arXiv subjects

Udit Khanna

Publications and source records attributed to Udit Khanna.

At least 19 recordsLinked to original sources

arXiv2026

Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the $\mathcal{N}{=}2$ Landau levels of Bernal-stacked bilayer graphene

Bernal-stacked bilayer graphene (BLG), in which a graphene layer is stacked atop another and laterally shifted by a lattice constant, offers remarkable tunability in its single-particle states under applied magnetic and displacement fields. Owing to this tunability, recent transport and scanning tunneling microscopy experiments in the presence of a perpendicular magnetic field and finite interlayer displacement fields have observed even-denominator fractional quantum Hall (FQH) states at half-filling in the first excited, namely, $\mathcal{N}{=}2$, Landau level (LL) of BLG. In contrast, at zero displacement field, a gapless composite fermion Fermi liquid (CFFL) is realized at half-filling of the $\mathcal{N}{=}2$ LL. Motivated by these experiments, we compute the phase diagram as a function of the displacement field in the half-filled $\mathcal{N}{=}2$ LL of BLG by studying the competition between the CFFL and the Moore-Read state---a candidate even-denominator FQH state---by calculating their thermodynamic energies in this setting. We find that the modified effective Coulomb interaction, induced by changes in the single-particle states with increasing displacement field, softens the inter-electronic repulsion at short distances, thereby stabilizing the Moore-Read state over the CFFL in the $\mathcal{N}{=}2$ LL of BLG. We also study the nature of FQH states at fillings $2/5$, $3/7$, $4/9$, and $6/13$ in the $\mathcal{N}{=}2$ LL of BLG. Our results suggest that, with increasing displacement field, the Jain composite-fermion states at $3/7$, $4/9$, and $6/13$ transition into states with distinct topological order that are well-captured by parton wave functions.

cond-mat.mes-hall↗

arXiv2026

Topological zero-reflection points in multi-terminal quantum wire junctions

We study scattering in noninteracting multi-terminal quantum wire junctions and show that junctions with dihedral symmetry can exhibit exact zero-reflection points for $N \ge 4$ terminals. By analyzing the scattering matrix, we identify these reflectionless points in the $(E,t')$ parameter space, where $E$ is the incident particle energy and $t'$ is the junction hopping amplitude. These points exhibit an even-odd dependence on $N$ and converge asymptotically to a common limiting value in the large-$N$ limit. We show that the reflectionless points are characterized by an integer winding number associated with the phase of the reflection amplitude, providing a topological description for their stability against weak on-site disorder. We also consider junctions with broken time-reversal symmetry and find that a magnetic flux can induce additional reflectionless points, including for the $N = 3$ case. For a four-terminal junction threaded by a $π$-flux, we identify a unique parameter regime in which the reflection amplitude vanishes over the entire energy band. Finally, we discuss experimental signatures through the behavior of Friedel oscillations and examine the stability of these reflectionless points in the presence of weak interactions.

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arXiv2026

Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene

Even-denominator fractional quantum Hall states (FQHSs) at half filling are of particular interest because they can host non-Abelian quasiparticles. Here we report the emergence of such states in the zeroth Landau level ($N=0$) of ABA trilayer graphene (TLG), challenging the conventional expectation that they are confined to the first excited Landau level. We observe robust incompressible states at $ν=7/2$, $9/2$, and $5/2$ with their associated Levin--Halperin daughter states: $ν=59/17$ and $46/13$ near $7/2$; $ν=58/13$ and $77/17$ near $9/2$; and $ν=43/17$ near $5/2$. These states appear exclusively within a finite displacement-field window coincident with crossings between symmetry-broken $N=0$ Landau levels carrying distinct isospin indices. The quantitative correspondence between the calculated crossing loci and the experimentally determined stability regions identifies Landau-level mixing as the microscopic origin. We attribute the stabilization of these even-denominator states to inversion-symmetry breaking in TLG, which enhances valley-resolved Landau-level hybridization and renormalizes short-range Coulomb interactions. Our results expand the landscape of even-denominator FQHSs to multilayer graphene and establish TLG as a tunable platform for realizing non-Abelian anyons.

