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Related Concept Videos

Resistivity01:22

Resistivity

4.6K
When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The current density that results depends on the electrical field and the properties of the material. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as:
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In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and resistance is known as Ohm's law. Nonohmic devices do not exhibit a linear relationship between voltage and current. One such device is the semiconducting circuit element known as a diode. A diode is a circuit device that allows current flow in only one direction.
Consider a simple circuit consisting of a battery, a diode, and a resistor. A...
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Ohm's Law01:19

Ohm's Law

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Resistors are fundamental components in electrical circuits, often manufactured from metallic alloys or carbon compounds. They model a material's ability to resist the flow of electric current, a characteristic that is crucial in controlling and regulating electrical power within a circuit.
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Ohm's Law01:21

Ohm's Law

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Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm’s law. The current that flows through most substances is directly proportional to the voltage applied to them. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied. Any material, component, or device that obeys Ohm’s law, where the current...
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Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Drüde called the “Electron Sea Model”. 
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Resistance01:19

Resistance

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When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known as the resistance of the material and is represented by R. Every material has its own resistance. In the case of conductors, heat is emitted whenever a current passes through them. Resistance depends on the resistivity of the material. Resistivity is a characteristic of the material used to fabricate electrical components, whereas the...
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Ultrasound Velocity Measurement in a Liquid Metal Electrode
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Resistivity bound for hydrodynamic bad metals.

Andrew Lucas1, Sean A Hartnoll1

  • 1Department of Physics, Stanford University, Stanford, CA 94305 hartnoll@stanford.edu ajlucas@stanford.edu.

Proceedings of the National Academy of Sciences of the United States of America
|October 27, 2017
PubMed
Summary
This summary is machine-generated.

We derived a rigorous upper bound for electrical resistivity in electron fluids with short mean free paths. This bound unifies Fermi liquid and quantum critical behaviors observed in various materials.

Keywords:
bad metalshydrodynamicsthermoelectric transport

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Transport Theory

Background:

  • Electron fluid resistivity in materials like transition metal oxides often exhibits a linear-T dependence, posing a challenge for existing theories.
  • Understanding the interplay between short electronic mean free paths and spatial inhomogeneities is crucial for explaining observed transport phenomena.

Purpose of the Study:

  • To derive a rigorous upper bound for electrical resistivity in electron fluids with short electronic mean free paths.
  • To establish a unified theoretical mechanism for the observed resistivity behaviors in various metallic systems.
  • To incorporate the influence of nonthermal diffusion processes on electrical resistivity.

Main Methods:

  • Derivation of a rigorous upper bound on resistivity for hydrodynamic electron fluids.
  • Analysis of nonthermal diffusion processes, such as imbalance modes between electronic bands.
  • Investigation of the dependence of the resistivity bound on microscopic scattering rates and temperature.

Main Results:

  • A rigorous upper bound on resistivity [Formula: see text] is obtained for electron fluids with short mean free paths.
  • When nonthermal diffusion is present, the resistivity bound transitions to [Formula: see text], where [Formula: see text] is temperature-independent.
  • The derived mechanism unifies [Formula: see text] behavior in Fermi liquids and the crossover to [Formula: see text] in quantum critical regimes without invoking umklapp scattering.
  • Phonon contributions to diffusion constants, including thermal diffusion, are shown to directly influence electrical resistivity.

Conclusions:

  • The study provides a unified mechanism for anomalous transport phenomena observed in diverse materials.
  • The derived hydrodynamic bound offers a new perspective on the factors governing electrical resistivity.
  • This work bridges the gap between theoretical transport models and experimental observations in complex metallic systems.