arXiv subjects

Marcel Franz

Publications and source records attributed to Marcel Franz.

At least 37 records · Page 2Linked to original sources

arXiv2024

NMon: enhanced transmon qubit based on parallel arrays of Josephson junctions

We introduce a novel superconducting qubit architecture utilizing parallel arrays of Josephson junctions. This design offers a substantialy improved relative anharmonicity, typically within the range of $|α_r| \approx 0.1 - 0.3$, while maintaining transition matrix elements in both the charge and flux channels that are on par with those of transmon qubits. Our proposed device also features exceptional tunability and includes a parameter regime akin to an enhanced version of the fluxonium qubit. Notably, it enables an additional order of magnitude reduction in matrix elements influenced by flux noise, thus further enhancing its suitability for quantum information processing applications.

quant-ph↗

arXiv2024

Quantum-Geometric Origin of Out-of-plane Stacking Ferroelectricity

Stacking ferroelectricity (SFE) has been discovered in a wide range of van der Waals materials and holds promise for applications, including photovoltaics and high-density memory devices. We show that the microscopic origin of out-of-plane stacking ferroelectric polarization can be generally understood as a consequence of nontrivial Berry phase borne out of an effective Su-Schrieffer-Heeger model description with broken sublattice symmetry, thus elucidating the quantum-geometric origin of polarization in the extremely non-periodic bilayer limit. Our theory applies to known stacking ferroelectrics such as bilayer transition-metal dichalcogenides in 3R and T$_{\rm d}$ phases, as well as general AB-stacked honeycomb bilayers with staggered sublattice potential. Our explanatory and self-consistent framework based on the quantum-geometric perspective establishes quantitative understanding of out-of-plane SFE materials beyond symmetry principles.

cond-mat.mtrl-sci↗

arXiv2023

Quantum error mitigation in quantum annealing

Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude.

quant-ph↗

arXiv2023

Cu-substituted lead phosphate apatite as an inversion-asymmetric Weyl semimetal

Based on symmetry arguments and the latest density functional results for the copper-substituted lead phosphate apatite (`LK-99'), we show that, at the non-interacting level, the material is an inversion-asymmetric Weyl semimetal. A pair of Weyl nodes with opposite chiralities emerge at different energies in the vicinity of the time-reversal-invariant $Γ$ and ${\rm A}$ points of the 3D Brillouin zone. These are characterized by unusual Weyl charges of $C_{\rm W} = \pm 2$ and are connected by two branches of topologically protected Fermi arc states on surfaces parallel to the principal $c$-axis. We further study important effects of the atomic spin-orbit coupling on the band structure and the electronic properties of the material in general. Possible implications of the proposed band topology on the strong correlation physics are also discussed.

cond-mat.mtrl-sci↗

arXiv2023

$d$-mon: transmon with strong anharmonicity

We propose a novel qubit architecture based on a planar $c$-axis Josephson junction between a thin flake $d$-wave superconductor ($d$SC), such as a high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$, and a conventional $s$-wave superconductor. When operated in the transmon regime the device -- that we call "$d$-mon" -- becomes insensitive to offset charge fluctuations and, importantly, exhibits at the same time energy level spectrum with strong anharmonicity that is widely tunable through the device geometry and applied magnetic flux. Crucially, unlike previous qubit designs based on $d$-wave superconductors the proposed device operates in a regime where quasiparticles are fully gapped and can be therefore expected to achieve long coherence times.

