Scanning Tunneling Spectroscopy Experiments Research Articles

Dynamical Correlations and Order in Magic-Angle Twisted Bilayer Graphene

The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion 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 100 K, (ii) the ordering of the local isospin moments around 10 K 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 by Rozen [] and by Saito []. 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 ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments. Published by the American Physical Society 2024

Low‐Defect Quantum Dot Lasers Directly Grown on Silicon Exhibiting Low Threshold Current and High Output Power at Elevated Temperatures

The direct growth of III‐V materials on silicon is a key enabler for developing monolithically integrated lasers, offering substantial potential for ultradense photonic integration in vital communications and computing technologies. However, the III‐V/Si lattice and thermal expansion mismatch pose significant hurdles, leading to defects that degrade lasing performance. This study overcomes this challenge, demonstrating InAs/GaAs‐on‐Si lasers that perform on par with top‐tier lasers on native GaAs substrates. This is achieved through a newly developed epitaxial approach comprising a series of rigorously optimized growth strategies. Atomic‐resolution scanning tunneling microscopy and spectroscopy experiments reveal exceptional material quality in the active region and elucidate the impact of each growth strategy on defect dynamics. The optimized III‐V‐on‐silicon ridge‐waveguide lasers demonstrate a continuous‐wave threshold current as low as 6 mA and high‐temperature operation reaching 165 °C. At 80 °C, critical for data center applications, they maintain a 12 mA threshold and 35 mW output power. Furthermore, lasers fabricated on both Si and GaAs substrates using identical processes exhibit virtually identical average threshold current. By eliminating the performance limitations associated with the GaAs/Si mismatch, this study paves the way for robust and high‐density integration of a broad spectrum of critical III‐V photonic technologies into the silicon ecosystem.

Evidence of Nodal Superconductivity in Monolayer 1H-TaS2 with Hidden Order Fluctuations.

Unconventional superconductors represent one of the fundamental directions in modern quantum materials research. In particular, nodal superconductors are known to appear naturally in strongly correlated systems, including cuprate superconductors and heavy-fermion systems. Van der Waals materials hosting superconducting states are well known, yet nodal monolayer van der Waals superconductors have remained elusive. Here, using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) experiments, it is shown that pristine monolayer 1H-TaS2 realizes a nodal superconducting state. Non-magnetic disorder drives the nodal superconducting state to a conventional gapped s-wave state. Furthermore, many-body excitations emerge close to the gap edge, signalling a potential unconventional pairing mechanism. The results demonstrate the emergence of nodal superconductivity in a van der Waals monolayer, providing a building block for van der Waals heterostructures exploiting unconventional superconductingstates.

Effect of Coulomb impurities on the electronic structure of magic angle twisted bilayer graphene

In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1°). This suggests that the critical value of the defect charge in magic-angle tBLG should also be very small. We find that charged defects give rise to significant changes in the low-energy electronic structure of tBLG. Depending on the defect position in the moiré unit cell, it is possible to open a band gap or to induce an additional flattening of the low-energy valence and conduction bands. Our calculations suggest that the collapse states of the two monolayers hybridize in the twisted bilayer. However, their in-plane localization remains largely unaffected by the presence of the additional twisted layer because of the different length scales of the moiré lattice and the monolayer collapse state wavefunctions. These predictions can be tested in scanning tunneling spectroscopy experiments.

Search for large topological gaps in atomic spin chains on proximitized superconducting heavy-metal layers

One-dimensional systems comprising s-wave superconductivity with meticulously tuned magnetism realize topological superconductors hosting Majorana modes whose stability is determined by the gap size. However, for atomic spin chains on superconductors, the effect of the substrate’s spin-orbit coupling on the topological gap is largely unexplored. Here, we introduce an atomic layer of the heavy metal gold on a niobium surface combining strong spin-orbit coupling and a large superconducting gap with a high crystallographic quality, enabling the assembly of defect-free iron chains using a scanning tunneling microscope tip. Scanning tunneling spectroscopy experiments and density functional theory calculations reveal ungapped Yu–Shiba–Rusinov bands in the ferromagnetic chain despite the heavy substrate. By artificially imposing a spin spiral state, the calculations indicate minigap opening and zero-energy edge state formation. The methodology enables a material screening of heavy-metal layers on elemental superconductors for ideal systems hosting Majorana edge modes protected by large topological gaps.

