Theory of Anderson localization in weak magnetic fields

We derive self-consistency equations determining the transverse dynamical conductivity for the case of Wegner's local gauge invariant model in a weak magnetic field B. The solution in the critical regime connected with Anderson localization is given for dimensionalities d = 2, 3. In d = 2 the self-consistency equations generate a logarithmic singularity in second order in the coupling constant. This is shown to be in agreement with the loop expansion and yields localization for arbitrarily weak coupling. In d = 3 there is a metal-insulator transition. In its vicinity the self-consistency equations reduce to a two-parameter scaling law, which is consistent with the results of Khmelnitskii and Larkin.     

Random magnetic field and quasiparticle transport in the mixed state of high- Tc cuprates

By a singular gauge transformation, the quasiparticle transport in the mixed state of high- Tc cuprates is mapped into a charge-neutral Dirac moving in short-range correlated random scalar and long-range correlated vector potential. A fully quantum mechanical approach to longitudinal and transverse thermal conductivities is presented. The semiclassical Volovik effect is presented in a quantum mechanical way. The quasiparticle scattering from the random magnetic field which was completely missed in all the previous semiclassical approaches is the dominant scattering mechanism at sufficient high magnetic field. The implications for experiments are discussed.     

Doped Mott insulators are insulators: hole localization in the cuprates

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbor singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the noncommutativity of the two limits U-->infinity (U the on-site Coulomb repulsion) and L -->infinity (the system size).     

Memory-function conductivity formula and transport coefficients in underdoped cuprates

The two-band memory-function conductivity formula is derived from the quantum kinetic equation in the pseudogap state of underdoped cuprates. The conduction electrons are described by using the adiabatic version of the nested Fermi liquid model, and the effects of Mott correlations are taken into account phenomenologically. The linear dependence of the low-temperature effective number of conduction electrons on the doping level δ (for not too large δ) is found to be in agreement with experimental observation. The momentum distribution function turns out to play an important role in describing temperature effects. The closing of the antiferromagnetic pseudogap at temperatures of the order of room temperature is shown to be a direct consequence of a relatively large width of the quasiparticle peak in this distribution function. The coupling of conduction electrons to external magnetic fields is included in the two-band transport equations in the usual semiclassical way. It is shown that the low-temperature Hall number is proportional to δ as well (again for not too large δ) and that it exhibits singular behaviour when the Fermi surface changes from the hole-like shape into the electron-like shape.     

Random magnetic field and weak localization effects in a dimpled 2D electron gas

We have studied negative magnetoresistance due to the weak localization effects in a 2D electron gas (2DEG) grown on dimpled substrates. Since the 2DEG is sensitive only to the normal component of B, depending on the orientation of the external magnetic field, electrons will move in a spatially inhomogeneous (B perpendicular to the substrate-B_⊥) or sign alternating, random magnetic field (B parallel to the substrate B_∥). A difference in the magnetoresistance at B_∥ and B_⊥ is seen for the sample with a coherence length larger than the spatial periodicity of magnetic field. We believe that the difference in the magnetic flux through the closed electron trajectories at B_∥ and B_⊥, taken into account random character of B_∥, is responsible for this behaviour. Features connected with Aharonov Bohm flux through the different areas on the dimpled surface were observed.     

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport

We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions (determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample boundaries. Received 19 August 2002 Published online 19 November 2002     

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature T_c, the regionT _c⪯ T ⪯ T* is a vast fluctuation regime.T _c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field H_c2 bounding the superconducting response and the pseudogap closing field H_pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi₂Sr₂CaCu₂O_8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field H_c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.     

Mooij rule and weak localization

It has been shown that the observed correlation between the resistivity ρ of high-resistivity metallic alloys and the sign of the temperature derivative of their resistivity can be explained by taking into account the weak localization effect. This correlation is as follows: the derivative dρ/dT is negative for alloys with resistivity in the range of 150–300 μΩ cm, which corresponds to the mean free path of electrons about the interatomic distance; however, this derivative is positive for alloys with lower resistivities (Mooij rule).     

High-field interlayer tunnelling transport in layered cuprates: Uncovering the pseudogap state

In high temperature (high T _c ) cuprate superconductors the gap in the electronic density of states is not fully filled at T _c ; it evolves into a partial (pseudo)gap that survives way beyond T _c , challenging the conventional views. We have investigated the pseudogap phenomenon in the field-temperature (H-T) diagram of Bi₂Sr₂CaCu₂O_{8 + y} over a wide range of hole doping ( ). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field H _pg . We found that H _pg and the pseudogap onset temperature T ^* are related via a Zeeman relation , irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO₂ planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of H _pg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.Received: 2 February 2004, Published online: 10 August 2004PACS: 74.25.Dw Superconductivity phase diagrams - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Hs Bi-based cuprates     

Interplay between the magnetic fluctuations and superconductivity in lanthanum cuprates

We report an analysis of the magnetic fluctuations in superconducting La_2?xSr_xCuO₄ and related lanthanum cuprates that have different symmetry of the low-temperature structure. NMR and ESR investigations revealed a dynamical coexistence of superconductivity and the antiferromagnetic correlations in most of the superconductivity region of the phase diagram. We show that, for all compounds, regardless of their low-temperature symmetry and their superconducting properties, the enhancement of the spin stiffness near 1/8 doping takes place.