arXiv subjects

Ipsita Mandal

Publications and source records attributed to Ipsita Mandal.

At least 55 records · Page 3Linked to original sources

arXiv2024

Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization

We investigate gap-closings in one- and two-dimensional tight-binding models with two bands, containing non-Hermitian hopping terms, and open boundary conditions (OBCs) imposed along one direction. We compare the bulk OBC spectra with the periodic boundary condition (PBC) spectra, pointing out that they do not coincide, which is an intrinsic characteristic of non-Hermitian systems. The non-Hermiticity, thus, results in the failure of the familiar notions of bulk-boundary correspondence found for Hermitian systems. This necessitates the search for topological invariants which can characterize gap-closings in open non-Hermitian systems correctly and unambiguously. We elucidate the behaviour of two possible candidates applicable for one-dimensional slices - (1) the sum of winding numbers for the two bands defined on a generalized Brillouin zone and (2) the biorthogonal polarization (BP). While the former shows jumps/discontinuities for some of the non-Hermitian systems studied here, at points when an edge mode enters the bulk states and becomes delocalized, it does not maintain quantized values in a given topological phase. On the contrary, BP shows jumps at phase transitions, and takes the quantized value of one or zero, which corresponds to whether an actual edge mode exists or whether that mode is delocalized and absorbed within the bulk (not being an edge mode anymore).

quant-ph↗

arXiv2024

Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain

We continue our investigation of the response tensors in planar Hall (or planar thermal Hall) configurations where a three-dimensional Weyl/multi-Weyl semimetal is subjected to the combined influence of an electric field $\mathbf E $ (and/or temperature gradient $\nabla_{\mathbf r } T$) and an effective magnetic field $\mathbf B_χ$, generalizing the considerations of Phys. Rev. B 108 (2023) 155132 and Physica E 159 (2024) 115914. The electromagnetic fields are oriented at a generic angle with respect to each other, thus leading to the possibility of having collinear components, which do not arise in a Hall set-up. The net effective magnetic field $\mathbf B_χ$ consists of two parts -- (a) an actual/physical magnetic field $\mathbf B $ applied externally; and (b) an emergent magnetic field $\mathbf B_5 $ which quantifies the elastic deformations of the sample. $\mathbf B_5 $ is an axial pseudomagnetic field because it couples to conjugate nodal points with opposite chiralities with opposite signs. Using a semiclassical Boltzmann formalism, we derive the generic expressions for the response tensors, including the effects of the Berry curvature (BC) and the orbital magnetic moment (OMM), which arise due to a nontrivial topology of the bandstructures. We elucidate the interplay of the BC-only and the OMM-dependent parts in the longitudinal and transverse (or Hall) components of the electric, thermal, and thermoelectric response tensors. Especially, for the co-planar transverse components of the response tensors, the OMM part acts exclusively in opposition (sync) with the BC-only part for the Weyl (multi-Weyl) semimetals.

cond-mat.mes-hall↗

arXiv2024

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable non-Fermi liquid phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g., optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-called Luttinger-Abrikosov-Benelavskii phase of isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

cond-mat.str-el↗

arXiv2024

Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms

We investigate non-Hermitian versions of the Yao-Lee model, supplemented by various kinds of SO(3)-symmetry-breaking terms, preserving the solvability of the model. The parent model hosts three species of Majorana fermions, thereby serving as an extension of the two-dimensional Kitaev model on the honeycomb lattice. The non-Hermitian couplings represent generic situations when the system is coupled to the environment and, thus, undergoes dissipation. The resulting eigenvalue spectrum and the eigenmodes show a rich structure of exceptional points as well as non-Hermitian skin effects. We chart out such exotic behaviour for some representative parameter regimes.

