We study the Nernst effect and the spin Nernst effect, that a longitudinal thermal gradient induces a transverse voltage and a spin current. A mesoscopic four-terminal cross-bar device having the Rashba spin-orbit interaction (SOI) under a perpendicular magnetic field is considered. For zero SOI, the Nernst coefficient peaks when the Fermi level crosses the Landau Levels. In the presence of the SOI, the Nernst peaks split, and the spin Nernst effect appears and exhibits a series of oscillatory structures. The larger SOI is or the weaker magnetic field is, the more pronounced the spin Nernst effect is. The results also show that the Nernst and spin Nernst coefficients are sensitive to the detailed characteristics of the sample and the contacts. In addition, the Nernst effect is found to survive in strong disorder than the spin Nernst effect does.Comment: 5 pages, 5 figure

We report the investigation of electron transport through a four-terminal graphene-superconductor hybrid system. Because of the quantum interference of the reflected holes from two graphene-superconductor interfaces with a phase difference theta, it is found that the specular Andreev reflection vanishes at theta=0 while the Andreev retroreflection disappears at theta=pi. This means that retroreflection and specular reflection can be easily controlled and separated in this device. In addition, because of the diffraction effect in the narrow graphene nanoribbon, the reflected hole can exit from both graphene terminals. As the width of nanoribbon increases, the diffraction effect gradually disappears and the reflected hole eventually exits from a particular graphene terminal depending on the type of Andreev reflection.

The influence of dephasing on the quantum spin Hall effect (QSHE) is studied. In the absence of dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Thus, these quantum plateaus only survive in mesoscopic samples. Moreover, the longitudinal resistance increases linearly with the sample length but is insensitive to the sample width. These characters are in excellent agreement with the recent experimental results [science 318, 766 (2007)]. In addition, we define a new spin Hall resistance that also exhibits quantum plateaus. In particular, these plateaus are robust against any type of dephasing and therefore, survive in macroscopic samples and better reflect the topological nature of QSHE. Recently, the quantum spin Hall effect (QSHE), existed in a new quantum state of matter with a non-trivial topological property, has generated great interest.[1] QSHE occurs in the topological insulator with a bulk energy gap and two helical edge states crossing inside the gap. This energy-band structure guarantees that the carriers only flow along the boundary and that carriers with opposite spin-polarizations move in opposite directions on a given edge. The other key ingredient for QSHE is the presence of the spin-orbit interaction (SOI). When electrons move under an electric field, the SOI drives the electrons with opposite spins to deflect to the opposite transverse boundaries, and the special energy-band structure leads to the quantum spin Hall conductance.[1] The existence of QSHE was first proposed in a graphene film in which the SOI opens a bandgap around the Dirac-points and establishes the edge states. [2,3]. Soon afterwards, QSHE was predicted to exist in some other two-or threedimensional systems. [4,5,6,7] In particular, Bernevig et al. recently found that CdTe/HgTe/CdTe quantum well has an "inverted" type energy-band structure with proper well thicknesses [7] where QSHE naturally exists. Soon after this work, QSHE was successfully realized in an experiment [8,9] in which a quantized longitudinal resistance plateau was observed when the sample's electron density was varied in the absence of a magnetic field. [8] However, in the experiment of Ref.[8], the quantized longitudinal resistance plateaus could only emerge in mesoscopic samples. This character is very different from the regular quantum Hall effect (QHE). In QHE, the Hall resistance plateaus exist in macroscopic samples, robust against the impurity scattering as well as the inelastic (dephasing) scattering. This leads some to speculate that the inelastic scattering which induces phase relaxation, destroys the quantized plateaus in QSHE [1,7], however, there has been no theoretical or experimental investigation thus far.In this Letter, we study how QSHE is affected by de- In a realistic sample, there are in general a number of possible dephasing processes, but these can be classified into two categories. In the fir...

Figure 3. The performance of model I in the presence of disorder. The results for Anderson (long range) disorder is exhibited in a1-f1 (a2-f2). The other parameters are d=20 and M=100. AbstractIn addition to electron charge and spin, novel materials host another degree of freedom, the valley. For a junction composed of valley filter sandwiched by two normal terminals, we focus on the valley efficiency under disorder with two valley filter models based on monolayer and bilayer graphene. Applying the transfer matrix method, valley resolved transmission coefficients are obtained. We find that: (i) under weak disorder, when the line defect length is over about 15 nm, it functions as a perfect channel (quantized conductance) and valley filter (totally polarized); (ii) in the diffusive regime, combination effects of backscattering and bulk states assisted intervalley transmission enhance the conductance and suppress the valley polarization; (iii) for very long line defect, though the conductance is small, polarization is indifferent to length. Under perpendicular magnetics field, the characters of charge and valley transport are only slightly affected. Finally we discuss the efficiency of transport valley polarized current in a hybrid system.