arXiv subjects

Tutul Biswas

Publications and source records attributed to Tutul Biswas.

At least 19 recordsLinked to original sources

arXiv2026

Spin-valley physics in anomalous thermoelectric responses of the spin-orbit coupled $\alpha$-$T_3$ system with broken time-reversal symmetry

We extract spin-valley physics in the anomalous Hall and Nernst responses of the spin-orbit coupled $\alpha$-$T_3$ system in the presence of a time-reversal symmetry breaking staggered magnetization. We show that the interplay between the SOI, magnetization, and a model parameter $\alpha$ for the $\alpha$-$T_3$ lattice enables efficient tuning of spin- and valley-dependent Hall and Nernst signals. The spin-valley physics of the Hall and Nernst responses in the absence and presence of the magnetization are well explained. The peak-dip features of the Nernst responses are also understood from the corresponding Hall responses through the Mott relation. We find that the magnetization introduces highly tunable spin and valley polarizations, which are calculated from the spin- and valley-resolved Nernst conductivities. It is shown that both the spin and valley polarizations can attain nearly complete polarization over extended regions of the parameter space.

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arXiv2024

Orbital magnetization senses the topological phase transition in a spin-orbit coupled $α$-$T_3$ system

The $α$-$T_3$ system undergoes a topological phase transition(TPT) between two distinct quantum spin-Hall phases across $α=0.5$ when the spin-orbit interaction of Kane-Mele type is taken into consideration. As a hallmark of such a TPT, we find that the Berry curvature and the orbital magnetic moment change their respective signs across the TPT. We also find the trails of the TPT in another physical observable, namely, the orbital magnetization(OM) that can be, in principle, detected experimentally through the circular dichroism associated with optical absorption. The topological features of the OM are understood in terms of valley and spin physics. The valley-resolved OM(VROM) and the spin-resolved OM(SROM) exhibit interesting characteristics related to the valley and the spin Chern number when the chemical potential is tuned in the forbidden gap(s) of the energy spectrum. In particular, we find that the slope of the VROM versus the chemical potential in the forbidden gap changes its sign abruptly across the TPT, which is also consistent with the corresponding change in the valley Chern number. Moreover, the slope of the SROM demonstrates a sudden jump by one unit of $e/h$ (where $e$ is the electronic charge and $h$ is the Planck's constant) across the TPT, which is also in agreement with the corresponding change in the spin Chern number. It is further seen that a definite spin-valley optical selection rule governs the circular dichroism. The $k$-resolved degree of the optical polarization and the low-frequency differential optical absorbance manifest sign change across the TPT. We discuss experimentally viable signatures of different quantum spin-Hall phases in the optical absorbance.

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arXiv2023

Effect of magnetic field on the electronic properties of an $α$-$T_3$ ring

We consider a quantum ring of a certain radius R built from a sheet of the $α$-$T_3$ lattice and solve for its spectral properties in presence of an external magnetic field. The energy spectrum consists of a conduction band, a valence band and a zero energy flat band, all having a number of discrete levels therein which can be characterized by the angular momentum quantum number, m. The energy levels in the flat band are infinitely degenerate irrespective of the value of $α$. We reveal a two-fold degeneracy of the levels in the conduction band as well as in the valence band for $α$ = 0 and $α$ = 1. However, the m = 0 level for $α$ = 1 is an exception. Corresponding to an intermediate value of $α$, namely, 0 <$α$< 1, the energy levels become nondegenerate. The scenario remains unaltered when the ring is threaded by a magnetic flux which is an integer multiple of the flux quantum. We also calculate the persistent current which exhibits quantum oscillations as a function of the magnetic field with a period of one flux quantum at a particular Dirac point, which is often referred to as a valley. The total current oscillates with a periodicity of one flux quantum for any intermediate value of $α$. We have also explored the effect of a mass term (that breaks the sublattice symmetry) in the Hamiltonian. In the absence of a magnetic field, the energy levels in the flat band become dispersive, except for the m = 0 level in the case of $α$ = 1. In presence of the field, each of the flat band levels becomes dispersive for any $α\neq$ 0. Finally, we also see the effect of the mass term on the behaviour of the persistent current, which shows periodicity of one flux quantum, but the total current remains finite for all values of $α$.

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arXiv2022

Probing Topological signatures in an optically driven $α$-${T_3}$ Lattice

The $α$-$T_3$ lattice, an interpolation model between the honeycomb lattice of graphene($α=0$) and the dice lattice($α=1$), undergoes a topological phase transition across $α=1/\sqrt{2}$ when exposed to a circularly polarized off-resonant light. We study Berry phase mediated bulk magnetic and anomalous thermoelectric responses in order to capture the topological signatures of a driven $α$-$T_3$ lattice. It is revealed that both the Berry curvature and the orbital magnetic moment associated with the flat band change their respective signs across $α=1/\sqrt{2}$. The off-resonant light distorts the flat band near the Dirac points when $0<α<1$ which eventually introduces two distinct well separated forbidden gaps of equal width in the quasienergy spectrum. The orbital magnetization varies linearly with the chemical potential, in the forbidden gaps. The slopes of the linear regions in the orbital magnetization are closely related to the respective Chern numbers on either side of $α=1/\sqrt{2}$. We find that the slope for $α>1/\sqrt{2}$ is approximately two times of that for $α<1/\sqrt{2}$ which essentially indicates a topological phase transition across $α=1/\sqrt{2}$. However, the anomalous Nernst coefficient vanishes when the chemical potential is tuned in the forbidden gaps. The anomalous Hall conductivity in the forbidden gap(s) approaches different quantized values on either side of $α=1/\sqrt{2}$. All these topological signatures can be observed experimentally.

