Direct signatures of $d$-level hybridization and dimerization in magnetic adatom chains on a superconductor

This study demonstrates that Fe adatoms on 2H-NbSe$_2$ undergo spin quenching via $d$-level hybridization to form stable non-magnetic dimers, resulting in distinct ground states for even and odd chains where odd chains host a switchable end-state magnetic atom, thereby highlighting the potential for engineering topological systems through controlled dimerization.

The Gist

Imagine you are a tiny architect working on a microscopic construction site. Your building material is a superconductor (a special metal that conducts electricity with zero resistance), and your "bricks" are individual iron atoms.

This paper is about what happens when you stack these iron bricks on top of the superconductor, specifically looking at how they behave when they are far apart versus when they are glued right next to each other.

Here is the story of their interactions, explained simply:

1. The Lonely Iron Atom (The Soloist)

When you place a single iron atom on this superconductor, it acts like a loud, energetic soloist.

• The Spin: The atom has a "magnetic spin" (think of it as a tiny internal compass or a spinning top). In this case, it's spinning quite vigorously (a spin of 2).
• The Echo: Because the atom is magnetic and sitting on a superconductor, it creates a special "echo" or ripple in the superconductor's energy field. Scientists call these Yu-Shiba-Rusinov (YSR) states. You can hear these echoes as distinct peaks in a spectrograph.
• The Result: A single atom is magnetic, loud, and clearly visible in the data.

2. The Neighbors Get Too Close (The Duet)

Now, imagine you push a second iron atom right next to the first one, so they are touching (nearest neighbors).

• The Hybridization: Instead of just standing next to each other, their internal "d-levels" (the electron clouds where their magic happens) start to merge. It's like two singers trying to harmonize so perfectly that they become a single voice.
• The Silence: When they merge, something magical happens: The magnetism disappears. The two atoms pair up their spins in opposite directions (one up, one down), canceling each other out. They form a "singlet" state.
• The Result: The loud soloist echoes (YSR states) vanish completely. The pair becomes a quiet, non-magnetic unit. It's as if the two atoms held hands and decided to go to sleep together, ignoring the superconductor around them.

3. Building a Chain (The Line of Dancers)

The researchers then started building long chains of these iron atoms. They noticed a fascinating pattern based on whether the chain had an even or odd number of atoms.

• Even Numbered Chains (The Perfect Pairs):
  If you build a chain with 2, 4, or 6 atoms, the atoms naturally pair up into "dimers" (couples).

  • Analogy: Imagine a line of dancers holding hands in pairs. Everyone is paired up.
  • Outcome: Since everyone is paired and their spins cancel out, the whole chain is non-magnetic. It's a quiet, stable line.

• Odd Numbered Chains (The Lonely Outcast):
  If you build a chain with 3, 5, or 7 atoms, you can't pair everyone up perfectly.

  • Analogy: Imagine the same line of dancers, but there's one extra person left over. The pairs form, but one dancer is left standing alone at the end of the line.
  • Outcome: This "lonely" atom at the end keeps its spin. It acts like the original soloist. It creates those "echoes" (YSR states) again. The rest of the chain remains quiet, but the end is loud and magnetic.

4. The Switchable Switch

Here is the coolest part: The researchers found they could use the tip of their microscope (which acts like a tiny, precise finger) to push that "lonely" atom from one end of the chain to the other.

• The Metaphor: It's like a game of musical chairs where the music stops, and the last person standing (the magnetic atom) can be teleported from the left side of the room to the right side just by a gentle nudge.
• Why it matters: This shows that the chain is "bistable"—it has two stable states, and we can switch between them. This is a crucial step toward building tiny switches for future quantum computers.

5. The Big Picture: Why Do We Care?

The scientists were trying to see if they could create a specific type of "topological" material (a fancy kind of matter that is robust and protected from errors).

• They hoped to create a chain where the "hopping" strength (how easily electrons jump between atoms) alternated, like a pattern of Strong-Weak-Strong-Weak. This is known as the SSH model (named after the physicists who invented the theory).
• The Reality Check: While the atoms did naturally pair up (creating a Strong-Weak pattern), the connection between the pairs was too weak to create the exotic "topological" states they were hoping for.
• The Takeaway: Even though they didn't find the "Holy Grail" of topological states in this specific setup, they proved that by manipulating atoms, we can control whether a chain is magnetic or not, and we can move that magnetism around. This is a vital building block for designing future quantum technologies.

Summary

• Single Atom: Loud and magnetic.
• Two Atoms (Touching): Quiet and non-magnetic (they cancel each other out).
• Even Chain: All quiet (everyone is paired).
• Odd Chain: Quiet in the middle, but loud and magnetic at the very end.
• The Magic: We can move that magnetic end from one side to the other, like flipping a switch.

This research is like learning the rules of a microscopic game of musical chairs, showing us how to engineer the behavior of matter one atom at a time.

Technical Summary

1. Problem Statement

Magnetic adatom chains on superconducting substrates are a primary platform for engineering topological superconductivity and Majorana zero modes. Previous studies have largely focused on the hybridization of Yu-Shiba-Rusinov (YSR) states (bound states within the superconducting gap induced by magnetic impurities) to form bands. However, the direct hybridization of the atoms' intrinsic $d$-orbitals and its impact on the magnetic ground state (specifically spin quenching) in densely packed chains has been less explored.

