Quantum transport is a diverse field, sometimes combining seemingly contradicting concepts - quantum and classical, conduction and insulating - within a single nanodevice. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the nanoscale. This textbook is a comprehensive introduction to the rapidly developing field of quantum transport. The authors present the comprehensive theoretical background, and explore the groundbreaking experiments that laid the foundations of the field. Ideal for graduate students, each section contains control questions and exercises to check readers' understanding of the topics covered. Its broad scope and in-depth analysis of selected topics will appeal to researchers and professionals working in nanoscience.

The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene 1-8 make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities 9-14 offers exquisite position sensitivity 10 and enables the preparation and detection of mechanical systems in the quantum ground state 15,16 . Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-Q superconducting cavity. Using thermo-mechanical noise as calibration, we achieve a displacement sensitivity of 17 fm/ √ Hz. Optomechanical coupling is demonstrated by optomechanically induced reflection (OMIR) and absorption (OMIA) of microwave photons [17][18][19] . We observe 17 dB of mechanical microwave amplification 13 and signatures of strong optomechanical backaction. We extract the cooperativity C, a characterization of coupling strength, quantitatively from the measurement with no free parameters and find C = 8, promising for the quantum regime of graphene motion. Here, we present a multilayer graphene mechanical resonator coupled to a superconducting cavity. Using a deterministic all-dry transfer technique 22 and a novel microwave coupling design, we are able to combine these two without sacrificing the exceptional intrinsic properties of either. Although multilayer graphene has a higher mass than a monolayer, it could be advantageous for coupling to a superconducting cavity due to its lower electrical resistance. In Figure 2, we characterize the mechanical properties of the multilayer graphene resonator using a homodyne measurement scheme 9 . Here, the cavity is used as an interferometer to detect motion while injecting a microwave signal near ω c and exciting the mechanical resonator with an AC voltage applied to the gate. The mechanical resonance frequency is much larger than the cavity linewidth (ω m /κ ∼ 150), placing us in the sideband resolved limit, a prerequisite for ground state cooling. The cavity can also be used to detect the undriven motion, such as thermomechanical noise of the drum shown in the inset of Figure 2(a) corresponding to a mechanical mode temperature of 96 mK (see SI for additional details). The thermal motion peak serves as a calibration for the displacement sensitivity. While driving the cavity at its resonance and utilizing its full dynamic range before the electrical nonlinearity set in (-41 dBm injected power) we estimate a displacement sensitivity for mechanical motion of 17 fm/ √ Hz. Using a DC voltage applied to the gate electrode, we can also tune the frequency of the multilayer graphene resonator shown in Figure 2(b). The decrease in resonance frequency ω m for non-zero gate voltage is due to electrostatic softening of the spring constant and has been observed before 3 .In Figure 3, we demonstrate optomechanical coupling between the multilayer graphene mechanical resona...

We study the model of a molecular switch comprised of a molecule with a soft vibrational degree of freedom coupled to metallic leads. In the presence of strong electron-ion interaction, different charge states of the molecule correspond to substantially different ionic configurations, which can lead to very slow switching between energetically close configurations ͑Franck-Condon blockade͒. Application of transport voltage, however, can drive the molecule far out of thermal equilibrium and thus dramatically accelerate the switching. The tunneling electrons play the role of a heat bath with an effective temperature dependent on the applied transport voltage. Including the transport-induced "heating" self-consistently, we determine the stationary currentvoltage characteristics of the device and the switching dynamics for symmetric and asymmetric devices. We also study the effects of an extra dissipative environment and demonstrate that it can lead to enhanced nonlinearities in the transport properties of the device and dramatically suppress the switching dynamics.

We report a theory for the coherent and incoherent chiral pumping of spin waves into thin magnetic films through the dipolar coupling with a local magnetic transducer, such as a nanowire. The ferromagnetic resonance of the nanowire is broadened by the injection of unidirectional spin waves that generates a non-equilibrium magnetization in only half of the film. A temperature gradient between the local magnet and film leads to a unidirectional flow of incoherent magnons, i.e., a chiral spin Seebeck effect.

Spin waves—the elementary excitations of magnetic materials—are prime candidate signal carriers for low-dissipation information processing. Being able to image coherent spin-wave transport is crucial for developing interference-based spin-wave devices. We introduce magnetic resonance imaging of the microwave magnetic stray fields that are generated by spin waves as a new approach for imaging coherent spin-wave transport. We realize this approach using a dense layer of electronic sensor spins in a diamond chip, which combines the ability to detect small magnetic fields with a sensitivity to their polarization. Focusing on a thin-film magnetic insulator, we quantify spin-wave amplitudes, visualize spin-wave dispersion and interference, and demonstrate time-domain measurements of spin-wave packets. We theoretically explain the observed anisotropic spin-wave patterns in terms of chiral spin-wave excitation and stray-field coupling to the sensor spins. Our results pave the way for probing spin waves in atomically thin magnets, even when embedded between opaque materials.