arXiv subjects

Tarun Kanti Ghosh

Publications and source records attributed to Tarun Kanti Ghosh.

At least 37 records · Page 2Linked to original sources

arXiv2019

RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems

We consider Mn-doped bulk zinc-blende semiconductors described by the 4 $ \times$ 4 Luttinger Hamiltonian. In these semiconductors, Mn atom acts as an acceptor providing the system a mobile hole, and also acts like a magnetic impurity of spin $S=5/2$. We obtain exact analytical expressions of the hole mediated Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction between two Mn${}^{2+}$ ions. The RKKY interaction of the Luttinger system consists of collinear Heisenberg-like and Ising-like interactions. The characteristic beating patterns appear in the range functions of the RKKY interaction owing to the presence of multiple Fermi wave-vectors of the underlying $j=3/2$ states. As an application of the analytical form of the range function, from the finite temperature evaluation of the correlation functions, we calculate the contribution of RKKY interaction to the Curie-Weiss temperatures of a particular dilute magnetic semiconductor ZnMnTe where $4\times4$ Luttinger Hamiltonian is valid.

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arXiv2019

Floquet topological phase transition in $α$-$\mathcal{T}_3$ lattice

We investigate topological characteristics of the photon-dressed band structure of $α$-$\mathcal{T}_3$ lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at $ {\bf K}$ and ${\bf K}^{\prime}$ (except at $α=0$ and 1), which reveals the absence of inversion symmetry in the system. At $α=1/\sqrt{2}$, the gap between flat and valence bands closes at ${\bf K}$, while that between conduction and flat bands closes at ${\bf K}^{\prime}$, thereby restoring a semimetalic phase. At the gap closing point ($α=1/\sqrt{2}$) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around ${\bf K}$ and ${\bf K}^{\prime}$ points. Under the influence of the circularly polarized radiation, the $α$-$\mathcal{T}_3$ lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by non-zero Chern number. The system undergoes a topological phase transition from $\mathcal{C} = 1 (-1)$ to $\mathcal{C}=2 (-2)$ at $α=1/\sqrt{2}$, where $\mathcal{C}$ is the Chern number of the valence (conduction) band. This sets an example of a multiband system having larger Chern number. These results are supported by the appearance of chiral edge states in irradiated $α$-$\mathcal{T}_3$ nanoribbon.

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arXiv2018

Photoinduced valley and electron-hole symmetry breaking in $ α$-$T_3$ lattice: The role of a variable Berry phase

We consider $α$-$T_3$ lattice illuminated by intense circularly polarized radiation in terahertz regime. We present quasienergy band structure, time-averaged energy spectrum and time-averaged density of states of $α$-$T_3$ lattice by solving the Floquet Hamiltonian numerically. We obtain exact analytical expressions of the quasienergies at the Dirac points for all values of $α$ and field strength. We find that the quasienergy band gaps at the Dirac point decrease with increase of $α$. Approximate forms of quasienergy and band gaps at single and multi-photon resonant points are derived using rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasi energy flat band remains unaltered in presence of radiation for dice lattice ($α=1$). However, it acquires a dispersion in and around the Dirac and even-photon resonant points when $0<α<1$. The valley degeneracy and electron-hole symmetry in the quasienergy spectrum are broken for $0<α<1$. Unlike graphene, the mean energy follows closely the linear dispersion of the Dirac cones till near the single-photon resonant point in dice lattice. There are additional peaks in the time-averaged density of states at the Dirac point for $0 < α\leq 1$.

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arXiv2018

Dynamics of a quasiparticle in the $α$-T$_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}

We consider the $α$-$T_3$ 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 $α$. We study the dynamics of a wave packet representing a quasiparticle in the $α$-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 $α$ i.e. for $0<α<1$ 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 $α=0$ and $α=1$. It is also unveiled that the frequency of ZB corresponding to $α=1$ gets exactly half of that corresponding to the $α=0$ 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 $α$. 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 $α$.

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arXiv2017

Electrical and thermoelectric transport properties of two-dimensional fermionic systems with $k$-cubic spin-orbit coupling

We investigate the effect of $k$-cubic spin-orbit interaction on electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions $θ^\prime = (2n+1)π/3 $ with $ n=1,2,3$. We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of $k$-cubic Rashba spin-orbit coupling (RSOC) at low temperature. In the presence of quantizing magnetic field, the signature of the RSOC is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant.

