Violation of Fluctuation-Dissipation Theorem Results in Robustness of Fluctuation Against Localization
© The Physical Society of Japan
This article is on
Robustness of Equilibrium Off-Diagonal Current Fluctuation against Localization of Electron States in Macroscopic Two-Dimensional Systems
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 024004 (2022).
We study equilibrium current fluctuations in systems without time-reversal symmetry, violating the fluctuation-dissipation theorem. Notably, the off-diagonal fluctuation is insensitive to system imperfections in contrast to other fluctuations and conductivity.

The fluctuation-dissipation theorem (FDT) claims that the current fluctuation in a macroscopic equilibrium system is equal to the product of the temperature and electrical conductivity. This “theorem” was proved for classical systems for all components of fluctuations including off-diagonal fluctuations, namely cross-time correlations between currents flowing in different directions.
However, the validity of the FDT in quantum systems was questioned, because disturbances by quantum measurement often play a crucial role, which was ignored in the proof of the FDT for classical systems. Recently, this long-standing question was formally solved, and the FDT was shown to be violated even when the fluctuation is measured in a way that simulates the classical ideal measurement as closely as possible. However, this formal solution neither gave concrete systems that exhibit the FDT violation nor estimated the magnitude of violation.
We propose a two-dimensional electron system in a magnetic field as a real physical system in which the FDT is violated. We clarify the conditions for large violations and show that the magnitude of violation is macroscopically large. In fact, the FDT for the off-diagonal component is significantly violated in a strong magnetic field at low temperatures, whereas the FDT for the diagonal component holds for any values of the parameters. In the standard setup used in the quantum Hall effect experiments, the off-diagonal current fluctuation is several tens of times larger than the product of temperature and Hall conductivity (off-diagonal conductivity).
Such a large violation implies novel properties of off-diagonal current fluctuations that are yet to be studied. Localized states of electrons contribute to the off-diagonal current fluctuation to the same extent as extended states, and hence, the off-diagonal fluctuation is insensitive to system imperfections. This is in sharp contrast to the Hall conductivity that is very sensitive to the imperfections because only extended states contribute. Moreover, as an application of this finding, we propose a new method for estimating the electron number density by measuring the off-diagonal fluctuation. Because fluctuations are a cause of error and noise, our results are expected to provide fundamental design guidelines for applications.
(Written by K. Kubo, K. Asano, and A. Shimizu)
Robustness of Equilibrium Off-Diagonal Current Fluctuation against Localization of Electron States in Macroscopic Two-Dimensional Systems
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 024004 (2022).
Share this topic
Fields
Related Articles
-
Spin Transport in a Two-Dimensional Tilted Dirac Electron System
Electronic transport in condensed matter
Electronic structure and electrical properties of surfaces and nanostructures
2022-4-13
We propose that spin current in an organic conductor, α-(BETS)2I3, is an appropriate physical quantity to detect the topological nature of the material whose electrons obey a quasi-two-dimensional Dirac equation.
-
Topological Aspects of a Nonlinear System: The Dimerized Toda Lattice
Electronic structure and electrical properties of surfaces and nanostructures
Electronic transport in condensed matter
2022-3-16
A nonlinear topological phase is shown to emerge in the dimerized Toda lattice. It is experimentally detectable by measuring the voltage propagation in electric circuits.
-
Unusual Nonlinear Conductivity in Charge-Ordered α-(BEDT-TTF)2I3
Electronic transport in condensed matter
2022-3-9
Unusual nonlinear conduction is detected in organic molecular salt α-(BEDT-TTF)2I3. The observed third-order nonlinear conductivity implies a quadrupole instability hidden in this charge-ordered organic salt.
-
Economic Irreversibility: The Universal Guiding Principle of Infection Control
Statistical physics and thermodynamics
Cross-disciplinary physics and related areas of science and technology
2022-3-1
It is preferable to avoid lockdowns, as lockdowns at seriously spread phases are very expensive. It would be economically better to utilize less intense countermeasures as early as possible to avoid lockdowns in later phases.
-
Phosphorous-Based Zintl Compounds as Viable Semimetals
Electronic structure and electrical properties of surfaces and nanostructures
Structure and mechanical and thermal properties in condensed matter
Electron states in condensed matter
2022-2-4
A black-phosphorus-derived Zintl compound, MoP4, is obtained by high-pressure synthesis. The material exhibits a non-quadratic large magnetoresistance and semi-metallic Seebeck behavior, as predicted by the first principles calculations yielding massive and non-symmorphic Dirac semimetal states.