# hall conductivity

### 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### 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 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 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.

### 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

### 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

### 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-

### 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

### 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### 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.

### Spin Hall conductivityLunds tekniska högskola

· It was shown soon after Sinova s article that this system was not robust to disorder. First order corrections to the spin Hall conductivity very exactly cancel out the zeroth order conductivity Raimondi and Schwab PRB 71 (2005) and quantum corrections are zero Chalaev and Loss PRB 71 (2005) meaning a total disappearance of the spin Hall effect.

### 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.

### 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

### 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.

### 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.

### Giant unconventional anomalous Hall effect in the

· In these insulators the anomalous Hall conductivity (σ AHE) becomes modulated by the conductance quantum while the longitudinal conductivity (σ xx) approaches zero resulting in the AHA (tan −1 (σ AHE σ xx))approaching 90° (11 12). The AHE can be broadly divided into two categories intrinsic and extrinsic .

### Ab initio calculation of the anomalous Hall conductivity

· integer quantum Hall effect 13 and also closely related to the Berry-phase theory of polarization.14 The dc anomalous Hall conductivity AHC is simply given as the Brillouin zone BZ integral of the Berry curvature weighted by the occu-pation factor of each state xy =− e2 n BZ dk 2 3 f n k n z k 1 where xy=− yx is the antisymmetric part of

### The Hall EﬀectUniversity of Washington

· failure of the simple model of metallic conductivity which we discuss below to account for many experimental measurements of the Hall eﬀect has been one of the principal motivators leading to a better understanding of electronic properties of materials 5 pp. 58–62 . 1.1 The simple theory of the Hall

### 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

### Ab initio calculation of the anomalous Hall conductivity

· integer quantum Hall effect 13 and also closely related to the Berry-phase theory of polarization.14 The dc anomalous Hall conductivity AHC is simply given as the Brillouin zone BZ integral of the Berry curvature weighted by the occu-pation factor of each state xy =− e2 n BZ dk 2 3 f n k n z k 1 where xy=− yx is the antisymmetric part of

### 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.

### 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

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

· The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors.

Cited by 136### 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 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.

### 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

### 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.

### The Hall EﬀectUniversity of Washington

· With the measurements he made Hall was able to determine forthe ﬁrst time the sign of chargecarriers in a conductor. Even today Hall eﬀect measurementscontinue to be a useful techniquefor characterizing the electrical transport properties of metals and semiconductors. Indeed thefailure of the simple model of metallic conductivity whichwe discuss below to account for manyexperimental measurements of the Hall eﬀect

### 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.

### 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.