quant-ph↗

arXiv2024

Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals

We compute the thermoelectric and thermal transport in the weakly disordered non-Fermi liquid phase of the Luttinger semimetals at zero doping, where the decay rate associated with the (strong) Coulomb interactions is much larger than the electron-impurity scattering rate. To this end, we implement the Mori-Zwanzig memory matrix method, that does not rely on the existence of long-lived quasiparticles in the system. We find that the thermal conductivity at zero electric field scales as $\barκ\sim T^{-n}$ (with $0\lesssim n\lesssim 1)$ at low temperatures, whereas the thermoelectric coefficient has the temperature dependence given by $α\sim T^{p}$ (with $1/2\lesssim p\lesssim 3/2)$. These unconventional properties turn out to be key signatures of this long sought-after non-Fermi liquid state in the Luttinger semimetals, which is expected to emerge in strongly correlated spin-orbit coupled materials like the pyrochlore iridates. Finally, our results indicate that these materials might be good candidates for achieving high figure of merit for thermoelectric applications.

cond-mat.str-el↗

arXiv2024

Circular dichroism as a probe for topology in three-dimensional semimetals

Higher-pseudospin fermions, associated with multiple band-crossings in topological semimetals, are the condensed matter analogues of higher-spin fermions in high-energy physics. In this paper, we demonstrate that analyzing the response of a circular drive is an effective way to detect the topology of the lowest-energy Bloch band, as it can be connected to a frequency-dependent probe. The dichroic response exhibits circular dichroism due to the differential excitation rates by the left- and right-circular orientations of a time-periodic drive, induced on a filled band, because of the geometrical properties of the Bloch bands. Our analytical approximation reveals that the dichroic response is quantized for isotropic systems, when the frequency of the drive is above a critical value, and thus correctly infers the ground-state Chern number. We demonstrate this through explicit numerical computations by considering three kinds of semimetals with pseudospin values of 1/2, 1, and 3/2, respectively, and all having linear dispersions. Furthermore, we investigate the effects of tilt and anisotropy on the systems, and find that although tilt does not have any effect on the response, the presence of anisotropy can drastically hamper the quantization. Our scheme thus provides an important methodology for designing future experiments to detect the topology of band structures.

cond-mat.mes-hall↗

arXiv2024

Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals

Luttinger semimetals represent materials with strong spin-orbit coupling, harbouring doubly-degenerate quadratic band touchings at the Brillouin zone center. In the presence of Coulomb interactions, such a system exhibits a non-Fermi liquid phase [dubbed as the Luttinger-Abrikosov-Beneslavskii (LAB) phase], at low temperatures and zero doping. However, a clear experimental evidence of this emergent state remains elusive to this date. Hence, we focus on extracting the Raman response as a complementary experimental signature. At frequencies much larger than the temperature, the Raman response exhibits a power-law behavior, which can be verified experimentally. On the other hand, at lower frequencies, the Raman response displays a quasi-elastic peak. We also compute the ratio of the shear viscosity and the entropy density, and the value obtained is a consequence of the hyperscaling violation that emerges in the LAB phase.

cond-mat.str-el↗

arXiv2024

Andreev bound states in Josephson junctions of semi-Dirac semimetals

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor-barrier-superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum $\varepsilon $ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of $\varepsilon $ on the superconducting phase difference $ϕ$, we compute the variation of Josephson current as a function of $ϕ$.

cond-mat.supr-con↗

arXiv2024

Thermopower in an anisotropic two-dimensional Weyl semimetal

We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy, in both the presence and absence of a quantizing magnetic field. We show that the anisotropy leads to doping dependences of thermopower and thermal conductivities which are different from those in isotropic Dirac materials. Additionally, we find that a quantizing magnetic field in such systems leads to an interesting magnetic field dependence of the longitudinal thermopower, resulting in unsaturated thermoelectric coefficients. Thus the results presented here will serve as a guide to achieving high thermopower and a thermoelectric figure-of-merit in graphene-based materials, as well as organic conductors such as $α$-(BEDT-TTF)$_2$I$_3$.

cond-mat.mes-hall↗

arXiv2024

Andreev bound states in superconductor-barrier-superconductor junctions of Rarita-Schwinger-Weyl semimetals

