Using the well-known Kubo formula, we evaluate magnetotransport quantities, such as the collisional and Hall conductivities of the α-T model. The collisional conductivity exhibits a series of peaks at a strong magnetic field. Each of the conductivity peaks for [Formula: see text] (graphene) splits into two in the presence of a finite α. This splitting occurs due to a finite phase difference between the contributions coming from the two valleys. The density of states is also calculated to explore the origin of the splitting of conductivity peaks. As α approaches 1, the right split part of a conductivity peak comes closer to the left split part of the next conductivity peak. At [Formula: see text], they merge with each other to produce a new series of the conductivity peaks. On the other hand, the Hall conductivity undergoes a smooth transition from [Formula: see text] to [Formula: see text] with n  =  0,1,2,... as we tune α from 0-1. For intermediate α, we obtain the Hall plateaus at values 0,2,4,6,8,... in units of e/h.

We consider the $\alpha$-$T_3$ model which provides a smooth crossover between the honeycomb lattice with pseudospin $1/2$ and the dice lattice with pseudospin $1$ through the variation of a parameter $\alpha$. We study the dynamics of a wave packet representing a quasiparticle in the $\alpha$-T$_3$ model with zero and finite transverse magnetic field. For zero field, it is shown that the wave packet undergoes a transient $zitterbewegung$ (ZB). Various features of ZB depending on the initial pseudospin polarization of the wave packet have been revealed. For an intermediate value of the parameter $\alpha$ i.e. for $0<\alpha<1$ the resulting ZB consists of two distinct frequencies when the wave packet was located initially in $rim$ site. However, the wave packet exhibits single frequency ZB for $\alpha=0$ and $\alpha=1$. It is also unveiled that the frequency of ZB corresponding to $\alpha=1$ gets exactly half of that corresponding to the $\alpha=0$ case. On the other hand, when the initial wave packet was in $hub$ site, the ZB consists of only one frequency for all values of $\alpha$. Using stationary phase approximation we find analytical expression of velocity average which can be used to extract the associated timescale over which the transient nature of ZB persists. On the contrary the wave packet undergoes permanent ZB in presence of a transverse magnetic field. Due to the presence of large number of Landau energy levels the oscillations in ZB appear to be much more complicated. The oscillation pattern depends significantly on the initial pseudospin polarization of the wave packet. Furthermore, it is revealed that the number of the frequency components involved in ZB depends on the parameter $\alpha$.

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.

A theory of hot electron cooling power due to polar optical phonons P is developed in 3D Dirac semimetal (3DDS) CdAs taking account of hot phonon effect. Hot phonon distribution N and P are investigated as a function of electron temperature T , electron density n, and phonon relaxation time [Formula: see text]. It is found that P increases rapidly (slowly) with T at lower (higher) temperature regime. Whereas, P is weakly decreasing with increasing n. The results are compared with those for three-dimensional electron gas (3DEG) in CdAs semiconductor. Hot phonon effect is found to reduce P considerably and it is stronger in 3DDS CdAs than in CdAs semiconductor. P is also compared with the hot electron cooling power due to acoustic phonons P. We find that a crossover takes place from P dominated cooling at low T to P dominated cooling at higher T. The temperature at which this crossover occurs shifts towards higher values with the increase of n . Also, hot electron energy relaxation time [Formula: see text] is discussed. It is suggested that [Formula: see text] can be tuned to achieve faster or slower energy loss for suitable applications of CdAs.

A theory of low-temperature phonon-drag magnetothermopower S g xx is presented in graphene in a quantizing magnetic field. S g xx is found to exhibit quantum oscillations as a function of magnetic field B and electron concentration ne. Amplitude of the oscillations is found to increase (decrease) with increasing B (ne). The behavior of S

The spin-orbit interaction in heavy hole gas formed at p-doped semiconductor heterojunctions and electron gas at SrTiO3 surfaces is cubic in momentum. Here we report magnetotransport properties of k-cubic Rashba spin-orbit coupled two-dimensional fermionic systems. We study longitudinal and Hall component of the resistivity tensor analytically as well as numerically. The longitudinal resistivity shows beating pattern due to different Shubnikov-de Haas (SdH) oscillation frequencies f± for spin-up and spin-down fermions. We propose empirical forms of f± as exact expressions are not available, which are being used to find location of the beating nodes. The beating nodes and the number of oscillations between any two successive nodes obtained from exact numerical results are in excellent agreement with those calculated from the proposed empirical formula. In the Hall resistivity, an additional Hall plateau appears in between two conventional ones as spin-orbit coupling constant increases. The width of this additional plateau increases with spin-orbit coupling constant.

In this work we study wave packet dynamics and zitterbewegung, an oscillatory quantum motion, of heavy holes in III-V semiconductor quantum wells in presence of a quantizing magnetic field. It is revealed that a Gaussian wave-packet describing a heavy hole diffuses asymmetrically along the circular orbit while performing cyclotron motion. The wave packet splits into two peaks with unequal amplitudes after a certain time depending on spin-orbit coupling constant. This unequal splitting of the wave packet is attributed to the cubic Rashba interaction for heavy holes. The difference in the peak amplitudes disappears with time. At a certain time the two peaks diffuse almost along the entire cyclotron orbit. Then tail and head of the diffused wave packet interfere and as a result a completely randomized pattern of the wave packet is observed. The diffusion rate of the wave packet increases with increase of the spin-orbit interaction strength. Also strong spin-orbit coupling expedite the splitting and the randomization of the wave packet. We also study the zitterbewegung in various physical observables such as position, charge current and spin angular momentum of the heavy hole. The zitterbewegung oscillations are very much sensitive to the initial wave vector of the Gaussian wave packet and the strength of the Rashba spin-orbit coupling.

Noncentrosymmetric metals such as Li2(Pd1−xPtx)3B have different Fermi surface topology below and above the band touching point where spin-degeneracy is not lifted by the spin-orbit coupling. We investigate thermoelectric and optical response as probes for this Fermi surface topology change. We show that the chemical potential displays a dimensional crossover from a three-dimensional to one-dimensional characteristics as the descending Fermi energy crosses the band touching point. This dimensional crossover is due to the existence of different Fermi surface topology above and below the band touching point. We obtain an exact expression of relaxation time due to short-range scatterer by solving Boltzmann transport equations self-consistently. The thermoelctric power and figure of merit are significantly enhanced as the Fermi energy goes below the band touching point owing to the underlying one-dimensional-like nature of noncentrosymmteric bulk metals. The value of thermoelectric figure of merit goes beyond two as the Fermi energy approaches to the van Hove singularity for lower spin-orbit coupling. Similarly, the studies of the zero-frequency and finitefrequency optical conductivities in the zero-momentum limit reflect the nature of topological change of the Fermi surface. The Hall coefficient and optical absorption width exhibit distinct signatures in response to the changes in Fermi surface topology.PACS numbers: