Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of... more Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of electrons as information carriers, allowing generation of spin currents and detecting them via the electric voltage. In the standard arrangement, applied electric field induces transverse spin current with perpendicular spin polarization. Although conventional spin Hall effects are commonly used in spin-orbit torques or spin Hall magnetoresistance experiments, the possibilities to configure electronic devices according to specific needs are quite limited. Here, we investigate unconventional spin Hall effects that have the same origin as conventional ones, but manifest only in low-symmetry crystals where spin polarization, spin current and charge current are not enforced to be orthogonal. Based on the symmetry analysis for all 230 space groups, we have identified crystal structures that could exhibit unusual configurations of charge-to-spin conversion. The most relevant geometries have b...
Thermodynamics of Spin Orbit coupled Bose Einstein Condensate
In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo... more In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo spin-orbit coupling. We take equal Rashba and Dresselhaus spin orbit coupling which give rise to degenerate minima at �nite momenta in the ground state eigenvalue and hence form an unconvensional condensate. In this work, we �rst considered the quantum mechanics of this system to calculate energy eigenvalues and the wave function both of which posses a signature of spin orbit coupling. Then we consider the statistical mechanical properties of these systems. In the case of homogeneous system, we �rst calculate the density of states and then the critical temperature of the system. The critical temperature shows a non-analytic point at a particular value of a certain parameter the Raman Coupling which is also known as the point of quantum phase transition in the case of interacting system. Critical temperature at point shows a cusp like structure and drops down to a minimum value at the sa...
Algebraic structure of a class of differential equations including Heun is shown to be related wi... more Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown to describe a quasi-exactly solvable system, not connected with sl(2) symmetry. Known finite dimensional representations of sl(2) emerge under special conditions. We answer affirmatively the question raised by Turbiner: Are there quasi- exactly solvable problems which can not be represented in terms of sl(2) generators? and give the explicit deformed symmetry underlying this system.
Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and On... more Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variationinduced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semi-classical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.
Path integral formulation of quantum mechanics is presented through the formalism of coherent sta... more Path integral formulation of quantum mechanics is presented through the formalism of coherent state. Coherent states for bosons are also presented as an example for fields.
We consider Bose-Einstein condensation of an ideal bose gas with an equal mixture of 'Rashba' and... more We consider Bose-Einstein condensation of an ideal bose gas with an equal mixture of 'Rashba' and 'Dresselhaus' spin-orbit interactions and study its effect on the critical temperature. In uniform bose gas a 'cusp' and a sharp drop in the critical temperature occurs due to the change in the density of states at a critical Raman coupling where the degeneracy of the ground states is lifted. Relative drop in the critical temperature depends on the diluteness of the gas as well as on the spinorbit coupling strength. In the presence of a harmonic trap, the cusp in the critical temperature smoothened out and a minimum appears. Both the drop in the critical temperature and lifting of 'quasi-degeneracy' of the ground states exhibit crossover phenomena which is controlled by the trap frequency. By considering a 'Dicke' like model we extend our calculation to bosons with large spin and observe a similar minimum in the critical temperature near the critical Raman frequency, which becomes deeper for larger spin. Finally in the limit of infinite spin, the critical temperature vanishes at the critical frequency, which is a manifestation of Dicke type quantum phase transition.
The out-of-plane electric polarization at the surface of SrTiO 3 (STO), an archetypal perovskite ... more The out-of-plane electric polarization at the surface of SrTiO 3 (STO), an archetypal perovskite oxide, may stabilize new electronic states and/or host novel device functionality. This is particularly significant in proximity to atomically thin membranes, such as graphene, although a quantitative understanding of the polarization across graphene-STO interface remains experimentally elusive. Here, we report direct observation and measurement of a large intrinsic out-of-plane polarization at the interface of singlelayer graphene and TiO 2-terminated STO (100) crystal. Using a unique temperature dependence of anti-hysteretic gate-transfer characteristics in dual-gated graphene-on-STO field-effect transistors, we estimate the polarization to be as large as ≈12 μC cm −2 , which is also supported by the density functional theory calculations and low-frequency noise measurements. The anti-hysteretic transfer characteristics is quantitatively shown to arise from an interplay of band bending at the STO surface and electrostatic potential due to interface polarization, which may be a generic feature in hybrid electronic devices from two-dimensional materials and perovskite oxides.
Algebraic structure of a class of differential equations including Heun is shown to be related wi... more Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown to describe a quasi-exactly solvable system, not connected with sl(2) symmetry. Known finite dimensional representations of sl(2) emerge under special conditions. We answer affirmatively the question raised by Turbiner: Are there quasi- exactly solvable problems which can not be represented in terms of sl(2) generators? and give the explicit deformed symmetry underlying this system.
Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of... more Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of electrons as information carriers, allowing generation of spin currents and detecting them via the electric voltage. In the standard arrangement, applied electric field induces transverse spin current with perpendicular spin polarization. Although conventional spin Hall effects are commonly used in spin-orbit torques or spin Hall magnetoresistance experiments, the possibilities to configure electronic devices according to specific needs are quite limited. Here, we investigate unconventional spin Hall effects that have the same origin as conventional ones, but manifest only in low-symmetry crystals where spin polarization, spin current and charge current are not enforced to be orthogonal. Based on the symmetry analysis for all 230 space groups, we have identified crystal structures that could exhibit unusual configurations of charge-to-spin conversion. The most relevant geometries have b...
Thermodynamics of Spin Orbit coupled Bose Einstein Condensate
In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo... more In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo spin-orbit coupling. We take equal Rashba and Dresselhaus spin orbit coupling which give rise to degenerate minima at �nite momenta in the ground state eigenvalue and hence form an unconvensional condensate. In this work, we �rst considered the quantum mechanics of this system to calculate energy eigenvalues and the wave function both of which posses a signature of spin orbit coupling. Then we consider the statistical mechanical properties of these systems. In the case of homogeneous system, we �rst calculate the density of states and then the critical temperature of the system. The critical temperature shows a non-analytic point at a particular value of a certain parameter the Raman Coupling which is also known as the point of quantum phase transition in the case of interacting system. Critical temperature at point shows a cusp like structure and drops down to a minimum value at the sa...
Algebraic structure of a class of differential equations including Heun is shown to be related wi... more Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown to describe a quasi-exactly solvable system, not connected with sl(2) symmetry. Known finite dimensional representations of sl(2) emerge under special conditions. We answer affirmatively the question raised by Turbiner: Are there quasi- exactly solvable problems which can not be represented in terms of sl(2) generators? and give the explicit deformed symmetry underlying this system.
Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and On... more Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variationinduced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semi-classical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.
Path integral formulation of quantum mechanics is presented through the formalism of coherent sta... more Path integral formulation of quantum mechanics is presented through the formalism of coherent state. Coherent states for bosons are also presented as an example for fields.
We consider Bose-Einstein condensation of an ideal bose gas with an equal mixture of 'Rashba' and... more We consider Bose-Einstein condensation of an ideal bose gas with an equal mixture of 'Rashba' and 'Dresselhaus' spin-orbit interactions and study its effect on the critical temperature. In uniform bose gas a 'cusp' and a sharp drop in the critical temperature occurs due to the change in the density of states at a critical Raman coupling where the degeneracy of the ground states is lifted. Relative drop in the critical temperature depends on the diluteness of the gas as well as on the spinorbit coupling strength. In the presence of a harmonic trap, the cusp in the critical temperature smoothened out and a minimum appears. Both the drop in the critical temperature and lifting of 'quasi-degeneracy' of the ground states exhibit crossover phenomena which is controlled by the trap frequency. By considering a 'Dicke' like model we extend our calculation to bosons with large spin and observe a similar minimum in the critical temperature near the critical Raman frequency, which becomes deeper for larger spin. Finally in the limit of infinite spin, the critical temperature vanishes at the critical frequency, which is a manifestation of Dicke type quantum phase transition.
The out-of-plane electric polarization at the surface of SrTiO 3 (STO), an archetypal perovskite ... more The out-of-plane electric polarization at the surface of SrTiO 3 (STO), an archetypal perovskite oxide, may stabilize new electronic states and/or host novel device functionality. This is particularly significant in proximity to atomically thin membranes, such as graphene, although a quantitative understanding of the polarization across graphene-STO interface remains experimentally elusive. Here, we report direct observation and measurement of a large intrinsic out-of-plane polarization at the interface of singlelayer graphene and TiO 2-terminated STO (100) crystal. Using a unique temperature dependence of anti-hysteretic gate-transfer characteristics in dual-gated graphene-on-STO field-effect transistors, we estimate the polarization to be as large as ≈12 μC cm −2 , which is also supported by the density functional theory calculations and low-frequency noise measurements. The anti-hysteretic transfer characteristics is quantitatively shown to arise from an interplay of band bending at the STO surface and electrostatic potential due to interface polarization, which may be a generic feature in hybrid electronic devices from two-dimensional materials and perovskite oxides.
Algebraic structure of a class of differential equations including Heun is shown to be related wi... more Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown to describe a quasi-exactly solvable system, not connected with sl(2) symmetry. Known finite dimensional representations of sl(2) emerge under special conditions. We answer affirmatively the question raised by Turbiner: Are there quasi- exactly solvable problems which can not be represented in terms of sl(2) generators? and give the explicit deformed symmetry underlying this system.
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Papers by Arunesh Roy