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Angle of Twist: Problem Solving01:13

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque...
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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Topological Superconductivity in Twisted Multilayer Graphene.

Cenke Xu1, Leon Balents2

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA.

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|September 8, 2018
PubMed
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We found that electron interactions in twisted graphene can create a novel superconducting state. This state, a topological superconductor, exhibits unique half-vortices and protected edge states.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Quantum materials

Background:

  • Superconductivity arises from electron pairing.
  • Graphene multilayers exhibit complex electronic properties due to stacking and twisting.
  • Flat energy bands can lead to strong electron correlations and novel quantum phenomena.

Purpose of the Study:

  • Investigate superconductivity in correlated flat minibands of twisted graphene multilayers.
  • Explore the role of the valley degree of freedom in determining pairing states.
  • Identify topological superconducting states and their unique properties.

Main Methods:

  • Utilizing a minimal Hubbard model.
  • Analyzing the effects of superlattice modulation in twisted graphene.
  • Characterizing pairing states based on spin and valley degrees of freedom.

Main Results:

  • Identified spin triplet d+id pairing with a valley singlet structure as the preferred state.
  • Discovered two candidate topological superconducting states.
  • Observed half-vortices with half the usual superconducting flux quantum (hc/(4e)).
  • Found topologically protected gapless edge states.

Conclusions:

  • The valley degree of freedom is crucial for exotic superconductivity in twisted graphene.
  • The identified topological superconductors offer a platform for studying novel quantum phenomena.
  • These materials could have applications in topological quantum computing and low-flux devices.