Hall conductance $σ_{xy}$ as the Chern numbers of the Berry connection in the magnetic Brillouin zone is calculated for a realistic multi band tight-band model of graphene with non-orthogonal basis. It is confirmed that the envelope of $σ_{xy}$ coincides with a semi-classical result when magnetic field is sufficiently small.
The Hall resistivity $ρ_{xy}$ from the weak-field Boltzmann theory also explains the overall behaviour of the $σ_{xy}$ if the Fermi surface is composed of a single energy band. The plateaux of $σ_{xy}$ are explained from semi-classical quantization and necessary modification is proposed for the Dirac fermion regimes.
It is known that the conductance of a quantum point contact is quantized in units of $2e^2/h$ and this quantization is destroyed by a non-adiabatic scatterer in the point contact, due to backscattering. Recently, it was shown [Phys. Rev. Lett. 71, 137 (1993)] that taking many non-adiabatic scatterers periodically in a quantum channel, the quantization can be recovered. We study this conductance quantization of a periodic system in the presence of a strong defect. A periodic arrangement of double-stubs give remarkable quantization of conductance. A periodic arrangement of double-constrictions a…
We present numerical studies of conduction in graphene nanoribbons with different types of disorder. We find that even when defect scattering depresses the conductance to values two orders of magnitude lower than 2e^2/h, equally spaced conductance plateaus occur at moderately low temperatures due to enhanced electron backscattering near subband edge energies if bulk vacancies are present in the ribbon. This work accounts quantitatively for the surprising conductance quantization observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] in ribbons with such low conductances.
Notwithstanding the discreteness of metallic constrictions, it is shown that the finite elasticity of stable, single-atom gold constrictions allows for a continuous and reversible change in conductance, thereby enabling observation of channel saturation and conductance quantization. The observed channel saturation and signature for conductance quantization is achieved by superposition of atomic/subatomic-scale oscillations on a retracting/approaching gold tip against a gold substrate of a scanning probe. Results also show that conductance histograms are neither suitable for evaluating the stab…
Recent experiments on atomic-scale metallic contacts have shown that the quantization of the conductance appears clearly only after the average of the experimental results. Motivated by these results we have analyzed a simplified model system in which a narrow neck is randomly coupled to wide ideal leads, both in absence and presence of time reversal invariance. Based on Random Matrix Theory we study analytically the probability distribution for the conductance of such system. As the width of the leads increases the distribution for the conductance becomes sharply peaked close to an integer mu…
We fabricated strongly confined Schottky-gated quantum point contacts by etching Si/SiGe heterostructures and observed intriguing conductance quantization in units of approximately 1e2/h. Non-linear conductance measurements were performed depleting the quantum point contacts at fixed mode-energy separation. We report evidences of the formation of a half 1e2/h plateau, supporting the speculation that adiabatic transmission occurs through 1D modes with complete removal of valley and spin degeneracies.
We have studied ballistic transport in a 1D channel formed using surface gate techniques on a back-gated, high-mobility, bilayer 2D hole system. At millikelvin temperatures, robust conductance quantization is observed in the quantum wire formed in the top layer of the bilayer system, without the gate instabilities that have hampered previous studies of 1D hole systems. Using source drain bias spectroscopy, we have measured the 1D subband spacings, which are 5-10 times smaller than in comparable GaAs electron systems, but 2-3 times larger than in previous studies of 1D holes. We also report the…
We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.
We report on the fabrication and electronic transport characterisation of Schottky-gated strongly confined Si/SiGe quantum point contacts (QPC). At zero magnetic field and T=450mK the QPC conductance as a function of gate voltage shows a quantization in units of e^2/h, indicative of transport through 1D modes which appear to lack both spin and valley degeneracy.
We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to localization induced by edge scattering. We find that even for weak edge roughness, conductance steps are suppressed and transport gaps appear. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.
We theoretically study the electron transport through a magnetic point contact (PC) with special attention to the effect of an atomic scale domain wall (DW). The spin precession of a conduction electron is forbidden in such an atomic scale DW and the sequence of quantized conductances depends on the relative orientation of magnetizations between left and right electrodes. The magnetoresistance is strongly enhanced for the narrow PC and oscillates with the conductance.
