Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems

Using time-dependent current-density functional theory, we derive analytically the dynamical exchange-correlation correction to the dc conductance of nanoscale junctions. The correction pertains to the conductance calculated in the zero-frequency limit of time-dependent density functional theory within the adiabatic local-density approximation. In particular, we show that in linear response, the correction depends nonlinearly on the gradient of the electron density; thus, it is more pronounced for molecular junctions than for quantum point contacts. We provide specific numerical examples to illustrate these findings.     

What is measured in the scanning gate microscopy of a quantum point contact?

The conductance change due to a local perturbation in a phase-coherent nanostructure is calculated. The general expressions to first and second order in the perturbation are applied to the scanning gate microscopy of a two-dimensional electron gas containing a quantum point contact. The first-order correction depends on two scattering states with electrons incoming from opposite leads and is suppressed on a conductance plateau; it is significant in the step regions. On the plateaus, the dominant second-order term likewise depends on scattering states incoming from both sides. It is always negative, exhibits fringes, and has a spatial decay consistent with experiments.     

Correlated electron current and temperature dependence of the conductance of a quantum point contact

We investigate finite temperature corrections to the Landauer formula due to electron–electron interaction within the quantum point contact. When the Fermi level is close to the barrier height, the conducting wavefunctions become peaked on the barrier, enhancing the electron–electron interaction. At the same time, away from the contact the interaction is strongly suppressed by screening. To describe electron transport we formulate and solve a kinetic equation for the density matrix of electrons. The correction to the conductance G is negative and strongly enhanced in the region 0.5 × 2e²/h ≤ G ≤ 1.0 × 2e²/h. Our results for conductance agree with the so-called “0.7 structure” observed in experiments.     

Characteristics of quantum conductance in a quasi-one-dimension quantum wire containing cavity structures

Quantum-mechanical calculations of the conductance for model devices, consisting of dual semi-infinite quantum wires connected in series by a cavity, are carried out with use of the coupled-mode transfer method and mode matching technique. The effects of the mode-mode coupling and geometry-induced scattering on the quantum conductance are in detail studied by varying the geometric structure of the cavity. There are no traces of quantization conductance. The pattern of the conductance displays many peaks and dips. The threshold energy of the first onset of the conductance is lower than the normal value for opening the propagation channel of the lowest subband in the quantum wire. The overall character of the conductance exhibits heavy fluctuations around the classical conductance for the relevant point contact. The fluctuation amplitude is of order of 2e ²/h, similar to universal conductance fluctuations. The oscillatory structure becomes rich and dense as the scale of the cavity increases. There is a global trend for the conductance to rise as the cavity is compressed. The structures of resonant peaks and antiresonance dips in the conductance are originated from the mode coupling among the subbands in the cavity and quantum wires. The heavy conductance fluctuation may be caused by the quantum interference of the electron waves due to the multiple scattering (reflections) of electrons by the cavity boundaries.     

What lurks below the last plateau: experimental studies of the 0.7 × 2e(2)/h conductance anomaly in one-dimensional systems

The integer quantised conductance of one-dimensional electron systems is a well-understood effect of quantum confinement. A number of fractionally quantised plateaus are also commonly observed. They are attributed to many-body effects, but their precise origin is still a matter of debate, having attracted considerable interest over the past 15 years. This review reports on experimental studies of fractionally quantised plateaus in semiconductor quantum point contacts and quantum wires, focusing on the 0.7 × 2e(2)/h conductance anomaly, its analogues at higher conductances and the zero-bias peak observed in the dc source-drain bias for conductances less than 2e(2)/h.     

Experimental test of the dynamical coulomb blockade theory for short coherent conductors

We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical Coulomb blockade corrections, probed up to the second conductance plateau of the quantum point contact, are found to be accurately normalized by the same Fano factor as quantum shot noise, in excellent agreement with the theoretical predictions.     

Nonlinear conductance reveals positions of carbon atoms in metallic single-wall carbon nanotubes

Nonlinear quantum conductance in finite metallic single-wall carbon nanotubes due to presence of a single defect has been studied theoretically using π-orbital tight-binding model. The correction to the conductance induced by defects is sensitively dependent on wavefunction amplitudes of contributing electronic states. It has been shown that by calculating this correction to the first order, we can delineate the position of carbon atoms on tubular surface. It can also be used to specify the SWCNT at hand and its level spacing.     

Equilibration of Luttinger liquid and conductance of quantum wires

Luttinger liquid theory describes one-dimensional electron systems in terms of noninteracting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is controlled by the relaxation rate.     

How to find conductance tensors of quantum multiwire junctions through static calculations: application to an interacting Y junction

Conductance is related to dynamical correlation functions which can be calculated with time-dependent methods. Using boundary conformal field theory, we relate the conductance tensors of quantum junctions of multiple wires to static correlation functions in a finite system. We then propose a general method for determining the conductance through time-independent calculations alone. Applying the method to a Y junction of interacting quantum wires, we numerically verify the theoretical prediction for the conductance of the chiral fixed point of the Y junction and then calculate the thus far unknown conductance of its M fixed point with the time-independent density matrix renormalization group method.     

