Weak-field Magnetoresistance Research Articles

Magnetoresistance in noncentrosymmetric two-dimensional systems

The valley-contrasting geometric features of electronic wave functions manifested in Berry curvature and orbital magnetic moment have profound consequences on magnetotransport properties in both three- and two-dimensional systems. Although the importance of employing beyond-relaxation-time-approximation methods and intervalley scatterings in collision integral has been confirmed in three dimensions, they have been widely overlooked in previous studies on two-dimensional multi-valley systems. Here, we revisit the issue of weak-field magnetoresistance in two-dimensional multi-valley systems with broken inversion symmetry. We provide an exact solution to the Boltzmann equation and demonstrate that the inclusion of in-scattering terms in the collision integral can change the sign of the magnetoresistance in high-density regime. With an initial valley polarization, we also predict an orbital magnetic moment-induced intrinsic contribution to Hall conductivity in the time-reversal-broken situation, which is consistently negative, and in contrast to the anomalous Hall term, it does not depend on the polarization sign. Depending on which valley has the excess charge, our calculations show that a completely various behavior is exhibited in the magnetoresistance which can be considered as a valley-polarization probe in the experiment.

Recent progress of transport theory in Dirac quantum materials

Dirac quantum materials comprise a broad category of condensed matter systems characterized by low-energy excitations described by the Dirac equation. These excitations, which can manifest as either collective states or band structure effects, have been identified in a wide range of systems, from exotic quantum fluids to crystalline materials. Over the past several decades, they have sparked extensive experimental and theoretical investigations in various materials, such as topological insulators and topological semimetals. The study of Dirac quantum materials has also opened up new possibilities for topological quantum computing, giving rise to a burgeoning field of physics and offering a novel platform for realizing rich topological phases, including various quantum Hall effects and topological superconducting phases. Furthermore, the topologically non-trivial band structures of Dirac quantum materials give rise to plentiful intriguing transport phenomena, including longitudinal negative magnetoresistance, quantum interference effects, helical magnetic effects, and others. Currently, numerous transport phenomena in Dirac quantum materials remain poorly understood from a theoretical standpoint, such as linear magnetoresistance in weak fields, anomalous Hall effects in nonmagnetic materials, and three-dimensional quantum Hall effects. Studying these transport properties will not only deepen our understanding of Dirac quantum materials, but also provide important insights for their potential applications in spintronics and quantum computing. In this paper, quantum transport theory and quantum anomaly effects related to the Dirac equation are summarized, with emphasis on massive Dirac fermions and quantum anomalous semimetals. Additionally, the realization of parity anomaly and half-quantized quantum Hall effects in semi-magnetic topological insulators are also put forward. Finally, the key scientific issues of interest in the field of quantum transport theory are reviewed and discussed.

Electric current noise in mesoscopic organic semiconductors induced by nuclear spin fluctuations

We demonstrate that nuclear spin fluctuations lead to the electric current noise in the mesoscopic samples of organic semiconductors showing the pronounced magnetoresistance in weak fields. For the bipolaron and electron-hole mechanisms of organic magnetoresistance, the current noise spectrum consists of the high frequency peak related to the nuclear spin precession in the Knight field of the charge carriers and the low frequency peak related to the nuclear spin relaxation. The shape of the spectrum depends on the external magnetic and radiofrequency fields, which allows one to prove the role of nuclei in magnetoresistance experimentally.

Theory of Magnetoresistance in Tellurene and Related Mini-Gap Systems

The weak-field magnetoresistance is calculated in tellurene and related two-dimensional systems, characterized by interacting two bands having parabolic dispersion with their centers displaced from...

Crossover between Positive and Negative Magnetoresistance in Graphene: Roles of Absence of Backscattering

The magnetoresistance in weak magnetic fields is calculated in graphene containing “short-range” scatterers causing isotropic intra- and inter-valley scattering and “long-range” scatterers characte...

