the scan piezo and the tip below. The sample holder (gray) is at the bottom along with the sample (yellow). (d) The two-dimensional drawing of the cross section in (c) along with the dimensions (in mm) describing the inside cavity of the scan head.
• Figure 2: The Josephson current is plotted as function of the applied bias voltage for different amplitudes of the lock-in amplifier. Even though the lock-in signal is not shown here, the broadening of the features due to the lock-in modulation is clearly visible. Already the smallest amplitude of 1 $\upmu$V increases the benchmark value. The inset shows the benchmark value as function of the lock-in amplitude, which is the voltage difference between the positive and negative switching currents (see arrows). The red line is a convolution of the Josephson current without lock-in with a lock-in broadening of 15 $\upmu$eV, which fits very well to the Josephson current that was measured with the same lock-in amplitude. The setpoint current was 3 nA at 4 mV for all measurements.
• Figure 3: (a) Schematic of the scan head with the tunnel junction (shaded blue) and the low-pass filters (shaded red). The tunnel junction is modelled by the junction capacitance $C_\text{J}$ and the tunneling resistance $R_\text{T}$. (b) Equivalent circuit diagram of the tunnel junction and the low-pass filters. The low-pass filters are modelled by the filter capacitance $C_\text{F}$ and the filter inductance $L_\text{F}$. The schematic makes it more clear how the junction capacitance is shunted by the filter capacitances. (c) Radial and axial components of the cylindrical cavity modes are shown. The first four modes are shown for each direction. The cavity is described by its radius $R$ and its length $L$.
• Figure 4: The line width (full width at half maximum) is shown as function of temperature for thermal broadening, i.e. $3.5k_\text{B}T$, and $P(E)$-broadening assuming an ohmic environment. The $P(E)$-broadening is shown with (dark color) and without (light color) a constant contribution from an external noise source ($\lambda_\text{ext}=3\upmu$eV for the data of the mK-STM). With the external broadening, the $P(E)$-broadening converges to the constant value of the external broadening. Without the external broadening, the $P(E)$-broadening converges to $\pi\rho k_\text{B}T$. Since typically $\rho = \frac{R_\text{DC}}{R_\text{Q}} \ll 1$, the $P(E)$-broadening is much smaller than the thermal broadening (for details see text). The vertical dashed lines indicate the temperatures, at which the measurements were done with the mK-STM.