arXiv subjects

Gautam Rai

Publications and source records attributed to Gautam Rai.

14 recordsLinked to original sources

arXiv2025

Interplay between many-body correlations, strain and lattice relaxation in twisted bilayer graphene

In twisted bilayer graphene, a unified understanding of the mechanisms governing temperature-dependent electronic spectra and thermodynamic properties remains controversial despite extensive theoretical efforts. Here, we present a comprehensive theoretical framework that quantitatively accounts for scanning tunneling spectroscopy, quantum twisting microscopy, and thermodynamic properties of magic angle twisted bilayer graphene. We demonstrate that the observed behavior arises from the interplay between electron correlations and external symmetry-breaking induced by strain and lattice relaxation. These effects act cooperatively to shape the emergent electronic behavior, leaving characteristic signatures across spectroscopy, compressibility and entropy.

cond-mat.str-el↗

arXiv2025

Obtaining the Spectral Function of Moiré Graphene Heavy-Fermions Using Iterative Perturbation Theory

The spectral functions of twisted bilayer graphene (TBG) in the absence of strain have recently been investigated in both the symmetric and symmetry-broken phases using dynamical mean-field theory (DMFT). The theoretically predicted Mott-Hubbard bands and gapless semimetallic state at half-filling have since been confirmed experimentally. Here, we develop several second-order perturbation theory approaches to the topological heavy-fermion (THF) model of TBG and twisted symmetric trilayer graphene (TSTG). In the symmetric phase, we adapt, implement, and benchmark an iterative perturbation theory (IPT) impurity solver within DMFT, enabling computationally efficient yet accurate spectral function calculations. We present momentum- and energy-resolved spectra over a broad range of temperatures and fillings for both symmetric and symmetry-broken states. In addition, we derive analytic expressions for the spectral function within the ``Hubbard-I'' approximation of the THF model and, as expected, find that while it provides a tractable description of Mott physics, it does not capture the low-energy Kondo peak or the finite lifetime broadening of the bands. Our methodology can be extended to include strain, lattice relaxation, and parameter variations, thereby allowing systematic predictions of TBG and TSTG spectral properties across a wide range of physical regimes. Because our perturbative approaches are far less computationally intensive than DMFT with numerically exact impurity solvers, they can be used to efficiently benchmark and scan extensive phase diagrams of the THF parameters, paving the way for full DMFT analyses of the TBG spectral function in the presence of strain and relaxation.

cond-mat.str-el↗

arXiv2025

Site-polarized Mott phases competing with a correlated metal in twisted WSe$_2$

Twisted WSe$_2$ hosts superconductivity, metal-insulator phase transitions, and field-controllable Fermi-liquid to non-Fermi-liquid transport properties. In this work, we use dynamical mean-field theory to provide a coherent understanding of the electronic correlations shaping the twisted WSe$_2$ phase diagram. We find a correlated metal competing with three distinct site-polarized correlated insulators; the competition is controlled by interlayer potential difference and interaction strength. The insulators are characterized by a strong differentiation between orbitals with respect to carrier concentration and effective correlation strength. Upon doping, a strong particle-hole asymmetry emerges, resulting from a Zaanen-Sawatzky-Allen-type charge-transfer mechanism. The associated charge-transfer physics and proximity to a van Hove singularity in the correlated metal sandwiched between two site-polarized insulators naturally explains the interlayer potential-driven metal-to-insulator transition, particle-hole asymmetry in transport, and the coherence-incoherence crossover in $3.65^\circ$ twisted WSe$_2$.

cond-mat.str-el↗

arXiv2025

Resolving Intervalley Gaps and Many-Body Resonances in Moiré Superconductor

Magic-angle twisted multilayer graphene stands out as a highly tunable class of moiré materials that exhibit strong electronic correlations and robust superconductivity. However, understanding the relations between the low-temperature superconducting phase and the preceding correlated phases established at higher temperatures remains a challenge. Here, we employ scanning tunneling microscopy and spectroscopy to track the formation sequence of correlated phases established by the interplay of dynamic correlations, intervalley coherence, and superconductivity in magic-angle twisted trilayer graphene (MATTG). We discover the existence of two well-resolved gaps pinned at the Fermi level within the superconducting doping range. While the outer gap, previously associated with pseudogap phase, persists at high temperatures and magnetic fields, the newly revealed inner gap is more fragile in line with superconductivity MATTG transport experiments. Andreev reflection spectroscopy taken at the same location confirms a clear trend that closely follows the doping behaviour of the inner gap, and not the outer one. Moreover, spectroscopy taken at nanoscale domain boundaries further corroborates the contrasting behavior of the two gaps, with the inner gap remaining resilient to structural variations, as expected from the finite superconducting coherence length. By comparing our findings with recent topological heavy-fermion models, we identify that the outer gap originates from the splitting of the Abrikosov-Suhl-Kondo resonance due to the breaking of the valley symmetry arising from correlation-driven effects. Our results suggest an intricate but tractable hierarchy of correlated phases in twisted multilayer graphene.

