Crossover behavior of the anomalous Hall effect and anomalous nernst effect in itinerant ferromagnets

The anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) are experimentally investigated in a variety of ferromagnetic metals including pure transition metals, oxides, and chalcogenides, whose resistivities range over 5 orders of magnitude. For these ferromagnets, the transverse conductivity sigma{xy} versus the longitudinal conductivity sigma{xx} shows a crossover behavior with three distinct regimes in accordance qualitatively with a recent unified theory of the intrinsic and extrinsic AHE. We also found that the transverse Peltier coefficient alpha{xy} for the ANE obeys the Mott rule. These results offer a coherent and semiquantitative understanding of the AHE and ANE to an issue of controversy for many decades.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Unconventional integer quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.     

Spin chirality fluctuations and anomalous Hall effect in itinerant ferromagnets

The anomalous Hall effect due to the spin chirality order and fluctuation is studied theoretically in a Kondo lattice model without the relativistic spin-orbit interaction. Even without the correlations of the localized spins, sigma(xy) can emerge depending on the lattice structure and the spin anisotropy. We reveal the condition for this chirality-fluctuation driven mechanism for sigma(xy). Our semiquantitative estimates for a pyrochlore oxide Nd2Mo2O7 give a finite sigma(xy) approximately equal 10 Omega(-1) cm(-1) together with a high resistivity rho(xx) approximately equal 10(-4)-10(-3) Omega cm, in agreement with experiments.     

Spin Hall effect in doped semiconductor structures

In this Letter we present a microscopic theory of the extrinsic spin Hall effect based on the diagrammatic perturbation theory. Side-jump and skew-scattering contributions are explicitly taken into account to calculate the spin Hall conductivity, and we show that their effects scale as sigma(xy)SJ/sigma(xy)SS approximately (h/tau)/epsilonF, with tau being the transport relaxation time. Motivated by recent experimental work we apply our theory to n- and p-doped 3D and 2D GaAs structures, obtaining sigma(s)/sigma(c) approximately 10(-3)-10(-4), where sigma(s(c)) is the spin Hall (charge) conductivity, which is in reasonable agreement with the recent experimental results of Kato et al. [Science 306, 1910 (2004)] in n-doped 3D GaAs system.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.     

Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

Pressure tuning of the anomalous Hall effect in the kagome superconductor CsV3Sb5

Controlling the anomalous Hall effect(AHE)inspires potential applications of quantum materials in the next generation of electronics.The recently discovered quasi-2D kagome superconductor CsV₃Sb₅ exhibits large AHE accompanying with the charge-density-wave(CDW)order which provides us an ideal platform to study the interplay among nontrivial band topology,CDW,and unconventional superconductivity.Here,we systematically investigated the pressure effect of the AHE in CsV₃Sb₅.Our high-pressure transport measurements confirm the concurrence of AHE and CDW in the compressed CsV₃Sb₅.Remarkably,distinct from the negative AHE at ambient pressure,a positive anomalous Hall resistivity sets in below 35 K with pressure around 0.75 GPa,which can be attributed to the Fermi surface reconstruction and/or Fermi energy shift in the new CDW phase under pressure.Our work indicates that the anomalous Hall effect in CsV₃Sb₅ is tunable and highly related to the band structure.     

Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied, demonstrating a phase diagram with charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunneling we find quantum Hall phases with spin Hall coefficients of sigma(spin)(xy)=0,2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of approximately 0.96. In the presence of a Zeeman term an additional sigma(spin)(xy)=1 phase appears.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

Pure anomalous Hall effect in nonmagnetic zinc-blende semiconductors

We report the experimental observation of the pure anomalous Hall effect (AHE) in nonmagnetic zinc-blende semiconductors without application of the external magnetic fields. The AHE without any contribution from the ordinary Hall current originates from nonequilibrium magnetization induced by spin-polarized electrons generated by the circularly polarized light (σ). We measure the pure AHE as a function of the external bias, crystal temperature and pumping σ-photon energy. The results of their dependences are discussed.     

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.     

