arXiv subjects

Christian Spånslätt

Publications and source records attributed to Christian Spånslätt.

At least 19 recordsLinked to original sources

arXiv2026

Extracting the anyon charge from shot noise in complex fractional quantum Hall edges

Shot-noise measurements with a quantum point contact provide a direct probe of the quasiparticle charge in Laughlin fractional quantum Hall (FQH) states. However, the interpretation of such measurements becomes more subtle for multichannel edges, where the point-contact tunneling noise coexists with noise generated by intermode equilibration and heating. We develop a general framework that incorporates both these contributions and apply it to the paradigmatic $ν=2/3$ FQH edge. We derive expressions for the drain auto- and cross-correlations in a four-terminal QPC geometry and show that equilibration-induced heating affects the auto- and cross-correlations in parametrically different way than the intrinsic partition noise. This distinction permits us to propose a specific combination of the two correlations which strongly suppresses the heating contribution and fully recovers the tunneling quasiparticle charge. Our results thereby provide a systematic framework for interpreting shot-noise measurements in complex FQH edges and can be further extended to more general counterpropagating edge structures.

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arXiv2026

Non-equilibrium bosonization of fractional quantum Hall edges

Edge transport serves as a powerful probe of remarkable low-energy properties of fractional quantum Hall states, including the anyonic character of their excitations. Here, we develop a theory of fractional quantum Hall edges driven out of equilibrium, which is based on the Keldysh action for the bosonized chiral Luttinger liquid. With this non-equilibrium FQH bosonization framework, we first consider a single-mode Laughlin edge and analyze the full counting statistics of charge, the quasiparticle Green's functions, and tunneling transport properties through a quantum point contact, allowing for generic edge excitations. We then extend the formalism to multi-mode edges with inter-mode interactions, and explore, with focus on the $ν=4/3$ and $ν=2/3$ edges as paradigmatic examples, how interaction-induced fractionalization of anyons modifies the edge dynamics and the associated transport observables. While the full counting statistics probes the fractionalized charge of the excitations, the Green's functions and tunneling transport are governed by mutual braiding phases of fractionalized excitations and tunneling quasiparticles. We emphasize in particular the effect of interaction-induced fractionalization on the Fano factor $F$ and the differential Fano factor $F_d$, observables that can be measured experimentally. Our formalism, which provides a unified framework for non-equilibrium transport in FQH edges and Luttinger liquids, permits extracting anyonic braiding information from non-equilibrium edge-transport experiments, and paves the way to various extensions, including more involved experimental geometries and edge structures.

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arXiv2026

Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias

Continued improvement of heat control in mesoscopic conductors brings novel tools for probing strongly correlated electron phenomena. Motivated by these advances, we comprehensively study transport due to a temperature bias in a quantum point contact device in the fractional quantum Hall regime. We compute the charge-current noise (so-called delta-$T$ noise), heat-current noise, and mixed noise and elucidate how these observables can be used to infer strongly correlated properties of the device. Our main focus is the extraction of so-called scaling dimensions of the tunneling anyonic quasiparticles, of critical importance to correctly infer their anyonic exchange statistics.

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arXiv2025

Exchange-phase erasure in anyonic Hong-Ou-Mandel interferometry

Two-particle interferometry is an important tool for extracting the exchange statistics of quantum particles. We theoretically investigate the prospects of such interferometry to probe the statistics of point-like anyonic excitations injected in a Hong-Ou-Mandel (HOM) setup based on a quantum point contact device in the fractional quantum Hall regime. We compute the standard HOM ratio, i.e., the ratio of tunneling noises for two- and one-particle injections, and find that for point-like anyons, it only depends on the temperature and the anyon scaling dimension. Importantly, the latter is not necessarily related to the exchange phase. In fact, we establish that the HOM ratio does not reveal the exchange phase of the injected anyons: For injection-time delays that are small compared to the thermal time scale, we find that the exchange phase accumulated due to time-domain braiding between injected and thermally activated anyons is erased due to two mutually canceling sub-processes. In contrast, for time delays large compared to the thermal time, only a single sub-process contributes to the braiding, but the accumulated phase is canceled in the HOM ratio. These findings suggest caution when interpreting HOM interferometry experiments with anyons and approaches beyond the standard HOM ratio are thus necessary to extract anyonic statistics with two-particle interferometry experiments.

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arXiv2025

Thermodynamic and energetic constraints on transition probabilities of small-scale quantum systems

We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared at different temperatures, which both turn out to be particularly restrictive when the measured quantum system is small. These bounds take the form of a thermodynamic and of an energetic constraint, as they are associated with the dissipated heat and with the absorbed energy required to increase or to reduce the temperature of the system. The derived constraints apply to arbitrary system Hamiltonians, including interactions or non-linear energy spectra. We show the relevance of these constraints for the special case where transitions are induced by energy or particle exchange in weakly coupled bipartite systems out of equilibrium. This example is of interest for a wide range of experimentally relevant systems, from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise.