The central questions addressed are:

• How does the interaction mechanism change as the distance between Fe atoms is reduced from a few lattice constants to nearest-neighbor sites?
• Does direct $d$-level hybridization lead to a spin-singlet state, thereby suppressing magnetic moments and YSR states?
• Can such systems be engineered to realize a Su-Schrieffer-Heeger (SSH) model with alternating hopping amplitudes to create topological phases?

2. Methodology

The researchers utilized low-temperature Scanning Tunneling Microscopy (STM) and spectroscopy (STS) to manipulate and characterize Iron (Fe) atoms on a 2H-NbSe$_2$ superconducting substrate.

• Instrumentation: A JT-STM operating at 1.1 K with superconducting Nb-coated tips to enhance energy resolution beyond the Fermi-Dirac limit.
• Sample Preparation: Fe atoms were evaporated onto cleaved 2H-NbSe$_2$ crystals at temperatures below 12 K.
• Atomic Manipulation: Atoms were precisely positioned using the STM tip to create:
  • Isolated monomers.
  • Dimers at varying separations ($d = 3a, 2a, 1a$, where $a$ is the lattice constant).
  • Chains of varying lengths ($Fe_6$ and $Fe_7$).
• Spectroscopic Techniques:
  • $dI/dV$ Spectra: Recorded both with feedback loops off (for gap region) and on (for higher energies) to map YSR states and unoccupied $d$-levels.
  • Constant-Current Topography: To visualize atomic positions.
  • Constant-$dI/dV$ Topography: To map the spatial distribution of specific electronic states and identify nodal planes (crucial for distinguishing bonding vs. anti-bonding orbitals).

3. Key Contributions and Results

A. Transition from YSR Hybridization to $d$-Level Hybridization

The study systematically varied the inter-atomic distance:

• Dilute Limit ($d = 2a, 3a$): The atoms interact primarily via substrate-mediated exchange. The $d$-levels remain largely unperturbed, and the system exhibits four distinct YSR states per atom (consistent with an $S=2$ spin state).
• Dense Limit ($d = 1a$, Nearest Neighbor): When atoms are placed in nearest-neighbor sites, a drastic change occurs:
  • YSR Suppression: All YSR states disappear from the spectrum.
  • $d$-Level Hybridization: The unoccupied $d$-level spectra change from four resonances (monomer) to three distinct resonances on the dimer.
  • Orbital Characterization: Constant-$dI/dV$ imaging revealed a symmetric (bonding) orbital centered between the atoms and an antisymmetric (anti-bonding) orbital with a nodal plane between them.
  • Spin Quenching: The hybridization leads to a complete reorganization of the $d$-level occupation, resulting in a spin singlet ($S=0$) ground state. Consequently, the magnetic moment is quenched, and no YSR states are formed.

B. Spontaneous Dimerization in Chains

The researchers constructed longer chains ($Fe_n$) and observed a spontaneous dimerization phenomenon:

• Even-Numbered Chains ($Fe_6$): The chain spontaneously forms paired units (dimers) with weak coupling between them. The electronic structure of the bulk dimers resembles that of isolated dimers. The entire chain is non-magnetic (no YSR states).
• Odd-Numbered Chains ($Fe_7$): The chain forms dimers along the bulk, but one atom remains unpaired at one end.
  • This unpaired atom retains its high-spin state ($S=2$) and exhibits four YSR states.
  • The YSR wavefunctions extend along the chain, making the magnetic state detectable even at the dimer sites.

C. Bistability and Switching

• The position of the unpaired atom in odd-numbered chains is bistable. It can reside at either end of the chain.
• The authors demonstrated that the location of the single end atom can be switched using voltage pulses from the STM tip. This switching event was captured via a sudden jump in the $z$-trace (tip height) during spectroscopy, indicating a transition in the chain's energetic balance.

D. Implications for Topological Physics

• The system naturally creates an alternating hopping amplitude scenario (strong intra-dimer coupling, weak inter-dimer coupling), analogous to the Su-Schrieffer-Heeger (SSH) model.
• However, the authors conclude that while the system mimics the SSH geometry, the inter-dimer coupling is too weak to support a topological phase with protected edge states in the current configuration. The system remains in a trivial insulating state regarding the SSH topology, though it provides a robust platform for engineering such states.

4. Significance

• Mechanism of Spin Quenching: The paper provides direct experimental evidence that direct $d$-orbital hybridization in nearest-neighbor magnetic adatoms leads to a non-magnetic singlet ground state, distinct from the substrate-mediated YSR interactions seen in dilute chains.
• Engineering Quantum Ground States: It demonstrates that the magnetic properties of atomic chains can be fundamentally altered by controlling inter-atomic spacing, allowing for the creation of stable non-magnetic units (dimers) and switchable magnetic ends.
• Pathway to Topology: While the specific Fe chains on NbSe$_2$ did not yield a topological phase, the work establishes a methodology for creating alternating hopping amplitudes. This offers a blueprint for future designs aiming to realize topological superconductivity and Majorana modes by engineering specific bond strengths in magnetic atom arrays.
• Bistable Quantum Systems: The ability to switch the magnetic end of an odd chain via voltage pulses highlights the potential for using such chains as nanoscale memory elements or switches in quantum devices.

In summary, this work bridges the gap between isolated magnetic impurities and extended topological chains by revealing the critical role of direct $d$-level hybridization in determining the magnetic and topological properties of atomic-scale systems.