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arXiv2017

Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene

We present a detail theoretical study of the Drude weight and optical conductivity of 8-$Pmmn$ borophene having tilted anisotropic Dirac cones. We provide exact analytical expressions of $xx$ and $yy$ components of the Drude weight as well as maximum optical conductivity. We also obtain exact analytical expressions of the minimum energy ($ε_1$) required to trigger the optical transitions and energy ($ε_2$) needed to attain maximum optical conductivity. We find that the Drude weight and optical conductivity are highly anisotropic as a consequence of the anisotropic Dirac cone. The optical conductivities have a nonmonotonic behavior with photon energy in the regime between $ε_1$ and $ε_2$, as a result of the tilted parameter $v_t$. The tilted parameter can be extracted by knowing $ε_1$ and $ε_2$ from optical measurements. The maximum values of the components of the optical conductivity do not depend on the carrier density and the tilted parameter. The product of the maximum values of the anisotropic conductivities has the universal value $(e^2/4\hbar)^2$. The tilted anisotropic Dirac cones in 8-$Pmmn$ borophene can be realized by the optical conductivity measurement.

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arXiv2017

Phonon-drag magnetoquantum oscillations in graphene

A theory of low-temperature phonon-drag magnetothermopower $S_{xx}^g$ is presented in graphene in a quantizing magnetic field. $S_{xx}^g$ is found to exhibit quantum oscillations as a function of magnetic field $B$ and electron concentration $n_e$. Amplitude of the oscillations is found to increase (decrease) with increasing $B$ ($n_e$). The behavior of $S_{xx}^g$ is also investigated as a function of temperature. A large value of $S_{xx}^g $($\sim$ few hundreds of $μ$V/K) is predicted. Numerical values of $S_{xx}^g $ are compared with the measured magnetothermopower $S_{xx}$ and the diffusion component $S_{xx}^d$ from the modified Girvin-Jonson theory.

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arXiv2016

Magnetotransport properties of the $α$-T$_3$ model

Using the well-known Kubo formula, we evaluate magnetotransport quantities like the collisional and Hall conductivities of the $α$-T$_3$ model. The collisional conductivity exhibits a series of peaks at strong magnetic field. Each of the conductivity peaks for $α=0$ (graphene) splits into two in 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 the conductivity peak comes closer to the left split part of the next conductivity peak. At $α=1$, 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 $σ_{yx}=2(2n+1)e^2/h$ to $σ_{yx}=4ne^2/h$ with $n=0,1,2,...$ as we tune $α$ from $0$ to $1$. For intermediate $α$, we obtain the Hall plateaus at values $0,2,4,6,8,...$ in units of $e^2/h$.

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arXiv2016

Electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors

We study electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors described by the Luttinger Hamiltonian. We provide exact analytical expressions of the Drude conductivity, inverse relaxation time for various impurity potentials, Drude weight and optical conductivity in terms of the Luttinger parameters $γ_1 $ and $γ_2$. The back scattering is completely suppressed as a result of the helicity conservation of the heavy and light hole states. We find that the inverse relaxation time of heavy holes is much less than that of the light holes for Coulomb-type and Gaussian-type impurity potentials and vice-versa for short-range impurity potentials. The Drude conductivity increases non-linearly with the increase of the hole density. The exponent of the density dependence of the conductivity is obtained in Thomas-Fermi limit. The Drude weight varies linearly with the density even in presence of the spin-orbit coupling. The finite-frequency optical conductivity goes as $\sqrtω$ and its amplitude strongly depends on the Luttinger parameters. The Luttinger parameters can be extracted from the optical conductivity measurement.

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arXiv2016

Optical conductivity of a 2DEG with anisotropic Rashba interaction at the interface of LaAlO$_3$/SrTiO$_3$

We study optical conductivity of a two-dimensional electron gas with anisotropic $k$-cubic Rashba spin-orbit interaction formed at the LaAlO$_3$/SrTiO$_3$ interface. The anisotropic spin splitting energy gives rise to different features of the optical conductivity in comparison to the isotropic $k$-cubic Rashba spin-orbit interaction. For large carrier density and strong spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. The charge and optical conductivities remain isotropic despite anisotropic nature of the Fermi contours. An infinitesimally small photon energy would suffice to initiate inter-band optical transitions due to degeneracy along certain directions in momentum space. The optical conductivity shows a single peak at a given photon energy depending on the system parameters and then falls off to zero at higher photon energy. These features are lacking for systems with isotropic $k$-cubic Rashba spin-orbit coupling. These striking features can be used to extract the information about nature of the spin-orbit interaction experimentally and illuminate some light on the orbital origin of the two-dimensional electron gas.

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arXiv2016

Drude weight and optical conductivity of a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions

We present detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas(2DHG) with $k$-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of $k$-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with $k$-linear spin-orbit couplings. For large hole density and strong $k$-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with $k$-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of $k$-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.