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arXiv2024

Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime

We present a broad study of charge and heat transport in a mesoscopic system where one or several quantum Hall edge channels are strongly coupled to a floating Ohmic contact (OC). It is well known that charge-current fluctuations emanating from the OC along the edge channels are highly susceptible to the OC charge capacitance in the heat Coulomb blockade regime (an impeded ability of the OC to equilibrate edge channels). Here, we demonstrate how potential- and temperature fluctuations due to finite OC charge and heat capacities impact the heat-current fluctuations emitted from the OC. First, by assuming an infinite OC heat capacity, we show that the output heat-current noise is strongly dependent on the OC charge capacitance, following from a close relation between one-dimensional charge- and heat currents. When also the OC heat capacity is finite, an interplay of potential- and temperature fluctuations influences the heat transport. Concretely, we find that the effect of the charge capacitance on heat transport manifests in terms of a strongly increased energy relaxation time in the heat Coulomb blockade regime. Furthermore, we find expressions for a broad set of output observables, such as charge and heat auto- and cross correlations, as functions of input and OC fluctuations, depending on the relation between charge and energy relaxation times compared to the frequency of fluctuations and inverse (local) temperatures as well as on the number of edge channels attached to the OC. Finally, we show that a finite OC heat capacity transforms the full counting statistics of the output charge from Gaussian to non-Gaussian. Our findings provide novel opportunities to experimentally probe and harness the quantum nature of heat transport in strongly coupled electron circuits.

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arXiv2024

Fingerprints of anti-Pfaffian topological order in quantum point contact transport

Despite recent experimental developments, the topological order of the fractional quantum Hall state at filling $ν=5/2$ remains an outstanding question. We study conductance and shot noise in a quantum point contact device in the charge-equilibrated regime and show that, among Pfaffian, particle-hole Praffian, and anti-Pfaffian (aPf) candidate states, the hole-conjugate aPf state is unique in that it can produce a conductance plateau at $G=(7/3)e^2/h$ by two fundamentally distinct mechanisms. We demonstrate that these mechanisms can be distinguished by shot noise measurements on the plateaus. We also determine distinct features of the conductance of the aPf state in the coherent regime. Our results can be used to experimentally single out the aPf order.

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arXiv2023

Thermal conductance and noise of Majorana modes along interfaced $ν=5/2$ fractional quantum Hall states

We study transport along interfaced edge segments of fractional quantum Hall states hosting non-Abelian Majorana modes. With an incoherent model approach, we compute, for edge segments based on Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian topological orders, thermal conductances, voltage biased noise, and delta-$T$ noise. We determine how the thermal equilibration of edge modes impacts these observables and identify the temperature scalings of transitions between regimes of differently quantized thermal conductances. In combination with recent experimental data, we use our results to estimate thermal and charge equilibration lengths in real devices. We also propose an experimental setup which permits measuring several transport observables for interfaced fractional quantum Hall edges in a single device. It can, e.g., be used to rule out edge reconstruction effects. In this context, we further point out some subtleties in two-terminal thermal conductance measurements and how to remedy them. Our findings are consistent with recent experimental results pointing towards a particle-hole-Pfaffian topological order at filling $ν=5/2$ in GaAs/AlGaAs, and provide further means to pin-point the edge structure at this filling and possibly also other exotic fractional quantum Hall states.

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arXiv2023

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

Nonequilibrium situations where selected currents are suppressed are of interest in fields like thermoelectrics and spintronics, raising the question of how the related noises behave. We study such zero-current charge, spin, and heat noises in a two-terminal mesoscopic conductor. In the presence of voltage, spin and temperature biases, the nonequilibrium (shot) noises of charge, spin, and heat can be arbitrarily large, even if their average currents vanish. However, as soon as a temperature bias is present, additional equilibrium (thermal-like) noise necessarily occurs. We show that this equilibrium noise sets an upper bound on the zero-current charge and spin shot noises, even if additional voltage or spin biases are present. We demonstrate that these bounds can be overcome for heat transport by breaking the spin and electron-hole symmetries, respectively. By contrast, we show that the bound on the charge noise for strictly two-terminal conductors even extends into the finite-frequency regime.

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arXiv2023

Transport Signatures of Fractional Quantum Hall Binding Transitions

Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a ``binding transition'' remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling $ν=9/5$. We demonstrate theoretically that in the regime of non-equilibrated edge transport, the bound and unbound edge phases have distinct conductance and noise characteristics. We also show that for a quantum point contact in the strong back-scattering regime, the bound phase produces a minimum Fano-factor $F_{SBS}=3$ corresponding to three-electron tunneling, whereas single electron tunneling is strongly suppressed at low energies. Together with recent experimental developments, our results will be useful for detecting binding transitions in the fractional quantum Hall regime.