Using a generalized Landauer approach we study the non-linear transport in mesoscopic graphene with zig-zag and armchair edges. We find that for clean systems, the low-bias low-temperature conductance, G, of an armchair edge system in quantized as G/t=4 n e^2/h, whereas for a zig-zag edge the quantization changes to G/t t=4(n+1/2)e^2/h, where t is the transmission probability and n is an integer. We also study the effects of a non-zero bias, temperature, and magnetic field on the conductance. The magnetic field dependence of the quantization plateaus in these systems is somewhat different from…
We analyze the fractional quantization of the ballistic conductance associated with the light and heavy holes bands in Si, Ge and GaAs systems. It is shown that the formation of the localized hole state in the region of the quantum point contact connecting two quasi-1D hole leads modifies drastically the conductance pattern. Exchange interaction between localized and propagating holes results in the fractional quantization of the ballistic conductance different from those in electronic systems. The value of the conductance at the additional plateaux depends on the offset between the bands of t…
We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also …
Theory and a vast set of experimental work in metals, since a century, appear to show that the mean free path of conduction electrons in a real metal is about the min (bulk mean free path, smallest transversal size of the metal), a result that was already proposed by J. J. Thomson in 1901. This establishes, as discussed in this work, serious difficulties to justify conductance quantization and ballistic transport in atomic/nanocontacts or nanoconstrictions of real life metals. The ohmic resistance of the leads proves to be as important as the ballistic one of the constriction.
The conductance quantization and shot noise below the first conductance plateau $G_0 = 2e^2/h$ are measured in a quantum point contact fabricated in a GaAs/AlGaAs tunnel-coupled double quantum well. From the conductance measurement, we observe a clear quantized conductance plateau at $0.5G_0$ and a small minimum in the transconductance at $0.7 G_0$. Spectroscopic transconductance measurement reveals three maxima inside the first diamond, thus suggesting three minima in the dispersion relation for electric subbands. Shot noise measurement shows that the Fano factor behavior is consistent with t…
Ballistic transport through an impurity-free section of the Corbino disk in graphene is investigated by means of the Landauer-Büttiker formalism in the mesoscopic limit. In the linear-responce regime the conductance is quantized in steps close to integer multiples of $4e^{2}/h$, yet Fabry-Perot oscillations are strongly suppressed. The quantization arises for small opening angles $θ\lesssimπ/3$ and large radii ratios $R_2/R_1\gtrsim{}10$. We find that the condition for emergence of the $n$-th conductance step can be written as $\sqrt{n}θ/π\ll{}1$. A brief comparison with the conductance spectr…
Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one dimensional nanowires. We show that by improving the nanowire-metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally, studying the sub-band evolution in a rotating magnetic field reveals an orbital degeneracy betw…
We report on a striking departure from the canonical step sequence of quantized conductance in a ballistic, quasi-one-dimensional metallic channel. Ideally, in such a structure, each sub-band population contributes its Landauer conductance quantum independently of the rest. In a picture based exclusively on coherent single-carrier transmission, unitary back-scattering can lower a conductance step below ideal, but it is absolutely impossible for it to enhance the ideal Landauer conductance of a sub-band. Precisely such an anomalous and robust nonlinear enhancement has already been observed over…
Conductance quantization was measured in submicron constrictions of PbTe, patterned into narrow,12 nm wide quantum wells deposited between Pb$_{0.92}$Eu$_{0.08}$Te barriers. Because the quantum confinement imposed by the barriers is much stronger than the lateral one, the one-dimensional electron energy level structure is very similar to that usually met in constrictions of AlGaAs/GaAs heterostructures. However, in contrast to any other system studied so far, we observe precise conductance quantization in $2e^2/h$ units, {\it despite of significant amount of charged defects in the vicinity of …
The electronic and transport properties of atomic-size contacts are analyzed theoretically using a self-consistent tight-binding model. Our results show that, for s-like metals, a sufficiently narrow contact exhibits well defined resonant states at the Fermi energy, spatially localized in the neck region. These states are robust with respect to disorder and provide a simple explanation for the observed tendency to conductance quantization. It is also shown that these properties disappear for a sufficiently large contact area. The possible relevance of this resonant states in scanning tunneling…
The quantum of heat conductance of ballistic one-dimensional (1D) channels, being gQ=k0T with k0=pi^2*2kB^2/3h (T - temperature, kB - Boltzmann's constant, h - Planck's constant), is an important fundamental constant. While the quantization of the electrical conductance of 1D ballistic conductors has long been experimentally established, a demonstration of the quantization of thermal conductance proved to be much harder. It has already been accomplished for weakly interacting systems of phonons, photons, and electronic Fermi-liquids. Theoretically, however, the quantization must also hold in s…
We present detailed experimental studies of the temperature dependence of the plateau conductance of GaAs quantum point contacts in the temperature range from 0.3 K to 10 K. Due to a strong lateral confinement produced by a shallow-etching technique we are able to observe the following unexpected feature: a linear temperature dependence of the measured mid-plateau conductance. We discuss an interpretation in terms of a temperature dependent, intrinsic series resistance, due to non-ballistic effects in the 2D-1D transition region. These results have been reproduced in several samples from diffe…
Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron i…
We present numerical studies of non-linear conduction in graphene nanoribbons when a bias potential is applied between the source and drain electrodes. We find that the conductance quantization plateaus show asymmetry between the electron and hole branches if the potential in the ribbon equals the source or drain electrode potential and strong electron (hole) scattering occurs. The scattering may be at the ends of a uniform ballistic ribbon connecting wider regions of graphene or may be due to defects in the ribbon. We argue that, in ribbons with strong defect scattering, the ribbon potential …
In the present article we give a brief overview of the theories of the 0.7 anomaly of the ballistic conductance. The special attantion is given to the concept of a fractional quantization of the ballistic conductance arising from exchange interaction of the Heisenberg type between the carrier localized in the region of the quantum point contact and freely propagating carriers in electron and hole systems. ----- Brotaskömmtun skotleiðninnar í einvíðum rafeinda og holukerfum Í grein þessari verður skömmtun skotleiðninnar í einvíðum kerfum útskýrð og farið yfir nýjustu og helstu fræðilíkön á svið…
We present a theoretical analysis of recent experimental results of Yacoby et al. on transport properties of high quality quantum wires. We suggest an explanation of observed deviations of the conductance from the universal value $2e^2/h$ per channel in the wire. We argue that at low temperatures and biases the deviation can be a consequence of anomalously enhanced backscattering of electrons entering the 2DEG from the wire and is not connected to intrinsic properties of 1DEG.
Recent experiments on the conductance of high quality quantum wires have revealed an unexpected feature: the quantization step of the conductance is apparently system dependent. We provide the understanding of this behaviour using the appropriately extended random matrix approach. A single additional parameter governs the size of the conductance quantization steps. In effect the behaviour seems to remain `universal', generic for the conductance of a class of mesoscopic systems.
We report the experimental observation of conductance quantization in graphene nanoribbons, where 1D transport subbands are formed due to the lateral quantum confinement. We show that this quantization in graphene nanoribbons can be observed at temperatures as high as 80 K and channel lengths as long as 1.7 $μ$m. The observed quantization is in agreement with that predicted by theoretical calculations.
The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly e…
The transmission through quantum wires is studied within a noninteracting model taking into account the geometry of cleaved edge overgrowth devices. We show that the junction between wide contact and narrow wire has almost no influence on the transmission through these devices while a potential step between contact and wire strongly effects the conduction. Our results are compared with recent experimental findings.
Recent investigations of fractal conductance fluctuations (FCF) in electron billiards reveal crucial discrepancies between experimental behavior and the semiclassical Landauer-Buttiker (SLB) theory that predicted their existence. In particular, the roles played by the billiard's geometry, potential profile and the resulting electron trajectory distribution are not well understood. We present measurements on two custom-made devices - a 'disrupted' billiard device and a 'bilayer' billiard device - designed to probe directly these three characteristics. Our results demonstrate that intricate proc…
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal r…
Majorana Zero Modes (MZMs) are prime candidates for robust topological quantum bits, holding a great promise for quantum computing. Semiconducting nanowires with strong spin orbit coupling offers a promising platform to harness one-dimensional electron transport for Majorana physics. Demonstrating the topological nature of MZMs relies on braiding, accomplished by moving MZMs around each other in a certain sequence. Most of the proposed Majorana braiding circuits require nanowire networks with minimal disorder. Here, the electronic transport across a junction between two merged InSb nanowires i…
The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in natural units $ π^2 k_B^2 T /3 h$ ($T$ is temperature, $h$ the Planck constant, $k_B$ the Boltzmann constant). Such a value was indeed recently observed in a quantum-Hall system and a magnetic insulator. We show that a non-topological "thermal metal" phase that forms due to quenched disorder may disguise as a non-Abelian phase by well ap…
Using the mechanically controlled break junction technique at low temperatures and under cryogenic vacuum conditions we have studied atomic contacts of several magnetic (Fe, Co and Ni) and non-magnetic (Pt) metals, which recently were claimed to show fractional conductance quantization. In the case of pure metals we see no quantization of the conductance nor half-quantization, even when high magnetic fields are applied. On the other hand, features in the conductance similar to (fractional) quantization are observed when the contact is exposed to gas molecules. Furthermore, the absence of fract…
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
Conductance measurements of carbon nanotubes containing gated local depletion regions exhibit plateaus as a function of gate voltage, spaced by approximately e2/h, the quantum of conductance for a single (non-degenerate) mode. Plateau structure is investigated as a function of bias voltage, temperature, and magnetic field. We speculate on the origin of this surprising quantization, which appears to lack band and spin degeneracy.