Magnetoresistance due to Diamagnetic Response in Two-Dimensional System

The weak-field magnetoresistance is calculated in a two-dimensional system containing scatterers with short-range potential within a self-consistent Born approximation. The result obtained by a formula of the magnetoconductivity previously derived and by a direct expansion of the conductivity in a magnetic field are in agreement with each other, and their comparison gives good insight into roles of some terms of the formal formula. Explicit numerical results show that the magnetoresistance vanishes at sufficiently high energy in agreement with the Boltzmann result, but becomes positive and increases in the energy region near the band bottom. This positive magnetoresistance appears in the energy range where the diamagnetic susceptibility deviates from the density of states and is largely understood in terms of the velocity renormalization due to the diamagnetic response.

Linear magnetoresistance induced by intra-scattering semiclassics of Bloch electrons

The weak field magnetoresistance has seen a revived interest due to the distinct role played by the momentum-space Berry curvature of Bloch electrons. While most previous studies in this regard focus on the inter-scattering motion of semiclassical Bloch electrons in electromagnetic fields, the intra-scattering effects of the semiclassical dynamics augmented by the Berry curvature, magnetic moment and shift vector on the magnetoresistance have been largely overlooked. Here we uncover that these intra-scattering effects, which are neglected in the field-independent relaxation time approximation to the Boltzmann collision integral, can be as important as the inter-scattering ones. Concrete calculations on the two dimensional gapped Dirac model show that the sign of the negative linear magnetoresistance given by the Berry curvature alone is reversed when one considers the magnetic moment and shift vector.

Experimental Evidence for an Inhomogeneous State of the Correlated Two-Dimensional Electron System in the Vicinity of a Metal–Insulator Transition

From measurements of the oscillatory magnetoresistance in weak perpendicular magnetic fields, we found that the quantum oscillations in two-dimensional electron systems in Si-MOS structures are observed down to the critical carrier density nc of the transition to the strongly localized state. For such low densities, the oscillations exhibit an anticipated period, phase, and amplitude, even though the conductivity becomes less than e2/h, and, hence, the mean free path becomes less than the Fermi wavelength λF. We believe that this apparent contradiction with the Ioffe-Regel criterion for diffusive transport is caused by emergence of an inhomogeneous state of the 2D system, in which the regions of diffusive and hopping conduction are spatially separated.

Theory of Weak-Field Magnetoresistance in Bilayer Graphene

The magnetoconductivity, which is the correction to the diagonal conductivity proportional to the second power of magnetic-field strength, is calculated in bilayer graphene in the presence of scatt...

Weak-Field Magnetoresistance in Graphene with Long-Range Scatterers

The magnetoconductivity proportional to B2 with B the strength of applied magnetic field is calculated in monolayer graphene in a self-consistent Born approximation for scatterers with long-range p...

Formula of Weak-Field Magnetoresistance in Graphene

The formula of weak-field magnetoconductivity Δσ(B) proportional to B2, with B the strength of a magnetic field, is derived for systems corresponding to monolayer and bilayer graphenes. It is repre...

Sulfur passivation of semi-insulating GaAs: Transition from Coulomb blockade to weak localization regime

The sulfur passivation of the semi-insulating GaAs bulk (SI GaAs) grown in an excess phase of arsenic is used to observe the transition from the Coulomb blockade to the weak localization regime at room temperature. The I–V characteristics of the SI GaAs device reveal nonlinear behavior that appears to be evidence of the Coulomb blockade process as well as the Coulomb oscillations. The sulfur passivation of the SI GaAs device surface results in enormous transformation of the I–V characteristics that demonstrate the strong increase of the resistance and Coulomb blockade regime is replaced by the electron tunneling processes. The results obtained are analyzed within frameworks of disordering SI GaAs surface that is caused by inhomogeneous distribution of the donor and acceptor anti-site defects which affects the conditions of quantum- mechanical tunneling. Weak localization processes caused by the preservation of the Fermi level pinning are demonstrated by measuring the negative magnetoresistance in weak magnetic fields at room temperature. Finally, the studies of the magnetoresistance at higher magnetic fields reveal the h/2e Aharonov–Altshuler–Spivak oscillations with the complicated behavior due to possible statistical mismatch of the interference paths in the presence of different microdefects.

Weak localization effect in topological insulator micro flakes grown on insulating ferrimagnet BaFe₁₂O₁₉.

Many exotic physics anticipated in topological insulators require a gap to be opened for their topological surface states by breaking time reversal symmetry. The gap opening has been achieved by doping magnetic impurities, which however inevitably create extra carriers and disorder that undermine the electronic transport. In contrast, the proximity to a ferromagnetic/ferrimagnetic insulator may improve the device quality, thus promises a better way to open the gap while minimizing the side-effects. Here, we grow thin single-crystal Sb1.9Bi0.1Te3 micro flakes on insulating ferrimagnet BaFe12O19 by using the van der Waals epitaxy technique. The micro flakes show a negative magnetoresistance in weak perpendicular fields below 50 K, which can be quenched by increasing temperature. The signature implies the weak localization effect as its origin, which is absent in intrinsic topological insulators, unless a surface state gap is opened. The surface state gap is estimated to be 10 meV by using the theory of the gap-induced weak localization effect. These results indicate that the magnetic proximity effect may open the gap for the topological surface attached to BaM insulating ferrimagnet. This heterostructure may pave the way for the realization of new physical effects as well as the potential applications of spintronics devices.

Distinctive uniaxial magnetic anisotropy and positive magnetoresistance in (110)-oriented Fe3O4 films

Magnetite (Fe3O4) films were synthesized on (110)-oriented MgO, MgAl2O4, and SrTiO3 substrates for comparative studies of the substrates' effects on magnetic and magnetoresistance properties of the films. For the [-110] direction, the hysteresis loops of the Fe3O4 film on MgAl2O4 exhibited a good squareness with the largest coercivity of ∼1090 Oe, and the ratio of remanent magnetization to saturation magnetization was ∼0.995. For the [001] direction, positive magnetoresistance in weak magnetic fields was most distinct for the (110) SrTiO3 substrate with the largest lattice mismatch. Positive magnetoresistance in the (110) Fe3O4 films was presumably affected by imperfect atomic arrangements at anti-phase boundaries.

Signatures of localization in the effective metallic regime of high-mobility Si MOSFETs

Combining experimental data, numerical transport calculations, and theoretical analysis, we study the temperature-dependent resistivity of high-mobility 2D Si MOSFETs to search for signatures of weak localization induced quantum corrections in the effective metallic regime above the critical density of the so-called two-dimensional metal-insulator transition (2D MIT). The goal is to look for the effect of logarithmic insulating localization correction to the metallic temperature dependence in the 2D conductivity so as to distinguish between the 2D MIT being a true quantum phase transition versus being a finite-temperature crossover. We use the Boltzmann theory of resistivity including the temperature dependent screening effect on charged impurities in the system to fit the data. We analyze weak perpendicluar field magnetoresistance data taken in the vicinity of the transition and show that they are consistent with weak localization behavior in the strongly disordered regime $k_F\ell\gtrsim1$. Therefore we supplement the Botzmann transport theory with a logarithmic in temperature quantum weak localization correction and analyze the competition of the insulating temperature dependence of this correction with the metallic temperature dependence of the Boltzmann conductivity. Using this minimal theoretical model we find that the logarithmic insulating correction is masked by the metallic temperature dependence of the Botzmann resistivity and therefore the insulating $\log T$ behavior may be apparent only at very low temperatures which are often beyond the range of temperatures accessible experimentally. Analyzing the low-$T$ experimental Si MOSFET transport data we identify signatures of the putative insulating behavior at low temperature and density in the effective metallic phase.