Unconventional anomalous Hall effect enhanced by a noncoplanar spin texture in the frustrated Kondo lattice Pr2Ir2O7

We have investigated the Hall effect in the geometrically frustrated Kondo lattice Pr2Ir2O7. In its spin-liquid-like paramagnetic regime, the Hall resistivity rho(xy) is found to increase logarithmically on cooling. Moreover, in this low temperature region, the field dependence of the Hall conductivity sigma(xy) shows a large enhancement up to 30 Omega(-1) cm(-1) as well as a nonmonotonic change with the magnetization. Our results are far different from the anomalous Hall effect due to the spin-orbit coupling observed in ordinary magnetic conductors. We discuss the possible spin-chirality effect in the Ir 5d conduction band due to the noncoplanar texture of Pr<111> Ising-like moments.     

Hall resistivity of granular metals

We calculate the Hall conductivity sigma(xy) and resistivity rho(xy) of a granular system at large tunneling conductance g(T)>1. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula rho(xy)=H/(n*ec), where n* differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature T correction to rho(xy) in the range Gamma less or similar T less or similar min(g(T)E(c), E(Th)), where Gamma is the tunneling escape rate, E(c) is the charging energy, and E(Th) is the Thouless energy of the grain.     

Charge and spin Hall conductivity in metallic graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity sigma(xy)(SH). In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to sigma(xy)(SH) values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.     

Landau-level degeneracy and quantum Hall effect in a graphite bilayer

We derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase 2pi. Its high-magnetic-field Landau-level spectrum consists of almost equidistant groups of fourfold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, sigma(xy)(N), which exhibits plateaus at integer values of 4e2/h and has a double 8e2/h step between the hole and electron gases across zero density, in contrast to (4n + 2)e2/h sequencing in a monolayer.     

Quantization of the Hall conductivity well beyond the adiabatic limit in pulsed magnetic fields.

We measure the Hall conductivity, sigma(xy), on a Corbino geometry sample of a high-mobility AlGaAs/GaAs heterostructure in a pulsed magnetic field. At a bath temperature about 80 mK, we observe well expressed plateaux in sigma(xy) at integer filling factors. In the pulsed magnetic field, the Laughlin condition of the phase coherence of the electron wave functions is strongly violated and, hence, is not crucial for sigma(xy) quantization.     

Hall effect in a martensitic transformation in Ni-Co-Mn-In Heusler alloys

The Hall effect, transverse magnetoresistance, and magnetization of Ni₄₈Co₂Mn₃₅In₁₅ Heusler alloys have been studied at T = 77–300 K in magnetic fields up to 15 kOe. It has been shown that a martensitic transformation is accompanied by a change in the sign of the constant of the ordinary Hall effect, which means a strong change in the electronic spectrum in the martensitic transformation, while the anomalous Hall effect (AHE) constant is positive in both the austenite and martensite phases. In both phases, there are no correlations between the AHE constant and the square of the resistivity, which are characteristic of the side jump mechanism in the AHE theory. In the near vicinity of the martensitic transformation, the field dependences of the Hall resistance are complex and nonmonotonic, indicating a change in the relative concentrations of the austenite and martensite phases in strong fields.     

Intrinsic versus extrinsic anomalous Hall effect in ferromagnets

A unified theory of the anomalous Hall effect (AHE) is presented for multiband ferromagnetic metals with dilute impurities. In the clean limit, the AHE is mostly due to extrinsic skew scattering. When the Fermi level is located around anticrossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its nonperturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit coupling.     

Analysis of the anomalous Hall effect in a double layer of a ferromagnetic and a normal metal

A new method is suggested to investigate the mechanism of the anomalous Hall effect (AHE) in ferromagnetic metals. Using a double layer of a ferromagnet and a normal metal of increasing thickness one can manipulate the AHE in the ferromagnet without changing the ferromagnet's structure and electronic properties. The conduction electrons from the normal metal carry their drift velocity across the interface into the ferromagnetic film and induce an additional AHE conductance ΔG_xy. Its dependence on the mean free path in the normal metal distinguishes between the side jump and the skew scattering mechanisms for the AHE in the ferromagnet.