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arXiv2022

Determination of topological edge quantum numbers of fractional quantum Hall phases

To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream ($N_d$) and upstream ($N_u$) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance $G_{Q}$, which is purely governed by edge quantum numbers $N_d$ and $N_u$. Our experimental setup is realized with a hBN encapsulated graphite gated monolayer graphene device. For temperatures up to $35mK$, our measured $G_{Q}$ at $ν= $ 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime $(N_d + N_u)κ_{0}T$, where $κ_{0}T$ is a quanta of $G_{Q}$. With increasing temperature, $G_{Q}$ decreases and eventually takes the value of equilibrated regime $|N_d - N_u|κ_{0}T$. By contrast, at $ν= $1/3 and 2/5 (without CP modes), $G_Q$ remains robustly quantized at $N_dκ_{0}T$ independent of the temperature. Thus, measuring the quantized values of $G_{Q}$ at two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

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arXiv2022

Does delta-$T$ noise probe quantum statistics?

We study delta-T noise -- excess charge noise at zero voltage but finite temperature bias -- for weak tunneling in 1D interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process (more specifically, its scaling dimension). We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Boson-like particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This particularly implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the thermal noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons. Our findings show that delta-T noise can probe the nature of collective excitations in interacting 1D systems.

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arXiv2021

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream'' modes, moving against the direction of charge current flow, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here we report on noise measurements at the edges of fractional QH (FQH) phases realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at $L= 4\,μ$m or $10\,μ$m away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for ``hole-conjugate'' FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remaining independent of length together with a remarkable agreement with our theoretical analysis demonstrates the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems. Our investigation opens the door to the study of upstream transport in more complex geometries and in edges of non-Abelian phases in graphene.

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arXiv2021

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. This new understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state.

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arXiv2021

Vanishing thermal equilibration for hole-conjugate fractional quantum Hall states in graphene

Transport through edge-channels is responsible for conduction in quantum Hall (QH) phases. Topology dictates quantization of both charge and thermal transport coefficients. These turn out to approach robust quantized values when incoherent equilibration processes become dominant. Here, we report on measurements of both electrical and thermal conductances of integer and fractional quantum Hall (FQH) phases, realized in hBN encapsulated graphite gated bilayer graphene devices. Remarkably, for the complex edge at filling factors $ν=5/3$ and $ν=8/3$, which correspond to the paradigmatic hole-conjugate FQH phase $ν=2/3$ of the partially filled Landau level, we find vanishing thermal equilibration. This is striking, given that, at the same time, our results for the electrical conductance indicate efficient charge equilibration. These results are in accord with our theoretical analysis, pointing to a divergent thermal equilibration length in the limit of strong electrostatic interaction. Our results elucidate the subtle nature of the crossover from mesoscopic to robust topology-dominated transport in electronic two-dimensional topological phases.

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arXiv2020

Noise on the Non-Abelian $ν=5/2$ Fractional Quantum Hall Edge

The recent measurement of a half-integer thermal conductance for the $ν=5/2$ fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the shot noise at the edge of the three most prominent non-Abelian candidate states. We show that the noise scaling with respect to the edge length can, in combination with the thermal conductance, be used to experimentally distinguish between the Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian edge structures.

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arXiv2020

Distinguishing between Topological and Quasi Majorana Zero Modes with a Dissipative Resonant Level

Distinguishing between topological Majorana zero modes and quasi Majorana modes -- trivial low energy Andreev bound states -- is an important step towards realizing topological hybrid nanowire devices. We propose that this distinction can be made by connecting a hybrid nanowire to a dissipative resonant level realized by a quantum dot weakly coupled to high resistance leads. We show that the qualitative temperature scaling of the width of the resonant level zero bias conductance peak provides a signature unique to true Majorana zero modes. The degeneracy induced by a true Majorana zero mode is further shown to stabilize this conductance peak against particle-hole asymmetry.

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arXiv2019

Non-local order parameters for states with topological electromagnetic response

Chern insulators are states of matter characterized by a quantized Hall conductance, gapless edge modes but also a singular response to monopole configurations of an external electromagnetic field. In this paper, we describe the nature of such a singular response and show how it can be used to define a class of operators acting as non-local order parameters. These operators characterize the Chern-insulator states in the following way: for a given state, there exists a corresponding operator which has an algebraically decaying two-point function in that particular state, while it decays exponentially in all other states. The behaviour of the order parameter is defined only in terms of the electromagnetic response, and not from any microscopic properties, and we therefore claim to have found a generic order parameter for the Chern insulating states. We support this claim by numerically evaluating the order parameters for different insulating states. We also show how our construction can be generalized to other states with topological electromagnetic response, and use the states with a quantized magnetoelectric effect in three dimensions as an example. Besides providing novel insights into topological states of matter, our construction can be exploited to efficiently diagnose such states numerically.

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