We consider a superconductor-barrier-superconductor configuration built with Rarita-Schwinger-Weyl semimetal, which features four bands crossing at a single nodal point. Assuming a homogeneous s-wave pairing in each superconducting region, and the barrier region created by applying a voltage of magnitude $V_0 $ across a piece of normal state semimetal, we apply the BdG formalism to compute the discrete energy spectrum $\varepsilon $ of the subgap Andreev bound states in the short-barrier regime. In contrast with the two-band semimetals studied earlier, we find upto four pairs of localized states (rather than one pair for two-band semimetals) in the thin-barrier limit, and each value of $\varepsilon $ has a complicated dependence on the phase difference $φ_{12} $ via cosine and sine functions, which cannot be determined analytically. These are artifacts of multi-band nodes hosting quasiparticles of pseudospin values greater than $1/2$. Using the bound state energies, we compute the Josephson current across the junction configuration.

cond-mat.supr-con↗

arXiv2024

Superconducting instability in non-Fermi liquids

We use renormalization group (RG) analysis and dimensional regularization techniques to study potential superconductivity-inducing four-fermion interactions in systems with critical Fermi surfaces of general dimensions ($m$) and co-dimensions ($d-m$), arising as a result of quasiparticle interaction with a gapless Ising-nematic order parameter. These are examples of non-Fermi liquid states in $d$ spatial dimensions. Our formalism allows us to treat the corresponding zero-temperature low-energy effective theory in a controlled approximation close to the upper critical dimension $d=d_c(m)$. The fixed points are identified from the RG flow equations, as functions of $d$ and $m$. We find that the flow towards the non-Fermi liquid fixed point is preempted by Cooper pair formation for both the physical cases of $(d=3, m=2)$ and $(d=2, m=1)$. In fact, there is a strong enhancement of superconductivity by the order parameter fluctuations at the quantum critical point.

cond-mat.str-el↗

arXiv2023

Anatomy of plasmons in generic Luttinger semimetals

We investigate the parameter regimes favourable for the emergence of plasmons in isotropic, anisotropic, and band-mass symmetric and asymmetric Luttinger semimetals (LSMs). An LSM harbours a quadratic band-crossing point (QBCP) in its bandstructure, where the upper and lower branches of dispersion are doubly degenerate. While a nonzero temperature ($T$) can excite particle-hole pairs about the Fermi level due to thermal effects (even at zero doping), a finite doping ($μ$) sets the Fermi level away from the QBCP at any $T$, leading to a finite Fermi surface (rather than a Fermi point). Both these conditions naturally give rise to a finite density of states. A nonzero value of $T$ or $μ$ is thus a necessary condition for a plasmon to exist, as otherwise the zero density of states at the QBCP can never lead to the appearance of this collective mode. In addition to $T$ and $μ$, we consider the effects of all possible parameters like cubic anisotropy, band-mass asymmetry, and a material-dependent variable $X$ that is proportional to the mass (of the quasiparticle) and the number of fermion flavours. We implement a random-phase-approximation to compute the quasiparticle decay rate $ τ^{-1} $ (also known as the inelastic scattering rate) resulting from screened Coulomb interactions. A well-defined sharp peak in the profile of $τ^{-1}$ signals the appearance of a plasmon. From our results, we conclude that $X$ turns out to be a crucial tuning parameter, as higher values of $X$ assist in the emergence of plasmons. On the other hand, the features are broadly insensitive to cubic anisotropy and band-mass asymmetry.

cond-mat.str-el↗

arXiv2023

Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions

We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields, by applying the dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of $U(1)$ and $U(1)\times U(1)$ transverse gauge couplings, and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings. Our analysis allows us to treat a critical Fermi surface of a generic dimension $m$ perturbatively in an expansion parameter $ε=\left (2-m \right ) /\left (m+1 \right).$ One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain $U(1)\times U(1)$ theories, which was identified earlier for $m=1$ at one-loop order, the third-order diagrams do. However, this fixed line feature is also obtained for $m>1$, where the answer is one-loop exact due to UV/IR mixing.

cond-mat.str-el↗

arXiv2023

Generic deformation channels for critical Fermi surfaces in the collisionless regime

