Scanning tunneling spectroscopy

Scanning tunneling spectroscopy is based on the quantum mechanical phenomenon of electron tunneling between a sharp metallic tip and a conducting sample separated by a vacuum gap of a few angstroms. When a bias voltage is applied, electrons tunnel through the barrier, generating a current that is exponentially sensitive to the tip-sample distance. In STS, the tip is held at a fixed position above the sample, and the bias voltage is swept while the tunneling current is recorded. The derivative of the current with respect to voltage (dI/dV) is proportional to the local density of states of the sample at the energy corresponding to the bias voltage.¹ This relationship arises from the fact that the tunneling current is a convolution of the density of states of both the tip and the sample, and under certain conditions (e.g., constant tip DOS), the dI/dV signal directly reflects the sample's LDOS.

STS measurements are typically performed in ultra-high vacuum (UHV) to ensure clean surfaces and stable tunneling conditions. The tip is usually made of tungsten or platinum-iridium, and its electronic structure must be well-characterized or treated to minimize artifacts. The bias voltage is modulated with a small AC signal (typically a few millivolts) at a frequency above the feedback loop's cutoff, and the resulting modulation in the tunneling current is detected using a lock-in amplifier. This lock-in technique directly measures dI/dV, which is the quantity of interest. Measurements can be performed at room temperature, but low-temperature STS (down to millikelvin) is often employed to achieve higher energy resolution and to study superconducting gaps and other low-energy phenomena.

STS has been instrumental in visualizing the electronic structure of surfaces and nanostructures. It has been used to image the superconducting energy gap in high-temperature superconductors, revealing the spatial inhomogeneity of the gap and the presence of pseudogap states.² It has also been applied to study charge density waves in materials like NbSe2, where it can map the energy-dependent modulation of the density of states. In semiconductor physics, STS has been used to probe the electronic structure of quantum dots and quantum wells, providing insights into quantum confinement effects. Additionally, STS is a key tool in the study of topological insulators, where it can detect the Dirac cone surface states.³

Beyond the standard dI/dV mapping, STS offers several advanced modes. For instance, scanning tunneling shot noise spectroscopy measures the current fluctuations to probe the effective charge of tunneling carriers, which has been used to detect Majorana fermions in topological superconductors.⁴ Another variant is spin-polarized STS, which uses a magnetic tip to measure the spin-resolved density of states, enabling the study of magnetic domains and spin textures. A lesser-known historical fact is that the concept of STS was already present in the original STM paper by Binnig and Rohrer in 1982, where they demonstrated the dependence of the tunneling current on the bias voltage.⁵ Furthermore, STS can be performed in a spectroscopic imaging mode, where a full dI/dV spectrum is recorded at each pixel of a topographic image, producing a three-dimensional dataset of the LDOS as a function of position and energy. This technique, known as current imaging tunneling spectroscopy (CITS), was pioneered by Hamers and colleagues in the 1980s and has become a standard method for mapping electronic states on surfaces.⁶

Local density of states (LDOS)

The number of electronic states per unit energy and per unit area at a given location on the surface.

Lock-in amplifier

An instrument that extracts a signal of known frequency from a noisy background, used to measure the derivative of the tunneling current.

Charge density wave (CDW)

A periodic modulation of the electron density in a material, often accompanied by a lattice distortion.

Topological insulator

A material that is insulating in its bulk but conducts on its surface due to topologically protected states.

Majorana fermion

A quasiparticle that is its own antiparticle, predicted to exist in certain superconducting systems and a candidate for topological quantum computing.