arXiv subjects

Rahul Kaiwart

Publications and source records attributed to Rahul Kaiwart.

3 recordsLinked to original sources

arXiv2024

Realization of higher coordinated Er in high-pressure cotunnite phase of Er$_2$Ti$_2$O$_7$

In this article we report the structural stability of Er$_2$Ti$_2$O$_7$ cubic pyrochlore with pressure using x-ray diffraction, Raman spectroscopy, photoluminescence, x-ray absorption and ab-initio calculations. Our studies establish a phase transformation in Er$_2$Ti$_2$O$_7$ from ambient cubic phase to high-pressure orthorhombic (cotunnite) phase, initiated at ~40 GPa. The transformation is sluggish and it does not complete even at the highest measured pressure in our study i.e. ~60.0 GPa. This is further supported by the first principle calculations which reveal that cotunnite phase is energetically more stable than the ambient phase above ~53 GPa. After complete release of pressure, the high-pressure cotunnite phase is retained while the fraction of untransformed pyrochlore phase becomes amorphous. Furthermore, the EXAFS data of the recovered sample at L3 edge of Er3+ ion show an increase in the coordination number of cations from eight at ambient to nine in the high-pressure phase. The mechanism of structural transformation is explained in terms of accumulation of cation antisite defects and subsequent disordering of cations and anions in their respective sublattice. The amorphization of the pyrochlore phase upon release is interpreted as the inability of accommodating the point defects at ambient conditions, which are formed in the pyrochlore lattice under compression.

cond-mat.mtrl-sci↗

arXiv2017

Supersymmetric partner potentials arising from nodeless half bound states

A Half Bound State (HBS) $ψ_*(x)$ can be defined as a single, conditional, zero-energy, continuous solution of the one dimensional Schr{ö}dinger equation for a scattering potential well $V(x)$ ($s.t ~ V(\pm \infty)=0$). The non-normalizable and solitary HBS of a potential satisfies Neumann boundary condition that $ψ'_*(\pm \infty)=0$ and it can have $n$ (= 0,1,2,...) number of nodes indicating $n$ number of bound states in $V(x)$ below $E=0$. Here we show that starting with a nodeless HBS, we can construct a (supersymmetric) pair of finite potentials (well, double wells, well-barrier): $V_{\pm}(x)$ having no bound state and they enclose positive area on $x$-axis. On the contrary their negative counterparts $(-cV_{\pm}(x)),c>0$ do have at least one bound state for any arbitrary positive value of $c$. Furthermore, $c V_{\pm}(x),~ c >0$ which binds positive area on x-axis in conformity with Simon's theorem can have at least one bound state only conditionally for instance when $c>1$ or $c>>1$.

quant-ph↗

arXiv2017

The paradoxical zero reflection at zero energy

Usually, the reflection probability $R(E)$ of a particle of zero energy incident on a potential which converges to zero asymptotically is found to be 1: $R(0)=1$. But earlier, a paradoxical phenomenon of zero reflection at zero energy ($R(0)=0$) has been revealed as a threshold anomaly. Extending the concept of Half Bound State (HBS) of 3D, here we show that in 1D when a symmetric (asymmetric) attractive potential well possesses a zero-energy HBS, $R(0)=0$ $(R(0)<<1)$. This can happen only at some critical values $q_c$ of an effective parameter $q$ of the potential well in the limit $E \rightarrow 0^+$. We demonstrate this critical phenomenon in two simple analytically solvable models which are square and exponential wells. However, in numerical calculations even for these two models $R(0)=0$ is observed only as extrapolation to zero energy from low energies, close to a precise critical value $q_c$. By numerical investigation of a variety of potential wells, we conclude that for a given potential well (symmetric or asymmetric), we can adjust the effective parameter $q$ to have a low reflection at a low energy.

quant-ph↗