# Introduction

## Flux quantization

In superconductors, electrons condense into a quantum coherent state at low temperatures. The continuity of the macroscopic wavefunction of this condensate implies that a superconducting ring can only be threaded by a magnetic flux which is a multiple of the flux quantum, $$\Phi_0 = h/2e \approx 2.068~\textrm{fWb}$$.

The quantization of flux was predicted by Fritz London in 1948 and verified by Deaver, Fairbank, Doll, and Näubauer more than ten years later.

## Josephson junctions

When two superconductors are separated by a sufficiently thin barrier, Cooper pairs can tunnel across in a quantum coherent manner. This effect was predicted by Brian Josephson in 1962, for which he later won the Nobel prize. The superconductor-insulator-superconductor sandwich in which it occurs is called a Josephson junction.

The foundation for most of the research conducted in the group is the AC Josephson effect, which states that a Josephson junction with a DC voltage bias $$V$$ will emit photons of energy $$h\nu = 2eV$$. The proportionality constant between $$\nu$$ and $$V$$ is the inverse of the flux quantum and is called the Josephson constant, $$K_J = 2e/h = 483.6~\textrm{THz/V}$$.

# Research Projects

## Josephson Junction Spectroscopy

A Josephson junction can be used as a sensitive spectrometer to probe the energy levels of mesoscopic systems. Such spectroscopy could answer the following questions.

### Andreev States

In superconducting atomic contacts, single Cooper pairs or quasiparticles can be trapped in localized "Andreev Bound States." What is the lifetime of these "Andreev" pairs and quasiparticles? What are the decoherence and relaxation mechanisms?

### Gapped Graphene

Does graphene have a gap? In high-quality graphene samples, it has been predicted that electron-electron interactions or interaction with the substrate may open a gap at the Dirac point.

### Majorana States

In superconducting weak links in the presence of strong spin-orbit interaction and/or a Zeeman field, a topological phase transition may induce Andreev States to have a robust zero-energy crossing: Majorana "zero" modes, or states. Do these Majorana modes exist?