arXiv subjects

Nikhil Danny Babu

Publications and source records attributed to Nikhil Danny Babu.

6 recordsLinked to original sources

arXiv2026

Optical Signatures and Quantum Geometry in Proximity-Induced Topological Superconductors

Topological-insulator-superconductor (TI-SC) heterostructures provide a promising platform for proximity-induced topological superconductivity, but diagnosing superconductivity at a buried interface remains challenging for conventional surface-sensitive probes. Here, we develop a quantitative theory of the longitudinal optical response of a TI-SC heterostructure and show that the complex sheet conductance provides an interface-selective route to isolating and diagnosing the buried proximitized interface state. Starting from a minimal model, we derive a low-energy description of the heterointerface in which the induced gap emerges directly from the TI-SC coupling. Combined with a slab-based thickness-extrapolation procedure, this framework yields a practical protocol for separating the buried interfacial sheet conductance from bulk and exposed-surface optical contributions. The extracted interface response exhibits a robust, thickness-independent coherence peak at an energy set by the proximity-induced gap, clearly distinguishable from both the pair-breaking scale of the parent superconductor and the Dirac cone on the exposed TI surface. At low energies, the heterointerface is described by an effective time-reversal-invariant topological-superconducting theory, while the associated low-frequency optical spectral weight admits a quantum-geometric interpretation through the optical sum rule. Our results establish terahertz/infrared spectroscopy of thickness-extracted sheet conductance as a noninvasive route to identifying and quantifying proximity-induced superconductivity at buried TI-SC interfaces.

cond-mat.mes-hall↗

arXiv2024

Density-density correlation functions of chiral Luttinger liquids with a point-contact impurity

The density-density correlation functions (most singular parts) of chiral Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge are systematically derived in presence of a point-contact junction acting as a localised scalar impurity and are shown to be expressible as compact analytical functions with second order poles and involving the bare scale-independent reflection and transmission coefficients. The results are validated on comparison with standard fermionic perturbation theory. The linear response Hall conductance in the absence of a point-contact is recovered from the obtained density-density correlation functions (DDCF). The system under consideration is inhomogeneous with broken translational invariance and for such systems in one dimension, the connected moments of the density fluctuation operator beyond second order need not be included in order to retrieve the most singular parts of the correlations. The reason being that all odd moments of the density are zero and all higher order even moments are less singular than the quadratic moment. The implications of these results when used in conjunction with bosonization methods in presence of impurity backscattering is briefly discussed.

cond-mat.mes-hall↗

arXiv2023

Tunneling density of states of fractional quantum Hall edges: an unconventional bosonization approach

An unconventional bosonization approach that employs a modified Fermi-Bose correspondence is used to obtain the tunneling density of states (TDOS) of fractional quantum Hall (FQHE) edges in the vicinity of a point contact. The chiral Luttinger liquid model is generally used to describe FQHE edge excitations. We introduce a bosonization procedure to study edge state transport in Laughlin states at filling $ν= 1/m$ with $m$ odd (single edge mode) in the presence of a point contact constriction that brings the top and bottom edges of the sample into close proximity. The unconventional bosonization involves modifying the Fermi-Bose correspondence to incorporate backscattering at the point contact, leaving the action of the theory purely quadratic even in presence of the inhomogeneity. We have shown convincingly in earlier works that this procedure correctly reproduces the most singular parts of the Green functions of the system even when mutual forward scattering between fermions are included. The most singular part of the density-density correlation function (DDCF) relevant to TDOS calculation is computed using a generating functional approach. The TDOS for both the electron tunneling as well as the Laughlin quasiparticle tunneling cases is obtained and is found to agree with previous results in the literature. For electron tunneling the well-known universal power laws for TDOS viz. $ \sim \mbox{ }ω^{ m-1 }$ and for quasi-particle tunneling the power law $ \sim \mbox{ } ω^{ \frac{1}{m}-1 } $ are both correctly recovered using our unconventional bosonization scheme. This demonstrates convincingly the utility of the present method which unlike conventional approaches, does not treat the point-contact as an afterthought and yet remains solvable so long as only the most singular parts of the correlation functions are desired.

cond-mat.mes-hall↗

arXiv2023

Unconventional bosonization of chiral quantum wires coupled through a point-contact driven out of equilibrium

Non-chiral bosonization technique adapted to study chiral quantum wires with non-interacting fermions coupled through a point-contact with a constant bias between the wires is introduced and is shown to reproduce the exact Green functions of this system which was previously derived by the present authors analytically using standard methods. The tunneling I-V characteristics are obtained using the bosonized Green functions. The proposed unconventional bosonization scheme is also shown to be internally consistent as the four-point functions evaluated using NCBT are shown to be related to the two-point functions through Wick's theorem as it should be. In equilibrium, the equal space-time NCBT Green functions for an interacting Luttinger liquid with impurities obtained in a previous work shows universal scaling behaviour in accordance with Bethe ansatz and functional renormalization group predictions. We expect to obtain a similar scaling form of the tunneling properties out of equilibrium in presence of interparticle interactions.

cond-mat.str-el↗

arXiv2022

Non-Markovian transients in transport across chiral quantum wires using space-time non-equilibrium Green functions

We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson's equation analytically. Both the space-time dependent two and four-point functions are written down in a closed form in terms of simple functions of position and time. This allows us to obtain, among other things, the I-V characteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time evolution of the equal-time one-particle Green function. Our method can be easily applied to the problem of a double barrier contact whose internal properties can be adjusted to induce resonant tunneling leading to a conductance maximum. We then consider the case of a finite bandwidth in the point contact and calculate the non-equilibrium transport properties which exhibit non-Markovian behaviour. When a subsequently constant bias is suddenly switched on, the current shows a transient build up before approaching its steady state value in contrast to the infinite bandwidth case. This transient property is consistent with numerical simulations of lattice systems using time-dependent DMRG (tDMRG) suggesting thereby that this transient build up is merely due to the presence of a short distance cutoff in the problem description and not on the other details.

cond-mat.mes-hall↗

arXiv2020

Density-density Correlation Function of Strongly Inhomogeneous Luttinger Liquids

In this work, we show in pedagogical detail that the most singular contributions to the slow part of the asymptotic density-density correlation function of Luttinger liquids with fermions interacting mutually with only short-range forward scattering and also with localised scalar static impurities (where backward scattering takes place) has a compact analytical expression in terms of simple functions that have second order poles and involve only the scale-independent bare transmission and reflection coefficients. This proof uses conventional fermionic perturbation theory resummed to all orders, together with the idea that for such systems, the (connected) moments of the density operator all vanish beyond the second order - the odd ones vanish identically and the higher order even moments are less singular than the second order moment which is the only one included. This important result is the crucial input to the recently introduced "Non-Chiral Bosonization Technique" (NCBT) to study such systems. The results of NCBT cannot be easily compared with the results obtained using conventional bosonization as the former only extracts the most singular parts of the correlation functions albeit for arbitrary impurity strengths and mutual interactions. The latter, ambitiously attempts to study all the parts of the asymptotic correlation functions and is thereby unable to find simple analytical expressions and is forced to operate in the vicinity of the homogeneous system or the half line (the opposite extreme). For a fully homogeneous system or its antithesis viz. the half-line, all the higher order connected moments of the density vanish identically which means the results of chiral bosonization and NCBT ought to be the same and indeed they are.

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