cond-mat.supr-con↗

arXiv2023

Josephson diode effects in twisted nodal superconductors

Recent Josephson tunneling experiments on twisted flakes of high-$T_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ revealed a non-reciprocal behavior of the critical interlayer Josephson current - i.e., a Josephson diode effect. Motivated by these findings we study theoretically the emergence of the Josephson diode effect in twisted interfaces between nodal superconductors, and highlight a strong dependence on the twist angle $θ$ and damping of the junction. In all cases, the theory predicts diode efficiency that vanishes exactly at $θ= 45^\circ$ and has a strong peak at a twist angle close to $θ= 45^\circ$, consistent with experimental observations. Near $45^\circ$, the junction breaks time-reversal symmetry ${\cal T}$ spontaneously. We find that for underdamped junctions showing hysteretic behavior, this results in a \emph{dynamical} Josephson diode effect in a part of the ${\cal T}$-broken phase. The direction of the diode is trainable in this case by sweeping the external current bias. This effect provides a sensitive probe of spontaneous ${\cal T}$-breaking. We then show that explicit ${\cal T}$-breaking perturbations with the symmetry of a magnetic field perpendicular to the junction plane lead to a {\em thermodynamic} diode effect that survives even in the overdamped limit. We discuss an experimental protocol to probe the double-well structure in the Josephson free energy that underlies the tendency towards spontaneous ${\cal T}$-breaking even if ${\cal T}$ is broken explicitly. Finally, we show that in-plane magnetic fields can control the diode effect in the short junction limit, and predict the signatures of explicit ${\cal T}$-breaking in Shapiro steps.

cond-mat.supr-con↗

arXiv2022

Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors

Recent theoretical and experimental studies point to a novel spin-triplet valley-singlet (STVS) superconducting phase in certain two-valley electron liquids, including rhombohedral trilayer graphene, Bernal bilayer graphene and ZrNCl. This fully gapped phase is exotic in that it combines into Cooper pairs same-spin electrons from valleys centered around the opposing corners of a hexagonal Brillouin zone, but is, nevertheless, topologically trivial. Here, we predict that upon stacking two layers of an STVS material with an angular twist, a novel chiral topological phase -- an $f \pm if'$-wave superconductor -- emerges in the vicinity of the `maximal' twist angle of 30$^{\circ}$ where the system becomes an extrinsic quasi-crystal with 12-fold tiling. The resulting composite is a non-Abelian topological superconductor (TSC) with an odd number of chiral Majorana modes at its edges and a single Majorana zero mode (MZM) localized in the vortex core. Through symmetry analysis and detailed microscopic modelling based on a novel quasi-crystal band structure technique, we demonstrate that the non-Abelian TSC forms when the isolated Fermi pockets coalesce into a single connected Fermi surface around the center of the moiré Brillouin zone and is stable over a wide range of electron density. We further discuss how the energetics leading to the $f \pm if'$-wave phase results in anomalous $π$-periodic inter-layer Josephson effect, which can serve as a distinctive signature of the chiral phase. Distinct from the valley-preserving moiré physics in small-angle twisted graphene, our results establish the large-angle moiré physics arising near maximal twist as a new avenue toward intrinsic TSC with non-Abelian excitations.

cond-mat.supr-con↗

arXiv2022

Chiral Majorana Modes via Proximity to a Twisted Cuprate Bilayer

We propose a novel heterostructure to achieve chiral topological superconductivity in 2D. A substrate with a large Rashba spin-orbit coupling energy is brought in proximity to a twisted bilayer of thin films exfoliated from a high-temperature cuprate superconductor. The combined system is then exposed to an out-of-plane magnetic field. The rare $d + id$ pairing symmetry expected to occur in such a system allows for nontrivial topology; specifically, in contrast to the case of the twisted bilayer in isolation, the substrate induces an odd Chern number. The resulting phase is characterized by the presence of a Majorana zero mode in each vortex.

cond-mat.supr-con↗

arXiv2022

Twisted multilayer nodal superconductors

Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two high-symmetry stackings with alternating ($\pm θ$) and constant ($θ$) twist angles. In analogy to alternating-twist multilayer graphene, the former can be mapped to twisted bilayers with renormalized interlayer couplings, along with a remnant gapless monolayer when the number of layers $L$ is odd. In contrast, the latter exhibits physics beyond twisted bilayers, including the occurrence of `magic angles' characterized by cubic band crossings when $L \mod 4 = 3$. Owing to their power-law divergent density of states, such multilayers are highly susceptible to secondary instabilities. Within a BCS mean-field theory, defined in the continuum and on a lattice, we find that both stackings host chiral topological superconductivity in extended regions of their phase diagrams.