Quantum confinement of electrons at metal surfaces

Scanning tunneling microscopy and spectroscopy experiments on surface-localized electron states confined to nanometer-scaled resonators are reviewed from the first observations to the recently discovered novel reflection mechanism of electron de Broglie waves. The focus of the presented work is on lateral confinement and on processes leading to finite decay rates of the confined states.

Spin chain on a metallic surface: Dissipation-induced order versus Kondo entanglement

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, $J_k$, to a two-dimensional electron gas. At weak $J_k$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large $J_k$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a unique negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

Effective Exchange Energy in a Thin, Spatially Inhomogeneous CuNi Layer Proximized by Nb.

Thin films of diluted magnetic alloys are widely used in superconducting spintronics devices. Most studies rely on transport measurements and assume homogeneous magnetic layers. Here we examine on a local scale the electronic properties of the well-known two-layer superconductor/ferromagnet structure Nb/CuNi. Scanning tunneling spectroscopy experiments demonstrated significant spatial variations of the tunneling conductance on nanoscale, with characteristic gapped, nongapped, and strongly zero-bias peaked spectra. The microscopic theory successfully reproduced the observed spectra and relied them to spatial variations of CuNi film thickness and composition, leading to strong variations of the effective exchange energy. The observed inhomogeneities put constraints on the use of diluted magnetic alloys in nanoscale devices.

Quasiparticle focusing of bound states in two-dimensional s -wave superconductors

A magnetic impurity on a superconducting substrate induces in-gap Yu-Shiba-Rusinov (YSR) bound states, whose intricate spatial structure crucially influences the possibilities of engineering collective impurity states. By means of a saddle-point approximation, we study the scattering processes giving rise to YSR states in gapped, two-dimensional superconductors. Further, we develop a theory, which relates through a simple analytical expression, an arbitrary energy dispersion of normal electrons in a two-dimensional host to the spatial features of the YSR states. Namely, we find that flatter segments of the Fermi surface with large Fermi velocity enhance the local density of states (LDOS) around the impurity. Our analytical approximation is quantitatively accurate against tight-binding calculations on various lattices with different Fermi surfaces, and it allows to predict the shape and orientation of YSR states observed in scanning tunneling spectroscopy experiments. We illustrate our results with a model of ${\mathrm{NbSe}}_{2}$.

Converting electrons into emergent fermions at a superconductor–Kitaev spin liquid interface

We study an interface between a Kitaev spin liquid (KSL) in the chiral phase and a non-chiral superconductor. When the coupling across the interface is sufficiently strong, the interface undergoes a transition into a phase characterized by a condensation of a bound state of a Bogoliubov quasiparticle in the superconductor and an emergent fermionic excitation in the spin liquid. In the condensed phase, electrons in the superconductor can coherently convert into emergent fermions in the spin liquid and vice versa. As a result, the chiral Majorana edge mode of the spin liquid becomes visible in the electronic local density of states at the interface, which can be measured in scanning tunneling spectroscopy experiments. We demonstrate the existence of this phase transition, and the non-local order parameter that characterizes it, using density matrix renormalization group simulations of a KSL strip coupled at its edge to a superconductor. An analogous phase transition can occur in a simpler system composed of a one-dimensional spin chain with a spin-flip $\mathbb{Z}_2$ symmetry coupled to a superconductor.

Zooming in on heavy fermions in Kondo lattice models

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as $e^{-W/J_k}$ with $W$ the bandwidth and $J_k$ the Kondo coupling, the residue of the composite fermion tracks $J_k$. This result holds down to $J_k/W = 0.05$, and confirms the point of view that magnetic ordering, present below $J_k/W = 0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for SU($N$) generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large $J_k$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.

