# hall conductivity

### 1805.10532 Quantization of the thermal Hall conductivity

· Quantization of the thermal Hall conductivity at small Hall angles. Authors Mengxing Ye Gábor B. Halász Lucile Savary Leon Balents. (Submitted on 26 May 2018 ( v1 ) last revised 3 Oct 2018 (this version v2)) Abstract We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising

### Theory of quantised Hall conductivity in two dimensions

J. Phys. C Solid State Phys. 15 (1982) L717-L721. Printed in Great Britain LETTER TO THE EDITOR Theory of quantised Hall conductivity in two dimensions P Stieda Institute of Physics Czechoslovak Academy of Sciences Prague Czechoslovakia Received 10 December 1981 Abstract. On the basis of linear response theory the Hall conductivity is expressed as a sum

Cited by 489### Hall Electrical Conductivity CalculatorHall

Hall Electrical Conductivity Calculator The hall electrical conductivity of the space plasmas can be calculated based on the values electron number density electronic charge direct electrical conductivity conductivity and magnetic flux density.

### Phys. Rev. B 86 235438 (2012)Optical Hall conductivity

· Optical Hall conductivity σ x y as a function of photon energy for the 4 2 graphene antidot lattice. The conductivity is shown relative to the zero-frequency conductivity of graphene σ 0 times the square of the cyclotron energy ℏ ω c. The blue (red) lines show the real (imaginary) part of the conductivity.

### condensed matterHall conductivity from Kubo Bulk or

· Using the Kubo formula Thouless Kohmoto Nightingale and den Nijs (TKNN PRL 49 (1982)) proved that upon summing all the contributions of the filled states of an insulator the Hall conductivity must be an integer (the Chern number) times e 2/h.

### Spin-Hall conductivity in a two-dimensional Rashba

· Hall conductivity sH of a clean 2DEG and its in-plane magnetic susceptibility providing additional argu-ments in favor of the equilibrium nature of the spin-Hall constant sH = 2e g B 2m b 2 where m b is the band mass B is the Bohr magneton and g

### Hall conductivity as topological invariant in phase space

the Hall conductivity for the insulator is the topological invariant which is given by the expression of equation (35) 10 11 composed of the complete two-point Green s func-tion of the interacting model. However this work only stu-died anomalous quantum Hall conductivity in the absence of magnetic ﬁeld.

### Theory of Valley Hall Conductivity in Bilayer Graphene

· The above shows that the Hall conductivity can be-come nonzero in the vicinity of the gap opened by the applied electric eld but it can become rapidly smaller or can change sign with the increase of the absolute value of the energy ("˘ 1=2 for j∆j≪ 1). In the gap the Hall conductivity is quantized into ˙xy = gse2 h (21) with h = 2ˇ h

### Giant thermal Hall conductivity in the pseudogap phase

· A negative thermal Hall conductivity κ xy at low temperature is therefore a generic property of the pseudogap phase independent of material. Note that the electrical Hall conductivity σ xy measured on the same samples remains positive down to T → 0 (Fig. 2b d). We now move to much lower doping. In Fig. 1b we see that κ xy/T

### Hall Conductivity as the Topological Invariant in the

· The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the nonuniform magnetic field. The quantum Hall conductivity is represented as the topological invariant in phase space in terms of the Wigner transformed two-point Green s function.

### The Kubo Formula of Hall Conductivity Physics Forums

· Several papers (eg. Di Xiao et. al Berry phase effects on electronic properties RevModPhys 82 2010)mentioned a formula to calculate the Hall conductivity(See the picture).This formula is used in an two dimensional system v1 and v2 are velocity operators in x and y direction Phi0 and PhiN are ground and excited state vector. The papers claim that this formula can be derived from

### Hall Effect and Conductivity Measurements in Semiconductor

· In combination with a conductivity (σ) measurement the Hall mobility μ H of the sample can be calculated according to μ = σ/(qn). Though in principle simple the preparation of the Hall measurement samples and the interpretation of the measurements needs some care and the appropriate theory for the charge carrier transport in semiconductors.

### Hall Electrical Conductivity CalculatorHall

Hall Electrical Conductivity Calculator The hall electrical conductivity of the space plasmas can be calculated based on the values electron number density electronic charge direct electrical conductivity conductivity and magnetic flux density.

### Hall effect measurements for determining the band gap

· Hall effect measurements for determining the band gap energy of undoped germanium including the conductivity charge carrier type concentration and mobility for n-type and p-type doped germanium Hassan Mirza1 and Danny Morris1 1School of Physics and Astronomy Queen Mary University of London London E1 4NS England

### Fermi-surface calculation of the anomalous Hall

· Fermi-surface calculation of the anomalous Hall conductivity Xinjie Wang 1David Vanderbilt Jonathan R. Yates 2 3 and Ivo Souza2 3 1Department of Physics and Astronomy Rutgers University Piscataway New Jersey USA 2Department of Physics University of California Berkeley California 94720 USA 3Materials Science Division Lawrence Berkeley National Laboratory

### Hall Effect and Conductivity Measurements in Semiconductor

· In combination with a conductivity (σ) measurement the Hall mobility μ H of the sample can be calculated according to μ = σ/(qn). Though in principle simple the preparation of the Hall measurement samples and the interpretation of the measurements needs some care and the appropriate theory for the charge carrier transport in semiconductors.