cond-mat.supr-con↗

arXiv2024

SNS Junctions along the BCS-BEC Crossover

We present a theory of SNS junctions, a normal metal sandwiched between two superconductors, along the crossover from the BCS to the BEC regime. We calculate the Josephson current as a function of the chemical potential relative to the band edge in the superconducting region, $μ_S$, where the BEC phase is indicated by $μ_S <0$. The chemical potential relative to the band edge in the normal metal, $μ_N$, allows us to tune the junction between the SNS case ($μ_N>0$) and the SIS case, where the superconductors are separated by a tunneling barrier. We find that there are Andreev levels in the BEC regime, as long as there is sufficient density of states in the normal region, i.e. when $μ_N>Δ$, where $Δ$ is the amplitude of the superconducting order parameter. For 1D SNS junctions, we find the Josephson current $I_S$ carried by these Andreev levels to be a function of the ratio $Δ/Δ_d$, where $Δ_d$ is the Andreev level spacing. At zero temperature, the Josephson current has a maximum on the BCS side of the transition where $Δ$ is maximal. At finite temperature, however, we find that the maximum moves to the BEC side of the crossover. We identify the mechanism for this phenomenon to be the decrease in the number of Andreev levels at the BCS-BEC crossover, accompanied by an increase in excitation energy to the unoccupied levels, making it less likely that these states are thermally occupied. Thereby, at finite temperature, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover.

cond-mat.supr-con↗

arXiv2024

Dynamical correlations and order in magic-angle twisted bilayer graphene

In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order. We use Dynamical Mean Field Theory (DMFT) on the topological heavy Fermion (THF) model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100K, (ii) the ordering of the local isospin moments around 10K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a "bad metal" above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a "good metal" in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions and periodic variations of the electronic compressibility. Our findings provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments.

cond-mat.str-el↗

arXiv2024

Superconductivity in the Fibonacci Chain

Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperature superconducting phase in detail using the Bogoliubov-de Gennes mean-field approach. We obtain superconducting solutions as a function of the parameters controlling the physical properties of the system: the strength of the Hubbard attraction $U$, the chemical potential $μ$, and the strength of the modulation of the Fibonacci Hamiltonian, $w$. We find that there is a bulk transition at a critical temperature that obeys a power law in $U$. The local superconducting order parameter is self-similar both in real and perpendicular space. The local densities of states vary from site to site, however, the width of the superconducting gap is the same on all sites. The interplay between the Hubbard attraction and the intrinsic gaps of the Fibonacci chain results in a complex zero-temperature $μ$-$U$ phase diagram with insulating domes surrounded by superconducting regions. Finally, we show that tuning $w$ from weak to strong quasicrystalline modulation gives rise to qualitatively different thermodynamic behaviors as could be observed by measuring the specific heat.

cond-mat.supr-con↗

arXiv2022

Edge and corner superconductivity in a 2D topological model

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a non-trivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0 \leq r\leq 1$, the inhomogeneous superconducting phases induced by an attractive $U$ Hubbard interaction are studied using mean field theory. We show, analytically and by numerical diagonalization, that in lattices with open boundaries, phases with enhanced superconducting order on the corners or the edges can appear, depending on the filling. For finite samples at half filling, the corner site superconducting transition temperature can be much larger than that of the bulk. A novel proximity effect thus arises for $T_{c,bulk} < T<T_{c,corner}$, in which the corner site creates a nonzero tail of the superconducting order in the bulk. We show that such tails should be observable for a range of $r$ and $U$ values.

cond-mat.supr-con↗

arXiv2022

Real-space BCS-BEC crossover in FeSe monolayer

The quantum many body states in the BCS-BEC crossover regime are of long-lasting interest. Here we report direct spectroscopic evidence of BCS-BEC crossover in real-space in a FeSe monolayer thin film by using spatially resolved scanning tunneling spectra. The crossover is driven by the shift of band structure relative to the Fermi level. The theoretical calculation based on a two-band model qualitatively reproduces the measured spectra in the whole crossover range. In addition, the Zeeman splitting of the quasi-particle states is found to be consistent with the characteristics of a condensate. Our work paves the way to study the exotic states of BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale.

cond-mat.supr-con↗

arXiv2021

Bulk topological signatures of a quasicrystal

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

cond-mat.dis-nn↗

arXiv2020

Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real space Bogoliubov-de Gennes framework for three cases, namely, when states are i) extended, ii) localized or iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases i) and iii), stretched exponential in case ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable (case i) or of its logarithm (cases ii and iii). We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

cond-mat.supr-con↗

arXiv2019

Induced superconducting pair correlations in a quasicrystal coupled to a BCS superconductor

In this report, we describe the proximity effect which arises when a quasicrystal is placed in contact with a superconductor. We consider the simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all states are known to be critical. A hybrid ring is made by connecting a finite piece of such a Fibonacci chain to a BCS-type superconductor. Solving the resulting Bogoliubov-de Gennes equations self-consistently, we show that the proximity effect in the Fibonacci chain is long ranged, and that the induced superconducting order carries information on topological properties, namely, the winding numbers of edge states of the Fibonacci chain.

cond-mat.supr-con↗

arXiv2019

The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring

We compute the real-space profile of the superconducting order parameter (OP) in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter $ϕ$, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on $ϕ$ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly $larger$ than in a normal periodic conductor for special values of $ϕ$.

cond-mat.supr-con↗

arXiv2015

Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state has quantum features when the average fidelity of the outcomes is greater than 2/3. We use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the total average fidelity f_X to display quantum features, i.e., we find a threshold C_X for the concurrence of the channel. If the mechanism for redistributing fidelity is successfully applied then we find a filtrable outcome with normalized average fidelity f_{X,USE,0} greater than f_X. In addition, we find the threshold concurrence of the channel C_{X,USE,0} in order for the normalized average fidelity to display quantum features. Surprisingly, we find that the threshold concurrence C_{X,USE,0} can be lesser than C_X. Finally, we show that if the mechanism for redistributing fidelity fails then the respective filtrable outcome has average fidelity lesser than 2/3.

quant-ph↗