Correlations among STM observables in disordered unconventional superconductors

New developments in scanning tunneling spectroscopy now allow for the spatially resolved measurement of the Josephson critical current ${I}_{c}$ between a tip and a superconducting sample, a nearly direct measurement of the true superconducting order parameter. However, it is unclear how these ${I}_{c}$ measurements are correlated with previous estimates of the spectral gap taken from differential conductance measurements. In particular, recent experiments on an iron-based superconductor found almost no correlation between ${I}_{c}$ and the spectral gap obtained from differential conductance $g=dI/dV$ spectra, reporting instead a more significant correlation between ${I}_{c}$ and the coherence-peak height. Here we point out that the correlation---or the lack thereof---between these various quantities can be naturally explained by the effect of disorder on unconventional superconductivity. Using large-scale numerical simulations of a BCS $d$-wave pair Hamiltonian with many-impurity potentials, we observe that ``substitutional'' disorder models with weak pointlike impurities lead to a situation in which the true superconducting order parameter and ${I}_{c}$ are both uncorrelated with the spectral gap from $dI/dV$ measurements and highly correlated with the coherence-peak heights. The underlying mechanism appears to be the disorder-induced transfer of spectral weight away from the coherence peaks. On the other hand, smooth impurity potentials with a length scale larger than the lattice constant lead to a large positive correlation between the true superconducting order parameter and the spectral gap, in addition to a large correlation between the order parameter and the coherence-peak height. We discuss the applicability of our results to recent Josephson scanning tunneling spectroscopy experiments on iron-based and cuprate high-temperature superconductors.

Synthesis and Properties of Monolayer MnSe with Unusual Atomic Structure and Antiferromagnetic Ordering.

Transition metal chalcogenides (TMCs) are a large family of 2D materials that are currently attracting intense interest. TMCs with 3d transition metals provide opportunities for introducing magnetism and strong correlations into the material with manganese standing out as a particularly attractive option due to its large magnetic moment. Here we report on the successful synthesis of monolayer manganese selenide on a NbSe2 substrate. Using scanning tunneling microscopy and spectroscopy experiments and global structure prediction calculations at the density functional theory level, we identify the atomic structure and magnetic and electronic properties of the layered Mn2Se2 phase. The structure is similar to the layered bulk phase of CuI or a buckled bilayer of h-BN. Interestingly, our results suggest that the monolayer is antiferromagnetic, but with an unusual out-of-plane ordering that results in two ferromagnetic planes.

(Invited) Visualizing 2D Materials at the Atomic Scale

Understanding and controlling the properties of 2D materials to our advantage can be contemplated with the development of experimental tools to probe and manipulate electrons and their interactions at the atomic scale. In this talk, I will present scanning tunnelling microscopy and spectroscopy experiments aimed at: elucidating the nature of atomic-scale defects in 2D materials, visualizing moiré patterns between crystals with different symmetries and imaging surface and edge states in a magnetic topological system. Moreover, I will discuss how we leverage our expertise in probing and engineering electronic states at surfaces of 2D materials to further the development of graphene-based gas sensors and gated quantum dot circuits based on 2D semiconductors. Figure 1

General, Strong Impurity-Strength Dependence of Quasiparticle Interference

Quasiparticle interference (QPI) patterns in momentum space are often assumed to be independent of the strength of the impurity potential when compared with other quantities, such as the joint density of states. Here, using the $T$-matrix theory, we show that this assumption breaks down completely even in the simplest case of a single-site impurity on the square lattice with an $s$ orbital per site. Then, we predict from first-principles, a very rich, impurity-strength-dependent structure in the QPI pattern of TaAs, an archetype Weyl semimetal. This study thus demonstrates that the consideration of the details of the scattering impurity including the impurity strength is essential for interpreting Fourier-transform scanning tunneling spectroscopy experiments in general.

Dissimilar Decoupling Behavior of Two-Dimensional Materials on Metal Surfaces.

The efficiency of hexagonal boron nitride and graphene to separate the hydrocarbon molecule C64H36 from Ru(0001) and Pt(111) surfaces is explored in low-temperature scanning tunneling microscopy and spectroscopy experiments. Both 2D materials enable the observation of the Franck-Condon effect in both frontier orbitals. On hexagonal boron nitride, vibronic progression with two vibrational energies gives rise to sharp orbital sidebands that are clearly visible up to the second order of the vibrational quantum number with different Huang-Rhys factors. In contrast, on graphene, orbital and vibronic spectroscopic signatures exhibit broad line shapes, with the second-order progression being hardly discriminable. Only a single vibrational quantum energy leaves its fingerprint in the Franck-Condon spectrum.

