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Electronic transport in quantum conductors
In micrometer-scale electrical conductors at low temperatures, electronic transport is no longer governed by classical mechanics, which describes electron scattering from lattice defects and determines Drude conductivity. Instead, a quantum mechanical approach is required, where conductance is defined by the transmission of electronic waves through the conductor.
This course will cover various phenomena related to quantum electronic transport, such as conductance quantization, electronic interferences, quantum noise, quantum dots and their applications in semiconductor qubits, quantum Hall effects in 2D materials such as graphene and van der Waals heterostructures. Through these topics, the course aims to cover both the historical development of quantum transport since the 1980s and the most recent advances, along with their applications in quantum information processing and strongly correlated systems.
Syllabus
The course will be divided into three parts. Each lecture will be followed by a tutorial session, allowing students to apply the course concepts to examples drawn from emblematic experiments in the field.
The first part will introduce the fundamental concepts of quantum transport:
- The different scales of electronic transport: classical transport, quantum transport, diffusive and ballistic transport
- Conductance quantization and the Landauer formula
- Multi-terminal transport
- The quantum Hall effect
- Electronic interferometry
- Quantum noise
The second part will focus specifically on transport in quantum dots and their application to semiconductor qubits:
- Electrostatics of quantum dots
- The Anderson Hamiltonian
- Master equation and electrical current
- Applications to charge qubits and spin qubits
- Coupling to a bosonic cavity mode
The third part will focus specifically on transport in van der Waals heterostructures, particularly stacked monolayer conductors such as graphene:
- Transport in monolayer and bilayer graphene
- Klein tunneling
- Quantum Hall effects in graphene
- Flat bands and anomalous quantum Hall effect
Prerequisites
Examination
Written exam