We study the quantization of the supercurrent and conductance of a superconducting quantum point contact (SQPC) in a superconductor-two dimensional electrongas-superconductor (S-2DEG-S) Josephson junction with a split gate. The supercurrent and the conductance values change stepwise as a function of the gate voltage. We observe the onset of the first transport mode contributing both to the supercurrent and the conductance of the SQPC. Furthermore the steps in the supercurrent and the conductance appear at the same gate voltage values. This shows, that each transport mode in the SQPC contribute…
We present self-consistent calculations of electron transport in graphene nanoconstrictions within the Hartree approximation. We consider suspended armchair ribbons with V-shaped constrictions having perfect armchair or zigzag edges as well as mesoscopically smooth but atomically stepped constrictions with cosine profiles. Our calculations are based on a tight-binding model of the graphene and account for electron-electron interactions in both the constriction and the semi-infinite leads explicitly. We find that electron interactions result in (i) Electrons accumulating along edges of the unif…
We study the transport properties of a three dimensional atomic-scale contact in the ballistic regime. The results for the conductance and related transmission eigenvalues show how the properties of the ideal semi-infinite leads (i.e. measuring device) as well as the coupling between the leads and the conductor influence the transport in a two-probe geometry. We observe the evolution from conductance quantization to resonant tunneling conductance peaks upon changing the hopping parameter in the disorder-free tight-binding Hamiltonian which describes the leads and the coupling to the sample.
The robustness of the anomalous Hall conductance, $σ_{yx}^{}= σ_{H}^{}$, quantization in the model of a~two-dimensional disordered gas of massive Dirac electrons subjected to an external orthogonal magnetic field is investigated in the framework of Kubo--Středa formalism. Using the momentum representation for the averaged one-electron Green functions in a~magnetic field, an explicit analytical expression for the Středa term of $σ_{H}^{}$ is obtained. It is shown that this term is proportional to the topological Chern number, ${\rm Ch}=\pm 1/2$, if the Fermi level is in the energy gap. In this …
We analyze the conductance of the quantum point contact containing large localized spin J. The additional plateau is formed on a ballistic conductance staircase if only one propagating channel is rendered conducting. The conductance value at this plateau is shown to depend strongly on J and decrease from 3e^2/2h to e^2/h when J increases from 1/2 to infinity, which is in a good agreement with the experimental observations [D.J. Reilly, et al, Phys. Rev. B 63, 121311 (2001)].
As it is well known there may arise situations when an interaction between electrons is attractive. A weak attraction should manifest itself strongly in 1D systems, since it can create two-electron bound states. This paper interprets the 0.7 $(2e^2/h)$ conductance structure, observed recently in a one-dimensional constriction, as a manifestation of two-electron bound states formed in a barrier saddle-point. The value 0.75 $(2e^2/h)$ follows naturally from the 3:1 triplet-singlet statistical weight ratio for the two-electron bound states, if the triplet energy is lower. Furthermore, the value 0…
We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearence of delocalized states at the middle of the band under correlated disorder is strongly dependent upon the even-odd parity of the number of sites in the system. In samples with inversion symmetry the conductance equals $2e^{2}/h$ for odd samples, and is smaller for even parity. This result suggests that this even-odd behaviour found previously in the presence of electron correlations may be unrelated to charging effects …
The effect of the domain wall (DW) on the conductance in a ballistic ferromagnetic nanowire (FMNW) is revisited by exploiting a specific perturbation theory which is effective for a thin DW; the thinness is often the case in currently interested conductance measurements on FMNWs. Including the Hund coupling between carrier spins and local spins in a DW, the conductance of a FMNW in the presence of a very thin DW is calculated within the Landauer-Büttiker formalism. It is revealed that the conductance plateaus are modified significantly, and the switching of the quantization unit from $e^2/h$ t…
A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for the massless Dirac fermions in graphene than for the conventional electron gas. For the case of zigzag boundary conditions, one can expect a well-pronounced conductance quantization only for highly excited states. This difference is related to the relativistic Zitterbewegung effect in graphene.