Superconducting-Gap Anisotropy of Iron Pnictides Investigated via Combinatorial Microwave Measurements

One of the most significant issues for superconductivity is clarifying the momentum-dependent superconducting gap Δ({boldsymbol{k}}), which is closely related to the pairing mechanism. To elucidate the gap structure, it is essential to investigate Δ({boldsymbol{k}}) in as many different physical quantities as possible and to crosscheck the results obtained in different methods with each other. In this paper, we report a combinatorial investigation of the superfluid density and the flux-flow resistivity of iron-pnictide superconductors; LiFeAs and BaFe2(As1−xPx)2 (x = 0.3, 0.45). We evaluated Δ({boldsymbol{k}}) by fitting these two-independent quantities with a two-band model simultaneously. The obtained Δ({boldsymbol{k}}) are consistent with the results observed in angle-resolved photoemission spectroscopy (ARPES) and scanning-tunneling spectroscopy (STS) studies. We believe our approach is a powerful method for investigating Δ({boldsymbol{k}}) because it does not require a sample with clean surface unlike ARPES and STS experiments, or a rotational magnetic-field system for direct measurements of the angular dependence of thermodynamic quantities.

Proximity-Induced Superconductivity in Monolayer MoS2.

Proximity effects in superconducting normal (SN) material heterostructures with metals and semiconductors have long been observed and theoretically described in terms of Cooper pair wave functions and Andreev reflections. Whereas the semiconducting N-layer materials in the proximity experiments to date have been doped and tens of nanometers thick, we present here a proximity tunneling study involving a pristine single-layer transition-metal dichalcogenide film of MoS2 placed on top of a Pb thin film. Scanning tunneling microscopy and spectroscopy experiments together with parallel theoretical analysis based on electronic structure calculations and Green's function modeling allow us to unveil a two-step process in which MoS2 first becomes metallic and then is induced into becoming a conventional s-wave Bardeen-Cooper-Schrieffer-type superconductor. The lattice mismatch between the MoS2 overlayer and the Pb substrate is found to give rise to a topographic moiré pattern. Even though the induced gap appears uniform in location, the coherence peak height of the tunneling spectra is modulated spatially into a moiré pattern that is similar to but shifted with respect to the moiré pattern observed in topography. The aforementioned modulation is shown to originate from the atomic-scale structure of the SN interface and the nature of local atomic orbitals that are involved in generating the local pairing potential. Our study indicates that the local modulation of induced superconductivity in MoS2 could be controlled via geometrical tuning, and it thus shows promise toward the integration of monolayer superconductors into next-generation functional electronic devices by exploiting proximity-effect control of quantum phases.

Singularities and topologically protected states in twisted bilayer graphene

We have studied the structural and electronic properties of twisted bilayer graphene by scanning tunneling microscopy (STM). For twist angles in the range of about 1° to 4°, the twisted bilayer graphene possesses two Van Hove singularities in the vicinity of the Fermi level. We use the exact location of these Van Hove singularities to determine the twist angle dependent interlayer hopping energy. For a twist angle of 0.6°, we found a hexagonal network of topologically protected one-dimensional channels that run along the boundaries of the AB/BA domains. The electric field in the tunnel junction is responsible for the breaking of the symmetry of the AB and BA domains and the development of the hexagonal network of topologically protected states. The latter shows that the electric field in the tunneling junction can significantly affect the topological nature of two-dimensional materials, and therefore, one should be cautious when interpreting scanning tunneling microscopy and spectroscopy experiments of this class of materials.

Enhanced, homogeneously type-II superconductivity in Cu-intercalated PdTe2

Though the superconducting phase of the type-II Dirac semimetal PdTe2 was shown to be conventional in nature, the phase continued to be interesting in terms of its magnetic properties. While certain experiments indicated an unexpected type-I superconducting phase, other experiments revealed formation of vortices under the application of magnetic fields. Recently, scanning tunneling spectroscopy (STS) experiments revealed the existence of a mixed phase where type-I and type-II behaviours coexist. Here, based on our temperature and magnetic field dependent STS experiments on Cu-intercalated PdTe2, we show that as the critical temperature of the superconducting phase goes up from 1.7 K to 2.4 K on Cu-intercalation, the mixed phase disappears and the system becomes homogeneously type-II. This may be attributed to an averaging effect caused by quasiparticle exchange between type-I and type-II domains mediated by the Cu atoms and to decreased coherence length due to increased disorder.