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arXiv2026

Synthetic Flat Bands, Hierarchical Topology, and Phase-Fluctuation-Insensitive Quantized Transconductance in Josephson Junctions

We uncover hierarchy of topological phases within the synthetic Brillouin zone of a three-terminal Josephson junction's (3-TJJ's) Bogoliubov-de Gennes spectrum. We demonstrate that the above-gap continuum realizes a Chern insulator phase with quantized monopole charges (\pm 1), while the subgap Andreev bound states (ABS) are characterized by a quantized dipolar invariant. By breaking time-reversal symmetry at the junction, we induce synthetic flat bands that suppress DC Josephson currents across the entire phase-bias space. Furthermore, under voltage bias, the junction exhibits a robust quantization of the time-averaged transconductance that is reminiscent of a quantized Hall conductance plateau owing to the flat band limit and its dipole phase. As a byproduct, the flat band produces a global "sweet plateau" of phase insensitivity, surpassing localized sweet spots of conventional superconducting qubits and enabling a robust architecture for symmetry-protected Andreev qubits.

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arXiv2025

Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}{=}0$ and $\mathbf{n}{=}1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the $\mathbf{n}{=}0$ Landau level are bond-ordered, while those in the $\mathbf{n}{=}1$ Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [Amet, $\textit{et al.}$, Nat. Comm. $\mathbf{6}$, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

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arXiv2025

Energy Gap Modulation in Proximitized Superconducting Puddles of Graphene

We investigated proximity-induced superconductivity in a graphene-insulating InO bilayer system through gate-controlled transport measurements. Distinct oscillations in the differential conductance are observed across both the electron and hole doping regimes, with oscillation amplitudes increasing as the chemical potential moves away from the Dirac point. These findings are explained using a theoretical model of a normal-superconductor-normal (NSN) junction, which addresses reflection and transmission probabilities at normal incidence. From this model, we extract key parameters for the proximitized graphene, including the superconducting energy gap Delta and the effective length scale Ls of the superconducting regions. Near the Dirac point, we observe a minimal Ls and a maximal Delta, aligning with the theory that the gap in strongly disordered superconductors increases as the coherence length of localized pairs decreases. This suggests that spatial confinement in a low-density superconductor leads to an effective increase in the superconducting gap.

cond-mat.supr-con↗

arXiv2024

Decoherence in electron transport: back-scattering, effect on interference and rectification

Decoherence is an undesirable, but ubiquitous phenomenon in quantum systems. Here, we study the effect of partial decoherence, induced via a Büttiker probe, on two-terminal electronic transport across one-dimensional quantum wires and rings, in both the linear and non-linear regimes. We find that dephasing causes backscattering when introduced locally in a ballistic channel. Further, we find that decoherence results in rectification when inversion is broken in the two-terminal transport set-up by a combination of a local dephasing centre and a static impurity. Interestingly, the rectification strength and even its direction varies strongly with the relative distance between the probe and the scatterer. We further analyze how decoherence affects characteristic quantum effects in electronic transport, such as, Fabry-Pérot oscillations in double-barrier setups, and Aharonov-Bohm interference in one-dimensional rings, and find that the amplitude of oscillations in conductance is reduced by decoherence.

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arXiv2024

Fractional quantum Hall coexistence phases in higher Landau levels of graphene

Monolayer graphene under a strong magnetic field near charge neutrality manifests the integer and fractional quantum Hall effects. Since only some of the four spin/valley flavors available to the electrons in each Landau level manifold are filled, they also exhibit spontaneous symmetry breaking the in spin/valley sector, a phenomenon known as quantum Hall ferromagnetism. In this work, we study quantum Hall ferromagnets in the higher Landau level manifolds of monolayer graphene and show that there is an even richer set of symmetry-broken phases than in the lowest Landau level manifold. Specifically, both valley polarized and valley equatorial (where the occupied Landau levels are in an equal superposition of both valleys) ferromagnets, antiferromagnets, and canted antiferromagnets are found. Several types of spin valley entangled phases are found, all of which manifest the simultaneous spontaneous symmetry breaking of both magnetic and lattice symmetries.

