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Publication# Mixed state Hall effect in a twinned YBa2Cu3O7-[delta] single crystal

1999

EPFL thesis

EPFL thesis

Abstract

Resistivity measurements are used to study vortex dynamics in a high quality superconducting YBa2Cu3O7-δ twinned single crystal. Nine gold contacts have been deposited on one sample surface, allowing us to perform different kinds of investigations. Firstly, simple longitudinal resistivity data reveal the vortex phase transition. When the magnetic field is slightly tilted away from the twin planes, this transition is presumably of first order, separating a vortex liquid phase from a solid vortex lattice or Bragg glass. If on the other hand the magnetic field is parallel to the crystallographic c-axis, that is along the twin boundaries, the solid phase then apparently becomes a Bose glass. Secondly, measurements of the orientation and magnitude of the electric field as a function of the current direction in the ab plane yield much information about the influence of the twins on the vortex dynamics. We observe a partially guided vortex motion along the dominating twin plane family, already apparent in the vortex liquid, and becoming progressively more and more pronounced as the temperature or the magnetic field is reduced. There is no sharp change of the twin influence at the vortex phase transition. We also show that standard resistivity measurements in twinned samples, in which the current is applied along the a or b-axis, should be interpreted carefully, precisely because as a consequence of this guided motion the electric field is no longer parallel to the current. Finally, the mixed state Hall effect is studied, with particular focus given to the vortex phase transition. We observe the usual Hall anomaly, that is, a sign reversal of the Hall effect in the mixed state, and show that the often reported Hall resistivity scaling law ρxy ∝ ρxxβ remains unchanged in the vortex solid phase (ρxy is the Hall resistivity and ρxx the longitudinal resistivity). When the magnetic field is parallel to the twin boundaries, we obtain the critical exponent β = 2, naturally corresponding to a constant Hall conductivity below and slightly above the vortex phase transition. In the presence of a tilted magnetic field the exponent is then β = 1.4. In this case, we observe a sharp change of behavior in the Hall conductivity right at the vortex lattice melting point, its slope becoming much larger in the vortex solid phase. This effect being strongly dependent on the current density, we interpret it as a result of vortex pinning. Hence this demonstrates that the Hall conductivity is pinning dependent, hopefully solving a long term controversy with regards to this topic. We review some theoretical models concerning the Hall anomaly as well as the Hall scaling law in light of our data. A novel phenomenological model for the Hall resistivity scaling law is also given, directly inspired from the theory of percolation in metallic conductors.

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Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Electrical resistivity and conductivity

Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m).

Quantum Hall effect

The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,.

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