### Fermi-surface calculation of the anomalous Hall

· Fermi-surface calculation of the anomalous Hall conductivity Xinjie Wang 1David Vanderbilt Jonathan R. Yates 2 3 and Ivo Souza2 3 1Department of Physics and Astronomy Rutgers University Piscataway New Jersey USA 2Department of Physics University of California Berkeley California 94720 USA 3Materials Science Division Lawrence Berkeley National Laboratory

### Techniques and Methods of Hall Measurements

· – Conductivity or resistivityCarrier concentrationCarrier type sign of hall voltageMobility Temperature dependency can help determine basic properties of the material like scattering mechanisms Fermi level and excitation energies. 𝜎𝜎. 0 = 𝑛𝑛𝑛𝑛𝜇𝜇. 𝑛𝑛= 1 𝑛𝑛𝑅𝑅. 𝐻𝐻. 𝜇𝜇= 𝑅𝑅. 𝐻𝐻

File Size 1MB### Theory of Valley Hall Conductivity in Graphene with Gap

· Hall conductivity can become nonzero in the absence of a magnetic eld. For the K points the Hamilto-nian is obtained by replacing ⃗˙ with ⃗˙ which makes vy = (= h)˙y. As a result the ﬀe magnetic eld is in the opposite direction and the Hall conductivity has an opposite sign making the total Hall conductivity van-ish.

### Field-Modulated Anomalous Hall Conductivity and Planar

· A 22 enhancement of the intrinsic anomalous Hall conductivity (AHC) as compared to bulk material was observed. A magnetic field-modulated AHC which may be related to the changing Weyl point separation with magnetic field was also found. Furthermore we showed that the PHE in a hard magnetic WSM is a complex interplay between ferromagnetism

### Spin-Hall conductivity in a two-dimensional Rashba

· Hall conductivity sH of a clean 2DEG and its in-plane magnetic susceptibility providing additional argu-ments in favor of the equilibrium nature of the spin-Hall constant sH = 2e g B 2m b 2 where m b is the band mass B is the Bohr magneton and g

### Fermi-surface calculation of the anomalous Hall

· Fermi-surface calculation of the anomalous Hall conductivity Xinjie Wang 1David Vanderbilt Jonathan R. Yates 2 3 and Ivo Souza2 3 1Department of Physics and Astronomy Rutgers University Piscataway New Jersey USA 2Department of Physics University of California Berkeley California 94720 USA 3Materials Science Division Lawrence Berkeley National Laboratory

### condensed matterHall conductivity from Kubo Bulk or

· Hall conductivity from Kubo Bulk or edge Using the Kubo formula Thouless Kohmoto Nightingale and den Nijs (TKNN PRL 49 (1982)) proved that upon summing all the contributions of the filled states of an insulator the Hall conductivity must be an integer (the Chern number) times e 2/h. Their theorem uses periodic boundary

### 1. Anomalous Hall Conductivity

· Anomalous Hall Conductivity (AHC) Hall conductivity is enhanced by the magnetization of the host material. This is due to the spin-dependent scattering of the charged carrier. This quantity can be described using the Kubo formula as 𝜎 =න BZ 3𝑘 2𝜋3 ≠ ′ 2Im 𝒌 ′𝒌 ′𝒌 𝒌

### condensed matterHall conductivity from Kubo Bulk or

· Hall conductivity from Kubo Bulk or edge Using the Kubo formula Thouless Kohmoto Nightingale and den Nijs (TKNN PRL 49 (1982)) proved that upon summing all the contributions of the filled states of an insulator the Hall conductivity must be an integer (the Chern number) times e 2/h. Their theorem uses periodic boundary

### L17 Resistivity and Hall Effect Measurments

2. Resistivity / conductivity measurements 3. Hall effect measurements 4. The van der Pauw method 5. Summary Lundstrom ECE-656 F11 22 Hall effect 22 The Hall effect was discovered by Edwin Hall in 1879 and is widely used to characterize electronic materials. It also finds use magnetic field sensors. n-type semiconductor current in x-direction

### Quantized Hall conductivity in two dimensions

· Quantized Hall conductivity in tsto dimensions R B. Laughlin Bell Laboratories Murray Hill )Ver Jersey 07974 (Received 20 January 1981) It is shown that the quantization of the Hall conductivity of two-dimensional metals which has been observed recently by Klitzing Dorda and Pepper and by Tsui and Gossard is a conse-

### Ab initio Calculation of the Intrinsic Spin Hall Effect in

· Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge GaAs and AlAs is large ∼ 100 (ℏ / e) (Ω cm) − 1 showing the possibility of a spin Hall effect beyond the four-band Luttinger Hamiltonian.The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller indicating

### Hall conductivity of a two-dimensional graphite system

· Within a self-consistent Born approximation the Hall conductivity of a two-dimensional graphite system inthe presence of a magnetic ﬁeld is studied by quantum transport theory. The Hall conductivity is calculated forshort- and long-range scatterers. It is calculated analytically in the limit of strong magnetic ﬁelds and in theBoltzmann limit in weak magnetic ﬁelds. The numerical calculation shows that the Hall conductivity

### 1805.10532 Quantization of the thermal Hall conductivity

· Quantization of the thermal Hall conductivity at small Hall angles. Authors Mengxing Ye Gábor B. Halász Lucile Savary Leon Balents. (Submitted on 26 May 2018 ( v1 ) last revised 3 Oct 2018 (this version v2)) Abstract We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising

### Phys. Rev. B 86 235438 (2012)Optical Hall conductivity

· Optical Hall conductivity σ x y as a function of photon energy for the 4 2 graphene antidot lattice. The conductivity is shown relative to the zero-frequency conductivity of graphene σ 0 times the square of the cyclotron energy ℏ ω c. The blue (red) lines show the real (imaginary) part of the conductivity.