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arXiv2023

Quantum spin Hall insulator in proximity with a superconductor: Transition to the Fulde-Ferrell-Larkin-Ovchinnikov state driven by a Zeeman field

We investigate the effects of introducing a boost (a Zeeman field parallel to the spin quantization axis) at the proximitized helical edge of a two-dimensional (2D) quantum spin Hall insulator. Our self-consistent analysis finds that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting phase may emerge at the edge when the boost is larger than a critical value tied to the induced pairing gap. A non-trivial consequence of retaining the 2D bulk in the model is that this boundary FFLO state supports a finite magnetization as well as finite current (flowing along the edge). This has implications for a proper treatment of the ultra-violet cutoff in analyses employing the effective one-dimensional (1D) helical edge model. Our results may be contrasted with previous studies of such 1D models, which found that the FFLO phase either does not appear for any value of the boost (in non-self-consistent calculations), or that it self-consistently appears even for infinitesimal boost, but carries no current and magnetization.

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arXiv2023

Anomalous topology and synthetic flat band in multi-terminal Josephson Junctions

Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthetic band topology owing to their periodic dependence on the Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this topological character, i.e., gap closing points may or \textit{may not} correspond to change of Chern number, hence extending the standard paradigm for topological bands. We further show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the JJ hence indicating a universal behaviour of multi-terminal JJ. We also show that the chiral junction, supported by quantum Hall state at the junction region, leads to flat Andreev bands (implying absence of DC Josephson effects) that are devoid of Berry curvature ( implying absence of AC Josephson effects). Such electrically inert JJ may be useful for storage of quantum information in future quantum devices.

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arXiv2023

Phase diagram of the $ν= 2$ quantum Hall state in bilayer graphene

Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors $1 < ν\leq 2$ suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field $D^{*}$. We find the behavior of $D^{*}$ with $ν$ changes markedly as $B$ is reduced. At $ν= 2$, $D^{*}$ may even vanish when $B$ is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the $ν= 2$ state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for $D \sim D^{*}$ in the high $B$ regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.

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arXiv2022

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counterpropagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counterpropagating modes, which, by way of mode renormalization, may give rise to nontopological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.

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arXiv2022

Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes

Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of quantum Hall phases, and time-reversal invariant topological insulators. Here we study the edge of a 2D, topologically trivial insulating phase, as a function of the strength of the electronic interactions and the steepness of the confining potential. For sufficiently smooth confining potentials, alternating compressible and incompressible stripes appear at the edge. Our findings signal the emergence of gapless edge modes which may give rise to finite conductance at the edge. This would suggest a novel scenario of a nontopological metal-insulator transition in clean 2D systems. The incompressible stripes appear at commensurate fillings and may exhibit broken translational invariance along the edge in the form of charge density wave ordering. These are separated by structureless compressible stripes.

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arXiv2022

Parafermions in a multilegged geometry: Towards a scalable parafermionic network

Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero modes may also exist in multilegged star junctions of quantum Hall states. We demonstrate that the quantum states spanning the degenerate parafermionic Hilbert space may be detected and manipulated through protocols employing quantum antidots and fractional edge modes. Such star-shaped setups may be the building blocks of two-dimensional parafermionic networks.

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arXiv2022

Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

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arXiv2022

Enhancement of Superconductivity upon reduction of carrier density in proximitized graphene

The superconducting transition temperature (Tc) of a single layer graphene coupled to an Indium oxide (InO) film, a low carrier-density superconductor, is found to increase with decreasing carrier density and is largest close to the average charge neutrality point in graphene. Such an effect is very surprising in conventional BCS superconductors. We study this phenomenon both experimentally and theoretically. Our analysis suggests that the InO film induces random electron and hole-doped puddles in the graphene. The Josephson effect across these regions of opposite polarity enhances the Josephson coupling between the superconducting clusters in InO, along with the overall Tc of the bilayer heterostructure. This enhancement is most effective when the chemical potential of the system is tuned between the charge neutrality points of the electron and hole-doped regions.

cond-mat.supr-con↗

arXiv2022

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the $ν= 2/5$ phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream, and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at $ν= 1, 1/3$ and $2/5$ as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases, and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.

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arXiv2021

Fractional Edge Reconstruction in Integer Quantum Hall Phases

Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.

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