Spontaneous spin polarization in quantum point contacts

We use spatial spin separation by a magnetic focusing technique to probe the polarization of quantum point contacts. The point contacts are fabricated from p-type GaAs/AlGaAs heterostructures. A finite polarization is measured in the low-density regime, when the conductance of a point contact is tuned to < 2e2/h. Polarization is stronger in samples with a well-defined "0.7 structure."     

Kondo model for the "0.7 anomaly" in transport through a quantum point contact

Experiments on quantum point contacts have highlighted an anomalous conductance plateau around 0.7(2e(2)/h), with features suggestive of the Kondo effect. Here, an Anderson model for transport through a point contact analyzed in the Kondo limit. Hybridization to the band increases abruptly with energy but decreases with valence, so that the background conductance and the Kondo temperature T(K) are dominated by different valence transitions. This accounts for the high residual conductance above T(K). The model explains the observed gate-voltage, temperature, magnetic field, and bias-voltage dependences. A spin-polarized current is predicted even for low magnetic fields.     

Contact conductance between graphene and quantum wires

The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.     

Low-temperature fate of the 0.7 structure in a point contact: a Kondo-like correlated state in an open system

Besides the usual conductance plateaus at multiples of 2e(2)/h, quantum point contacts typically show an extra plateau at approximately 0.7(2e(2)/h), believed to arise from electron-electron interactions that prohibit the two spin channels from being simultaneously occupied. We present evidence that the disappearance of the 0.7 structure at very low temperature signals the formation of a Kondo-like correlated spin state. Evidence includes a zero-bias conductance peak that splits in a parallel field, scaling of conductance to a modified Kondo form, and consistency between peak width and the Kondo temperature.     

STM中量子点接触的电导计算

采用模式匹配和散射矩阵方法，对扫描隧道显微镜(STM)中量子点接触过程中的电导进行了计算.结果表明由量子点接触形成的纳米结构的电导呈现量子化特征，这种量子化现象随所形成的纳米结构的横向尺寸和锥角的减小而增强.而且在半导体材料中比金属中更易观察到电导量子化现象. 关键词： STM 量子点接触 量子化电导     

Interplay between weak localization and quantized conductance

The interplay between weak localization and conductance quantization through a narrow channel is considered. The “electrodes” are essentially two half planes with slight disorder. In this system weak localization results from a coherent echo in the electrodes towards the channel. Therefore one has an interesting mixture of dimensions, the channel being quasi-one dimensional and the electrodes being two dimensional. As a consequence the quantum interference correction to the conductance is non-universal.     

Junction of three quantum wires: restoring time-reversal symmetry by interaction

We investigate the transport of correlated fermions through a junction of three one-dimensional quantum wires pierced by a magnetic flux. We determine the flow of the conductance as a function of a low-energy cutoff in the entire parameter space. For attractive interactions and generic flux the fixed point with maximal asymmetry of the conductance is the stable one, as conjectured recently. For repulsive interactions and arbitrary flux we find a line of stable fixed points with vanishing conductance as well as stable fixed points with symmetric conductance (4/9)(e(2)/h).     

Scanning a metallic tip close to a quantum point contact

Low-temperature transport experiments on a quantum point contact under the influence of a scanning gate are reported. The scanning gate is the metallic tip of a scanning force microscope operating at a temperature of 300 mK. In particular, the influence of the scanning tip on conductance resonances observed in the gate-characteristics of the point contact is studied. The strongest conductance resonances appear to be related to the local potential within the channel of the point contact. As a consequence, the point contact with its conductance resonances can be used as a sensor for the local tip-induced potential.     

Resonantly enhanced nonlinear conductance in long quantum point contacts near pinch-off

We report on a remarkable resonance in the differential conductance of long quantum point contacts (QPCs) that is observed as a precursor to regular quantized transport. This effect is increasingly pronounced in longer QPCs, in which the differential conductance may resonantly exceed 2e2/h. From a study of the experimental characteristics of this feature, we suggest that it may be associated with the formation of a well-resolved energy gap that opens dynamically as a result of enhanced many-body interactions in long QPCs.     

Double point contact in quantum Hall line junctions

We show that multiple point contacts on a barrier separating two laterally coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the tunneling conductance. These quantum coherence effects provide new evidence for the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a two point contact, we identify coherent and incoherent regimes determined by the relative magnitude of their separation and the temperature. We analyze both regimes in the strong and weak tunneling amplitude limits as well as their temperature dependence. We find that the tunneling conductance should exhibit AB oscillations in the coherent regime, both at strong and weak tunneling amplitudes with the same period but with different functional form.