Hall Effect in Bismuth at Low Temperatures

Reynolds, J. M.; Hemstreet, H. W.; Leinhardt, T. E.; Triantos, D. D.

doi:10.1103/physrev.96.1203

Cited by 34 publications

(10 citation statements)

References 7 publications

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“…A relation of similar character for a cubic crystal has been investigated experimentally in germanium. 9 The two remaining relations appropriate to Eq. (6) have been found, but they are quite complicated and essentially worthless for experimental application.…”

Section: Theorymentioning

confidence: 98%

“…This device basically is the same as any dc amplifier which "chops" the input and then amplifies only the 9 1. The primary measuring circuit. The amplifier is used as a null detector and senses an unbalance between the voltage to be measured and that generated across a calibrated resistance R. For magnetoresistance experiments, the milliammeter is shunted to read only increments above a given value.…”

Section: Superconducting Chopper Amplifiermentioning

confidence: 99%

See 1 more Smart Citation

Small-Field Galvanomagnetic Tensor of Bismuth at 4.2°K

Zitter

1962

Phys. Rev.

115

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Values of carrier concentrations and mobilities in large monocrystalline samples of bismuth at 4.2 °K have been derived from measurements of all the galvanomagnetic tensor components through second order in magnetic field. Fields of the order of one gauss and less are required, and a superconducting chopper amplifier detects the minute voltages involved. The electron concentration is found to be 2.5X10 17 cm~3, and the concentration of "light" holes is very nearly the same. When compared with cyclotron resonance and de Haas-van Alphen experiments, the results are consistent with a three-ellipsoid model for electrons and a single ellipsoid for "light" holes. There is no indication of the presence of "heavy" holes in a concentration comparable to the other carriers. Electron and "light"-hole relaxation times are isotropic to within a factor of 2; for electrons, r = 2X 10~1 0 sec, and for holes, r == 5X 10~1 0 sec. Some of the effects of temperature and of larger magnetic fields are discussed.

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Section: Theorymentioning

confidence: 98%

Section: Superconducting Chopper Amplifiermentioning

confidence: 99%

Small-Field Galvanomagnetic Tensor of Bismuth at 4.2°K

Zitter

1962

Phys. Rev.

115

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“…Yet, it has been known for some time that many semimetals with electron and hole pockets exhibit pronounced oscillations of R xy as a function of magnetic field (23), which closely reflect SdH oscillations. It is a textbook exercise (10) that for two bands, the combined Hall coefficient R is given by (for magnetic fields of interest)…”

Section: Fermi Surface Reconstruction ͉ Hall Effectmentioning

confidence: 99%

Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors

Chakravarty

2008

Proc. Natl. Acad. Sci. U.S.A.

115

114

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Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle /2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets. Fermi surface reconstruction ͉ Hall effectA ny prospect of elucidating the mechanism of hightemperature superconductivity in cuprates is remote without answering some of the basic questions in clear terms. The most important of which is the notion of a Fermi surfacewhether or not it exists or is reconstructed because of a broken symmetry in the pseudogap state (1). An equally basic question is the extent to which a featureless spin liquid ground state, the resonating valence bond state (RVB), is important (2). In this respect, the recent experiments on quantum oscillations in high magnetic fields in high-quality samples of YBa 2 Cu 3 O y (Y123) and YBa 2 Cu 4 O 8 (Y124) have been striking (3-7).The quantum oscillations in the magnetization [de Haas-van Alphen effect (dHvA)], in the conductivity [Shubnikov-de Haas effect (SdH)], and in the Hall coefficient (R H ) have long been used to map out the Fermi surface and its topology in metals and semimetals (8). A Fermi surface differentiates the occupied electronic states from the unoccupied states in the momentum space and plays a fundamental role in quantum theory of matter. The highest occupied energy is an important parameter called the Fermi energy. The excitations from this surface determine the quasiparticles, which behave in many ways like bare particles, but their properties are modified by the collective interactions. An important notion is that a Fermi surface is a topological invarian...

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“…This is notably true of the measurements of the oscillatory components of the longitudinal magnetoresistance, 8 the transverse magnetoresistance, 7 and the Hall effect. 9 It is the principal purpose of this paper to present experimental evidence, from the Shubnikov-de Haas effect, that there are at least three and very likely four sets of carriers in bismuth. We have employed a derivative technique to measure dR/dH as a function of H, where R is the electrical resistance of the sample.…”

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confidence: 99%

Shubnikov-de Haas Effect in Bismuth

Lerner

1962

Phys. Rev.

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The oscillatory component of the transverse magnetoresistance of bismuth has been measured as a function of magnetic field orientation at liquid helium temperatures. A derivative technique was employed. In addition to sets of periods, observed in the de Haas-van Alphen effect by Shoenberg and by Brandt and attributed by them, respectively, to the electron and light-hole Fermi surfaces, we observe a new set of isotropic short periods, P = 0.72X10~5 G" 1 . The squares of the electron Fermi momenta w 0 /cn 2 , w 0 /c 2 2 2 , W0K33 2 , 7W0K23 2 are, respectively, 0.189, 45.4, 0.918, and -4.54 mo milli-electron volts (meV). For the light holes, moKu 2 and W0K33 2 are 1.51 and 21.0 Wo meV. For the new heavy carriers, w 0 «: 2 = 3.18 Wo meV. These data are fitted to two possible three-carrier models of the Fermi surface, and to a four-carrier model. Significant deviations of the oscillations from periodicity in H~l are observed for the electron part of the Fermi surface for certain magnetic field orientations.

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Hall Effect in Bismuth at Low Temperatures

Cited by 34 publications

References 7 publications

Small-Field Galvanomagnetic Tensor of Bismuth at 4.2°K

Small-Field Galvanomagnetic Tensor of Bismuth at 4.2°K

Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors

Shubnikov-de Haas Effect in Bismuth

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