Coherent topological transport on the surface of Bi2Se3

The two-dimensional surface of the three-dimensional topological insulator is in the symplectic universality class and should exhibit perfect weak antilocalization reflected in positive weak-field magneto-resistance. Previous studies in topological insulator thin films suffer from high level of bulk n-type doping making quantitative analysis of weak antilocalization difficult. Here we measure the magneto-resistance of bulk-insulating Bi2Se3 thin films as a function of film thickness and gate-tuned carrier density. For thick samples, the magnitude of weak antilocalization indicates two decoupled (top and bottom) symplectic surfaces. On reducing thickness, we observe first a crossover to a single symplectic channel, indicating coherent coupling of top and bottom surfaces via interlayer tunnelling, and second, a complete suppression of weak antilocalization. The first crossover is governed by the ratio of phase coherence time to the inter-surface tunnelling time, and the second crossover occurs when the hybridization gap becomes comparable to the disorder strength.

Hopping Magnetotransport via Nonzero Orbital Momentum States and Organic Magnetoresistance

In hopping magnetoresistance of doped insulators, an applied magnetic field shrinks the electron (hole) s-wave function of a donor or an acceptor and this reduces the overlap between hopping sites resulting in the positive magnetoresistance quadratic in a weak magnetic field, B. We extend the theory of hopping magnetoresistance to states with nonzero orbital momenta. Different from s states, a weak magnetic field expands the electron (hole) wave functions with positive magnetic quantum numbers, m>0, and shrinks the states with negative m in a wide region outside the point defect. This together with a magnetic-field dependence of injection/ionization rates results in a negative weak-field magnetoresistance, which is linear in B when the orbital degeneracy is lifted. The theory provides a possible explanation of a large low-field magnetoresistance in disordered π-conjugated organic materials.

Finite size suppression of the weak field magnetoresistance of lightly phosphorous-doped silicon

We report magnetoresistance measurements of lightly phosphorous doped silicon in samples that are fabricated from silicon-on-insulator wafers and so confined in one dimension. All three principal magnetic field orientations were studied at 50 and 270 K for thicknesses between 1.5−530 μm, and as thin as 150 nm at 270 K. The weak field magnetoresistance was suppressed in the orientations with the field in the sample plane when the sample is thinner than ∼1 μm at 270 K (∼10 μm at 50 K). This suppression occurred for samples that are much thicker than the carrier mean free path and the Debye screening length, and the relevant lengthscale is instead the energy relaxation length.

Effects of electron–electron scattering in wide ballistic microcontacts

We consider effects of electron–electron scattering in wide ballistic microcontacts. Using a semiclassical Boltzmann equation, we obtain a positive correction to the Sharvin conductance that results from electron–electron collisions in the leads. The correction is linearly dependent on temperature at high temperatures T⪢eV and proportional to |V| at high voltages eV⪢T. Magnetic field leads to strong suppression of this positive correction that results in a positive magnetoresistance in weak fields. As electron–electron scattering affects the conductance, it also influences the noise. At low voltages the noise is defined by the Nyquist relation and at high voltages it is related with the inelastic correction to the current by the Shottky formula δS=2eδI.

Magnetoresistivity and microstructure of YBa 2Cu 3O y prepared using planetary ball milling

We have studied the microstructure and the magnetoresistivity of polycrystalline YBa 2Cu 3O y (YBCO or Y-123 for brevity) embedded with nanoparticles of Y-deficient YBCO, generated by the planetary ball milling technique. Bulk samples were synthesized from a precursor YBCO powder, which was prepared from commercial high purity Y 2O 3, Ba 2CO 3 and CuO via a one-step annealing process in air at 950 °C. After planetary ball milling of the precursor, the powder was uniaxially pressed and subsequently annealed at 950 °C in air. Phase analysis by X-ray diffraction (XRD), granular structure examination by scanning electron microscopy (SEM), microstructure investigation by transmission electron microscopy (TEM) coupled with energy dispersive X-ray spectroscopy (EDXS) were carried out. TEM analyses show that nanoparticles of Y-deficient YBCO, generated by ball milling, are embedded in the superconducting matrix. Electrical resistance as a function of temperature, ρ( T), revealed that the zero resistance temperature, T co , is 84.5 and 90 K for the milled and unmilled samples respectively. The milled ceramics exhibit a large magnetoresistance in weak magnetic fields at liquid nitrogen temperature. This attractive effect is of high significance as it makes these materials promising candidates for practical application in magnetic field sensor devices.