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arXiv2015

An Effective Hamiltonian Approach to Quantum Random Walk

In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative \cite{Chandrasekhar:2013SREP08229}. We showed that in case of two-step walk, effectively the time evolution operator can have multiplicative form. In case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the Graphene Hamiltonian the walk has been studied on a Graphene lattice and we conclude the preference of additive approach over the multiplicative one.

quant-ph↗

arXiv2015

Zitterbewegung of a heavy hole in presence of spin-orbit interactions

We study the $zitterbewegung$ of a heavy hole in presence of both cubic Rashba and cubic Dresselhaus spin-orbit interactions. On contrary to the electronic case, $zitterbewegung$ does not vanish for equal strength of Rashba and Dresselhaus spin-orbit interaction. This non-vanishing of $zitterbewegung$ is associated with the Berry phase. Due to the presence of the spin-orbit coupling the spin associated with the heavy hole precesses about an effective magnetic field. This spin precession produces a transverse spin-orbit force which also generates an electric voltage associated with $zitterbewegung$. We have estimated the magnitude of this voltage for a possible experimental detection of $zitterbewegung$.

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arXiv2015

Understanding spin Hall effect in two-dimensional fermionic systems with generic spin-orbit interaction

We delve into spin Hall effect in generic spin-orbit coupled two-dimensional fermionic systems. We derive analytically the spin-orbit force responsible for the spin Hall effect, and find that it has `Lorentz force'-like form. We also derive the pseudo magnetic field responsible for this force. We establish the relation between the spin Hall conductivity, flux quanta and this pseudo magnetic field, similar to the one between charge Hall conductivity, flux quanta and the external field. We also present an exact closed-form expression of the spin Hall conductivity in a generic spin-orbit coupled system. Depending on the dimensionality of the spin-orbit interactions, the spin Hall conductivity depends on different combinations of Rashba parameter and fermion density.

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arXiv2014

Electron-phonon interaction in a spin-orbit coupled quantum wire with a gap

Interaction between electron and acoustic phonon in an in-plane magnetic field induced gapped quantum wire with Rashba spin-orbit interaction is studied. We calculate acoustic phonon limited resistivity ($ρ$) and phonon-drag thermopower ($S_g$) due to two well known mechanisms of electron-phonon interaction namely, deformation potential (DP) and piezoelectric (PE) scattering. In the so called Bloch-Gruneisen temperature limit both $ρ$ and $S_g$ depend on temperature ($T$) in a power law fashion i.e. $ρ$ or $S_g\sim T^{ν_T}$. For resistivity, $ν_T$ takes the value $5$ and $3$ due to DP and PE scattering respectively. On the other hand, $ν_T$ is $4$ and $2$ due to DP and PE scattering, respectively for phonon-drag thermopower. Additionally, we find numerically that $ν_T$ depends on Rashba parameter ($α$) and electron density ($n$). The dependence of $ν_T$ on $α$ becomes more prominent at lower density. We also study the variations of $ρ$ and $S_g$ with carrier density in the Bloch-Gruneisen regime. Through a numerical analysis a similar power law dependence $ρ$ or $S_g\sim n^{-ν_n}$ is established in which the effective exponent $ν_n$ undergoes a smooth transition from a low density behavior to a high density behavior. At a higher density regime, $ν_n$ matches excellently with the value obtained from theoretical arguments. Approximate analytical expressions for both resistivity and phonon-drag thermopower in the Bloch-Gruneisen regime are given.

cond-mat.mes-hall↗

arXiv2014

Wave packet dynamics in various two-dimensional systems: a unified description

In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long term dynamics displays the universal phenomena of spontaneous collapse and quantum revival. We estimate the timescales associated with these phenomena based on very general arguments for various materials, whose carrier dynamics is described either by the Schrödinger equation or by the Dirac equation.

cond-mat.mes-hall↗

arXiv2014

Magnetotransport properties of two-dimensional fermions with $k$-cubic Rashba spin-orbit interaction

The spin-orbit interaction in heavy hole gas formed at $p$-doped semiconductor heterojunctions and electron gas at {\mbox SrTiO}${}_3$ surfaces is cubic in momentum. Here we report magnetotransport properties of k-cubic Rashba spin-orbit coupled two-dimensional fermionic systems. We study longitudinal (Shubnikov-de Haas (SdH) oscillations) and Hall component of the resistivity tensor analytically as well as numerically. The longitudinal resistivity shows beating pattern due to different SdH oscillation frequencies $ f_{\pm} $ for spin-up and spin-down fermions. We propose empirical forms of $ f_{\pm} $ 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 form. 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.

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arXiv2014

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 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.

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