Quantization of particle transport

Thouless, D. J.

doi:10.1103/physrevb.27.6083

Cited by 1,709 publications

(1,761 citation statements)

References 6 publications

Supporting

Mentioning

1,722

Contrasting

Unclassified

Order By: Relevance

“…This possibility can be pursued both in the real and momentum spaces with the input of factors such as time-dependent currents, electric fields, distortion, and pressure, which can produce emergent electric fields. This is connected to the idea of topological charge pumping, proposed by Thouless in the adiabatic limit 120 .…”

Section: Review Articlesmentioning

confidence: 99%

Emergent functions of quantum materials

2017

View full text Add to dashboard Cite

Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence-collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric e ect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.E mergence is a concept developed for many-body systems, indicating the properties, phenomena, and functions that never appear in the individual elements but are realized only when a huge number of elements get together 1 . Inside materials, emergent phenomena are often seen due to the interaction of electronic states; with recent developments on electronic states in solids schematically summarized in Fig. 1a. Electrons in solids have several degrees of freedom: charge, spin and orbital, and are characterized by the topological nature determined by the atomic potential on the crystal lattice structure, as schematically shown in Fig. 1b. These five attributes are coupled together and determine the overall responses to stimuli, which appear as materials' electrical, magnetic, optical, thermal, and mechanical properties.These collective electrons demonstrate various macroscopic quantum phenomena, the representative example of which is superconductivity. One of the big challenges in condensed matter physics is to increase the temperature (T c ) at which superconductivity can be observed to above room temperature. However, there are many other macroscopic quantum phenomena that are already observable above room temperature. One is magnetism (by the Bohr-van Leeuwen theorem), and the other is ferroelectricity 2,3 . Remarkably, there are common features of these three macroscopic quantum phenomena: the order parameter, which is of quantum origin, behaves as a classical quantity, and the quantum topology plays a crucial role.The topological nature of the electronic states is the key concept in the most recent developments in understanding quantum materials. The quantum Hall effect, topological insulators, and topological superconductors are all characterized by nontrivial topologies in Hilbert space. The Berry phase, which describes the connection and curvature of the subspace of Hilbert space, plays the central role in the unified principle to describe this topological nature 4 . ...

show abstract

Section: Review Articlesmentioning

confidence: 99%

Emergent functions of quantum materials

2017

View full text Add to dashboard Cite

show abstract

“…As will soon become clearer, an interpretation in terms of reciprocal gauge field (strength) uncover the nature of various physical phenomena, such as anomalous Hall effect (AHE), [6,23,24,25], spin Hall effect, [10] and quantum charge/spin pumping. [14,15] 3.1 Assumption of slowly varying perturbation β(x, t) -concept of the local Hamiltonian and its local Bloch bands…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…[7] Then we combine our formalism with the Boltzmann transport theory to describe such phenomena as spin and orbital transport. Its relevance to quantum charge/spin pumping [14,15] will be also briefly discussed.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

2005

View full text Add to dashboard Cite

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest on the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a nonabelian gauge field associated with a geometric Berry phase.Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) timedependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields nonabelian.For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal (T ) and space inversion (I).

show abstract

“…In spatially periodic systems, Thouless showed quantized charge transport induced by adiabatic and periodic changes in the potential. 10 Later, a formulation using a scattering matrix appeared, 11,12 which is called Brouwer's formula. This formula is most conveniently applied to * E-mail: tokura.yasuhiro.ft@u.tsukuba.ac.jp a quantum adiabatic pumping in noninteracting systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum Adiabatic Pumping by Modulating Tunnel Phase in Quantum Dots

et al. 2016

View full text Add to dashboard Cite

In a mesoscopic system, under zero bias voltage, a finite charge is transferred by quantum adiabatic pumping by adiabatically and periodically changing two or more control parameters.We obtained expressions for the pumped charge for a ring of three quantum dots (QDs) by choosing the magnetic flux penetrating the ring as one of the control parameters. We found that the pumped charge shows a steplike behavior with respect to the variance of the flux.The value of the step heights is not universal but depends on the trajectory of the control parameters. We discuss the physical origin of this behavior on the basis of the Fano resonant condition of the ring.

show abstract

Quantization of particle transport

Cited by 1,709 publications

References 6 publications

Emergent functions of quantum materials

Emergent functions of quantum materials

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Quantum Adiabatic Pumping by Modulating Tunnel Phase in Quantum Dots

Contact Info

Product

Resources

About