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arXiv2021

Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system

Much having learned about Floquet dynamics of pseudospin-$1/2$ system namely, graphene, we here address the stroboscopic properties of a periodically kicked {three-band fermionic system such as $α$-T$_3$ lattice. This particular model provides an interpolation between graphene and dice lattice via the continuous tuning of the parameter $α$ from 0 to 1.} In the case of dice lattice ($α=1$), we reveal that one can, in principle, engineer various types of low energy dispersions around some specific points in the Brillouin zone by tuning the kicking parameter in the Hamiltonian along a particular direction. Our analytical analysis shows that one can experience different quasienergy dispersions for example, Dirac type, semi-Dirac type, gapless line, absolute flat quasienergy bands, depending on the specific values of the kicking parameter. Moreover, we numerically study the dynamics of a wave packet in dice lattice. The quasienergy dispersion allows us to understand the instantaneous structure of wave packet at stroboscopic times. We find a situation where absolute flat quasienergy bands lead to a complete dynamical localization of the wave packet. {Aditionally, we calculate the quasienergy spectrum numerically for $α$-T$_3$ lattice. A periodic kick in a perpendicular (planar) direction breaks (preserves) the particle-hole symmetry for $0<α<1$. Furthermore, it is also revealed that the dynamical localization of wave packet does not occur at any intermediate $α\ne 0,\,1$.}

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arXiv2019

Thermoelectric and optical probes for a Fermi surface topology change in noncentrosymmetric metals

Noncentrosymmetric metals such as Li$_2$(Pd$_{1-x}$Pt$_x$)$_3$B 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 finite-frequency 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.

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arXiv2018

Hot electron cooling in Dirac semimetal Cd$_3$As$_2$ due to polar optical phonons

A theory of hot electron cooling power due to polar optical phonons $P_{\rm op}$ is developed in three-dimensional Dirac semimetal($3$DDS) Cd$_3$As$_2$ taking account of hot phonon effect. Hot phonon distribution $N_q$ and $P_{\rm op}$ are investigated as a function of electron temperature $T_e$, electron density $n_e$, and phonon relaxation time $τ_p$. It is found that $P_{\rm op}$ increases rapidly (slowly) with $T_e$ at lower (higher) temperature regime. Whereas, $P_{\rm op}$ is weakly deceasing with increasing $n_e$. The results are compared with those for three-dimensional electron gas ($3$DEG) in Cd$_3$As$_2$ semiconductor. Hot phonon effect is found to reduce $P_{\rm op}$ considerably and it is stronger in 3DDS Cd$_3$As$_2$ than in Cd$_3$As$_2$ semiconductor. $P_{\rm op}$ is also compared with the hot electron cooling power due to acoustic phonons $P_{\rm ac}$. We find that a crossover takes place from $P_{\rm ac}$ dominated cooling at low $T_e$ to $P_{\rm op}$ dominated cooling at higher $T_e$. The temperature at which this crossover occurs shifts towards higher values with the increase of $n_e$. Also, hot electron energy relaxation time $τ_e$ is discussed and estimated.

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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

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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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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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.

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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.

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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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arXiv2014

Wave packet dynamics in monolayer MoS$_2$ with and without a magnetic field

We study the dynamics of electrons in monolayer Molybdenum Disulfide (MoS$_2$), in the absence as well as presence of a transverse magnetic field. Considering the initial electronic wave function to be a Gaussian wave packet, we calculate the time dependent expectation value of position and velocity operators. In the absence of the magnetic field, the time dependent average values of position and velocity show damped oscillations dependent on the width of the wave packet. In the presence of a transverse magnetic field, the wave packet amplitude shows oscillatory behaviour over short timescales associated with classical cyclotron orbit, followed by the phenomena of spontaneous collapse and revival over larger timescales. We relate the timescales of these effects and our results can be useful for the interpretation of experiments with trapped ions.

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arXiv2013

Phonon-drag magnetothermopower in Rashba spin-split two-dimensional electron systems

We study phonon-drag contribution to the thermoelectric power in a quasi-two-dimensional electron system confined in GaAs/AlGaAs heterostructure in presence of both Rashba spin-orbit interaction and perpendicular magnetic field at very low temperature. It is observed that the peaks in the phonon-drag thermopower split into two when the Rashba spin-orbit coupling constant is strong. This splitting is a direct consequence of the Rashba spin-orbit interaction. We show the dependence of phonon-drag thermopower on both magnetic field and temperature numerically. A power-law dependence of phonon-drag magnetothermopower on the temperature in the Bloch-Gruneisen regime is found. We also extract the exponent of the temperature dependence of phonon-drag thermopower for different parameters like electron density, magnetic field, and the spin-orbit coupling constant.

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arXiv2013

Phonon-drag thermopower and hot-electron energy-loss rate in a Rashba spin-orbit coupled two-dimensional electron system

We theoretically study phonon-drag contribution to the thermoelectric power and hot-electron energy-loss rate in a Rashba spin-orbit coupled two-dimensional electron system (2DES) in the Bloch-Gruneisen (BG) regime. We assume that electrons interact with longitudinal acoustic phonons through deformation potential and with both longitudinal and transverse acoustic phonons through piezoelectric potential. Effect of the Rashba spin-orbit interaction on magnitude and temperature dependence of the phonon-drag thermoelectric power and hot-electron energy-loss rate are discussed. We numerically extract the exponent of temperature dependence of the phonon-drag thermopower and the energy-loss rate. We find the exponents are strongly suppressed due to the presence of the Rashba spin-orbit coupling.

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