Tarun Kanti Ghosh

Conductance quantization and snake states in graphene magnetic waveguides

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.

Exact solutions for a Dirac electron in an exponentially decaying magnetic field

We consider a Dirac electron in the presence of an exponentially decaying magnetic field. We obtain exact energy eigenvalues with a zero-energy state and the corresponding eigenfunctions. We also calculate the probability density and current distributions.

Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene

Electronic waveguides in graphene formed by counterpropagating snake states in suitable inhomogeneous magnetic fields are shown to constitute a realization of a Tomonaga-Luttinger liquid. Due to the spatial separation of the right- and left-moving snake states, this non-Fermi liquid state induced by electron-electron interactions is essentially unaffected by disorder. We calculate the interaction parameters accounting for the absence of Galilei invariance in this system, and thereby demonstrate that non-Fermi liquid effects are significant and tunable in realistic geometries.

Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field

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.

Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields.

The present paper discusses magnetic confinement of the Dirac excitations in graphene in the presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to 1/r is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in the presence of the 1/r (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cutoff Coulomb potential to dictate the excitation spectra of graphene. The spectrum of the graphene excitations in the presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.

Zero-field spin splitting in a two-dimensional electron gas with the spin–orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Greens function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.

Wave packet dynamics and zitterbewegung of heavy holes in a quantizing magnetic field

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 ran...

Thermoelectric properties of an ultra-thin topological insulator

Thermoelectric coefficients of an ultra-thin topological insulator are presented here. The hybridization between top and bottom surface states of a topological insulator plays a significant role. In the absence of a magnetic field, the thermopower increases and thermal conductivity decreases with an increase in the hybridization energy. In the presence of a magnetic field perpendicular to the ultra-thin topological insulator, thermoelectric coefficients exhibit quantum oscillations with inverse magnetic field, whose frequency is strongly modified by the Zeeman energy and whose phase factor is governed by the product of the Landé g-factor and the hybridization energy. In addition to the numerical results, the low-temperature approximate analytical results for the thermoelectric coefficients are also provided. It is also observed that for a given magnetic field these transport coefficients oscillate with hybridization energy, at a frequency that depends on the Landé g-factor.

Magnetotransport properties of a magnetically modulated two-dimensional electron gas with the spin–orbit interaction

We study the electrical transport properties of a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction in the presence of a constant perpendicular magnetic field (B(0)( ̂z) which is weakly modulated by B1 = B1 cos(qx) ̂z, where B(1) ≪ B(0) and q = 2π/a with a the modulation period. We obtain the analytical expressions of the diffusive conductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and produce beating patterns in the amplitude of the Weiss and Shubnikov-de Haas oscillations. We show that the Rashba strength can be determined by analyzing the beating pattern in the Weiss oscillation. We find a simple equation which determines the Rashba spin-orbit interaction strength if the number of Weiss oscillations between any two successive nodes is known from the experiment. We compare our results with the electrically modulated 2DEG with the Rashba interaction. For completeness, we also study the beating pattern formation in the collisional and the Hall conductivities.

Thermoelectric probe for the Rashba spin–orbit interaction strength in a two dimensional electron gas

The thermoelectric coefficients of a two dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) are presented here. In the absence of a magnetic field, thermoelectric coefficients are enhanced due to the Rashba SOI. In the presence of a magnetic field, the thermoelectric coefficients of spin-up and spin-down electrons oscillate with different frequencies and produces beating patterns in the components of the total thermoelectric power and the total thermal conductivity. We also provide analytical expressions for the thermoelectric coefficients to explain the formation of the beating pattern. We obtain a simple relation which determines the strength of the Rashba SOI if the magnetic fields corresponding to any two successive beat nodes are known from the experiment.