The universal quantization of thermal conductance provides information on the topological order of a state beyond electrical conductance. Such measurements have become possible only recently, and have discovered, in particular, that the value of the observed thermal conductance of the 5/2 state is not consistent with either the Pfaffian or the anti-Pfaffian model, motivating several theoretical articles. The analysis of the experiments has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dop…
We report here direct measurements of the destruction of charge quantization in a single electron box, the first over the full range of box-to-lead conductance values from G ~ 0 to the conductance quantum G_q = 2e^2/h, using a sensitive single-electron transistor (SET) electrometer. The sensitivity of the electrometer is measured to be dq ~ 6 x 10^-5 e/sqrt{Hz} and its superiority to conductance measurements of charge fluctuations is clearly demonstrated. As the rate of quantum mechanical tunneling from the box to its lead is increased, the quantization of charge is destroyed, disappearing ent…
We report a theoretical investigation on the conductance and its fluctuation of three-dimensional topological insulators (3D TI) in $Bi_2Se_3$ and $Sb_2Te_3$ in the presence of disorders. Extensive numerical simulations are carried out. We find that in the diffusive regime the conductance is quantized with fractional value. Importantly, the conductance fluctuation is also quantized with a universal value. For 3D TI connected by two terminals, three independent conductances $G_{zz}$, $G_{xx}$ and $G_{zx}$ are identified where z is the normal direction of quintuple layer of 3D TI (see inset of F…
We present first-principles calculations for the transport properties of monoatomic Al wires sandwiched between Al(100) electrodes. The conductance of the monoatomic Al wires oscillates with the number of the constituent atoms as a function of the wire length, either with a period of four-atom for wires with the typical interatomic spacing or a period of six-atom with the interatomic spacing of the bulk fcc aluminum, indicating a dependence of the period of conductance oscillation on the interatomic distance of the monoatomic Al wires.
The conductance of a contact, having a radius smaller than the Fermi wave length, on the surface of a thin metal film is investigated theoretically. It is shown that quantization of the electron energy spectrum in the film leads to a step-like dependence of differential conductance G(V) as a function of applied bias eV. The distance between neighboring steps in eV equals the energy level spacing due to size quantization. We demonstrate that a study of G(V) for both signs of the voltage maps the spectrum of energy levels above and below Fermi surface in scanning tunneling experiments.
We present calculations of electronic quantum transport in graphene nanoribbons with adsorbed H, F, OH and O, based on a tight binding model derived from extended Huckel theory. The relaxed atomic geometries of the adsorbates and graphene are calculated using density functional theory. Our model includes the effects of the local rehybridization of the graphene from the sp2 to sp3 electronic structure that occurs when H, F, OH or O bonds covalently to the graphene. It captures the physics of the scattering resonances that are induced in the graphene near the Dirac point by the presence of these…
Conductance and shot noise of an open cavity with diffusive boundary scattering are calculated within the Boltzmann-Langevin approach. In particular, conductance contains a non-universal geometric contribution, originating from the presence of open contacts. Subsequently, universal expressions for multi-terminal conductance and noise valid for all chaotic cavities are obtained classically basing on the fact that the distribution function in the cavity depends only on energy and using the principle of minimal correlations.
We have investigated the conductance of long quantum wires formed in GaAs/AlGaAs heterostructures. Using realistic fluctuation potentials from donor layers we have simulated numerically the conductance of four different kinds of wires. While ideal wires show perfect quantization, potential fluctuations from random donors may give rise to strong conductance oscillations and degradation of the quantization plateaux. Statistically there is always the possibility of having large fluctuations in a sample that may effectively act as a microconstriction. We therefore introduce microconstrictions in t…
Over the last decade, interest in one-dimensional charge transport has progressed from the seminal discovery of Landauer quantization of conductance, as a function of carrier density, to finer-scale phenomena at the onset of quantization. This has come to be called the "0.7 anomaly", rather connoting a theoretical mystery of some profundity and universality, which remains open to date. Its somewhat imaginative appellation may tend to mislead, since the anomaly manifests itself over a range of conductance values: anywhere between 0.25 to 0.95 Landauer quanta. In this paper we offer a critique o…
We study quantization conditions of the Hall conductivity for a two dimensional system described by a double exchange Hamiltonian with and without an external magnetic field. This is obtained by an extension of the topological arguments familiar from the theory of the integer quantum Hall effect. The quantization conditions are related to spontaneous breaking of spin O(3), time-reversal, and spin chiral symmetries. Extension to systems with higher dimensions is briefly discussed.
We study the extra term of particle current in a 2D k-cubic Rashba spin-orbit coupling system and the integer quantization of the Hall conductance in this system. We provide a correct formula of charge current in this system and the careful consideration of extra currents provides a stronger theoretical basis for the theory of the quantum Hall effect which has not been considered before. The non-trivial extra contribution to the particle current density and local conductivity, which originates from the cubic dependence on the momentum operator in the Hamiltonian, will have no effect on the int…