Using a quantum Boltzmann equation framework, we analyse the nature of generic low-energy deformations of a critical Fermi surface, which exists at the non-Fermi liquid fixed point of a system consisting of fermions interacting with massless bosons. The non-Fermi liquid behaviour arises due to the itinerant quasiparticles of the Fermi surface interacting strongly with the massless bosons, which on the other hand undergo Landau damping as a result of the mutual interactions. Focussing on the collisionless regime, where we neglect the collision integral, we chalk out the possible excitations spanning the entire spectrum of angular momentum ($\ell$) channels (i.e., including both small and large values of $\ell$). The excitations are of two types: particle-hole like localized excitations forming an energy band (or continuum) and delocalized collective modes with discrete energies. Although we find a collective mode analogous to the zero sound of a Fermi liquid, its dispersion shows a crossover from a $Ω\sim |\mathbf q|^{6/5}$ behaviour to the usual $ Ω\sim |\mathbf q|$ dependence, where $Ω$ and $\mathbf q$ represent the frequency and momentum, respectively. We estimate the frequency scale at which this crossover takes place. We also determine the boundary for the particle-hole continuum in the $Ω$--$\mathbf q$ plane, and observe a crossover from $Ω\sim |\mathbf q|^{3/2}$ to $ Ω\sim |\mathbf q|$ behaviour, determined by another crossover frequency scale.

cond-mat.str-el↗

arXiv2023

Signatures of two- and three-dimensional semimetals from circular dichroism

Topological invariants are crucial quantities for classifying materials with topological phases. Hence, their connections with experimentally measurable quantities are extremely important. In this context, circular dichroism (CD) provides a protocol to detect the Chern number $\mathcal{C}_0$ of the lowest energy Bloch band (LBB) of a semimetal. This hinges on the unequal depletion rates of the Bloch electrons from a filled LBB, under the action of a time-periodic circular drive, depending on the chirality of the polarization. According to the dimensionality of the system (i.e., whether it is two- or three-dimensional), the integrated differential rate for depletion has to be formulated a bit differently in order to relate it to $\mathcal{C}_0$. Our aim is to capture the nature of the CD response for semimetals with anisotropic band dispersions. We show that while the quantization of the CD response for the three-dimensional cases is strongly sensitive to anisotropy, the two-dimensional counterparts show a perfectly quantized response.

cond-mat.mes-hall↗

arXiv2023

One-dimensional magnetism in synthetic Pauflerite, $β$-VOSO$_4$

We have synthesized single-crystal samples of $β$-VOSO$_4$ and fully characterized their magnetic properties. Our magnetic susceptibility, high field magnetization and powder inelastic neutron scattering results are in excellent agreement with theoretical expressions for a one-dimensional spin-1/2 Heisenberg chain with an exchange parameter of $3.83(2)$ meV. Ab initio calculations identify the superexchange pathway, revealing that the spin-chain does not run along the expected crystallographic chain $a$ direction but instead between V$^{4+}$O$_{6}$ octahedra that are linked via SO$_{4}$ tetrahedra along the $b$ axis. We do not detect any phase transition to a long-range magnetic order within our experimental conditions, indicating $β$-VOSO$_4$ is very close to an ideal one-dimensional magnetic system.

cond-mat.str-el↗

arXiv2023

Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points

Exceptional points (EPs) are degeneracy of non-Hermitian Hamiltonians, at which the eigenvalues, along with their eigenvectors, coalesce. Their orders are given by the Jordan decomposition. Here, we focus on higher-order EPs arising in fermionic systems with a sublattice symmetry, which restricts the eigenvalues of the Hamitlonian to appear in pairs of $\lbrace E, -E\rbrace $. Thus, a naive prediction might lead to only even-order EPs at zero energy. However, we show that odd-order EPs can exist and exhibit enhanced sensitivity in the behaviour of eigenvector-coalescence in their neighbourhood, depending on how we approach the degenerate point. The odd-order EPs can be understood as a mixture of higher- and lower-valued even-order EPs. Such an anomalous behaviour is related to the irregular topology of the EPs as the subspace of the Hamiltonians in question, which is a unique feature of the Jordan blocks. The enhanced eigenvector sensitivity can be described by observing how the quantum distance to the target eigenvector converges to zero. In order to capture the eigenvector-coalescence, we provide an algebraic method to describe the conditions for the existence of these EPs. This complements previous studies based on resultants and discriminants, and unveils heretofore unexplored structures of higher-order exceptional degeneracy.

quant-ph↗

arXiv2023

Zero sound and plasmon modes for non-Fermi liquids

We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Green's function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes exhibit the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.

cond-mat.str-el↗