cond-mat.supr-con↗

arXiv2022

Majorana zero modes in a magnetic and superconducting hybrid vortex

We propose and investigate a new platform for the realization of Majorana zero modes in a thin-film heterostructure composed of an easy-plane ferromagnet and a superconductor with spin-orbit coupling. The system can support an energetically favorable bound state comprising a magnetic and a superconducting vortex. We show that a hybrid vortex thus created can host a robust zero-energy Majorana bound state at its core over a wide range of parameters, with its partner zero mode located at the outer boundary of a disk-shaped topological region. We identify a novel mechanism underlying the formation of the topological phase that, remarkably, relies on the orbital effect of the magnetization field and not on the usual Zeeman effect. The in-plane components of magnetization couple to electrons as a gauge potential with non-zero curl, thus creating an emergent magnetic field responsible for the gapped topologically non-trivial region surrounding the vortex core. Our construction allows the mobility of magnetic vortices to be imposed on the Majorana zero mode at the core of the superconducting vortex. In addition, the system shows a rich interplay between magnetism and superconductivity which might aid in developing future devices and technologies.

cond-mat.supr-con↗

arXiv2022

Incoherent tunneling and topological superconductivity in twisted cuprate bilayers

Twisting two monolayers of a high-$T_c$ cuprate superconductor can engender a chiral topological state with spontaneously broken time reversal symmetry $\mathcal{T}$. A crucial ingredient required for the emergence of a gapped topological phase is electron tunneling between the CuO$_2$ planes, whose explicit form (in an ideal clean sample) is dictated by the symmetry of the atomic orbitals. However, a large body of work on the interlayer transport in cuprates indicates importance of disorder-mediated incoherent tunneling which evades the symmetry constraints present in an idealized crystal. The latter arises even in the cleanest single-crystal samples through oxygen vacancies in layers separating the CuO$_2$ planes, introduced to achieve the hole doping necessary for superconductivity. Here we assess the influence of incoherent tunneling on the phase diagram of a twisted bilayer. We show that the model continues to support a fully gapped topological phase with broken $\mathcal{T}$, even in the limit of disorder-mediated interlayer coupling. Compared to the model with a constant, momentum conserving interlayer coupling, the extent of the topological phase around the 45$^\circ$ twist decreases with increasing incoherence, but remains robustly present for parameters likely relevant to Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$.

cond-mat.supr-con↗

arXiv2022

Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS$_2$

We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1/2$-filling into a valley-polarized state, which realizes a correlated quantum anomalous Hall state with Chern number $\mathcal{C} = \pm 2$. Effects of displacement fields are discussed with comparison to nontrivial topology from layer-pseudospin magnetic fields.

cond-mat.mes-hall↗

arXiv2022

Spontaneous Polarization Induced Photovoltaic Effect In Rhombohedrally Stacked MoS$_2$

Stacking order in van der Waals materials determines the coupling between atomic layers and is therefore key to the materials' properties. By exploring different stacking orders, many novel physical phenomena have been realized in artificial vdW stacks. Recently, 2D ferroelectricity has been observed in zero-degree aligned hBN and graphene-hBN heterostructures, holding promise in a range of electronic applications. In those artificial stacks, however, the single domain size is limited by the stacking-angle misalignment to about 0.1 to 1 $μ$m, which is incompatible with most optical or optoelectronic applications. Here we show MoS$_2$ in the rhombohedral phase can host a homogeneous spontaneous polarization throughout few-$μ$m-sized exfoliated flakes, as it is a natural crystal requiring no stacking and is, therefore free of misalignment. Utilizing this homogeneous polarization and its induced depolarization field (DEP), we build a graphene-MoS$_2$ based photovoltaic device with high efficiency. The few-layer MoS$_2$ is thinner than most oxide-based ferroelectric films, which allows us to maximize the DEP and study its impact at the atomically thin limit, while the highly uniform polarization achievable in the commensurate crystal enables a tangible path for up-scaling. The external quantum efficiency of our device is up to 16% at room temperature, over one order larger than the highest efficiency observed in bulk photovoltaic devices, owing to the reduced screening in graphene, the exciton-enhanced light-matter interaction, and the ultrafast interlayer relaxation in MoS$_2$. In view of the wide range of bandgap energy in other TMDs, our findings make rhombohedral TMDs a promising and versatile candidate for applications such as energy-efficient photo-detection with high speed and programmable polarity.

cond-mat.mes-hall↗

arXiv2021

Magnetic suppression of non-Hermitian skin effects

Skin effect, where macroscopically many bulk states are aggregated towards the system boundary, is one of the most important and distinguishing phenomena in non-Hermitian quantum systems. We discuss a new aspect of this effect whereby, despite its topological origin, applying magnetic field can largely suppress it. Skin states are pushed back into the bulk and the skin topological area, which we define, is sharply reduced. As seen from exact solutions of representative models this is fundamentally rooted in the fact that the applied magnetic field restores the validity of the low-energy description that is rendered inapplicable in the presence of non-Bloch skin states. We further study this phenomenon using rational gauge fluxes, which reveals a unique irrelevance of the generalized Brillouin zone in the standard non-Bloch band theory of non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2021

Emergent Interfacial Superconductivity between Twisted Cuprate Superconductors

Twisted interfaces between stacked van der Waals cuprate crystals enable tunable Josephson coupling between in-plane anisotropic superconducting order parameters. Employing a novel cryogenic assembly technique, we fabricate Josephson junctions with an atomically sharp twisted interface between Bi2Sr2CaCu2O8+x crystals. The Josephson critical current density sensitively depends on the twist angle, reaching the maximum value comparable to that of the intrinsic junctions at small twisting angles, and is suppressed by almost 2 orders of magnitude yet remains finite close to 45 degree twist angle. Through the observation of fractional Shapiro steps and the analysis of Fraunhofer patterns we show that the remaining superconducting coherence near 45 degree is due to the co-tunneling of Cooper pairs, a necessary ingredient for high-temperature topological superconductivity.

cond-mat.supr-con↗

arXiv2021

Josephson effects in twisted cuprate bilayers

Twisted bilayers of high-$T_c$ cuprate superconductors have been argued to form topological phases with spontaneously broken time reversal symmetry ${\cal T}$ for certain twist angles. With the goal of helping to identify unambiguous signatures of these topological phases in transport experiments, we theoretically investigate a suite of Josephson phenomena between twisted layers. We find an unusual non-monotonic temperature dependence of the critical current at intermediate twist angles which we attribute to the unconventional sign structure of the $d$-wave order parameter. The onset of the ${\cal T}$-broken phase near $45^\circ$ twist is marked by a crossover from the conventional $2π$-periodic Josephson relation $J(φ)\simeq J_c\sinφ$ to a $π$-periodic function as the single-pair tunneling becomes dominated by a second order process that involves two Cooper pairs. Despite this fundamental change, the critical current remains a smooth function of the twist angle $θ$ and temperature $T$ implying that a measurement of $J_c$ alone will not be a litmus test for the ${\cal T}$-broken phase. To obtain clear signatures of the ${\cal T}$-broken phase one must measure $J_c$ in the presence of an applied magnetic field or radio-frequency drive, where the resulting Fraunhofer patterns and Shapiro steps are altered in a characteristic manner. We discuss these results in light of recent experiments on twisted bilayers of the high-$T_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$.

cond-mat.supr-con↗

arXiv2021

Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model

We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time reversal symmetry, which can be solved exactly in the limit of a large number $N$ of degrees of freedom. At low temperature, its phase diagram includes a compressible non-Fermi liquid and a strongly-correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a non-zero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction, and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.

cond-mat.str-el↗

arXiv2021

Probing time reversal symmetry breaking topological superconductivity in twisted double layer copper oxides with polar Kerr effect

Recent theoretical work predicted emergence of chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-$T_c$ cuprate monolayers, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. Here we identify large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the $\mathcal{T}$-broken phase. Our modelling predicts the Kerr angle $θ_K$ to be in the range of 10-100 $μ$rad, which is a factor of $10^3-10^4$ times larger than what is expected for the leading chiral supercondutor candidate Sr$_2$RuO$_4$. In addition we show that the optical Hall conductivity $σ_H(ω)$ can be used to distinguish between the topological $d_{x^2-y^2}\pm id_{xy}$ phase and the $d_{x^2-y^2}\pm is$ phase which is also expected to be present in the phase diagram but is topologically trivial.

cond-mat.supr-con↗