[Paper Review] Saddle point singularity and topological phase diagram in a tunable topological crystalline insulator (TCI)

Madhab Neupane, Su‐Yang Xu+16 more|arXiv (Cornell University)|Mar 6, 2014

Topological Materials and Phenomena27 references3 citations

TL;DR

This study reports the first experimental observation of a saddle point singularity in the topological surface states of a tunable topological crystalline insulator (TCI) Pb₀.₇Sn₀.₃Se using high-resolution angle-resolved photoemission spectroscopy (ARPES). The researchers identify van Hove singularities (VHS) at the saddle point, demonstrate tunability of the surface chemical potential via surface chemical gating, and establish a rich topological phase diagram in Pb₁₋ₓSnₓSe governed by lattice constant, band gap, spin-orbit coupling, and crystal structure transitions.

ABSTRACT

A topological crystalline insulator (TCI) is a new phase of topological matter, which is predicted to exhibit distinct topological quantum phenomena, since space group symmetries replace the role of time-reversal symmetry in the much-studied Z$_2$ topological insulators. Utilizing high-resolution angle-resolved photoemission spectroscopy (ARPES), we reveal the momentum space nature of interconnectivity of the Fermi surface pockets leading to a saddle point singularity within the topological surface state alone in the TCI Pb$_{0.7}$Sn$_{0.3}$Se. Moreover, we show that the measured momentum-integrated density of states exhibits pronounced peaks at the saddle point energies, demonstrating the van Hove singularities (VHSs) in the topological surface states, whose surface chemical potential, as we show, can be tuned via surface chemical gating, providing access to the topological correlated physics on the surface. Our experimental data reveal a delicate relationship among lattice constant, band gap and spin-orbit coupling strength associated with the topological phase transition in Pb$_{1-x}$Sn$_{x}$Se. Furthermore, we explore the robustness of the TCI phase with VHS in Pb$_{1-x}$Sn$_{x}$Se, which shows a variety of distinct topological phase transitions driven by either thermal instability or broken crystalline symmetry, and thus revealing a rich topological phase diagram connectivity in Pb$_{1-x}$Sn$_{x}$Se for the first time.

Motivation & Objective

• To investigate the momentum-space electronic structure topology of topological surface states in a tunable TCI, specifically Pb₀.₇Sn₀.₃Se.
• To determine whether saddle point singularities—associated with van Hove singularities (VHS)—can emerge in the surface states of a TCI, enabling access to correlated topological quantum phenomena.
• To map the topological phase diagram of Pb₁₋ₓSnₓSe by correlating structural, electronic, and topological properties across varying Sn composition.
• To explore the interplay between lattice constant, spin-orbit coupling, band gap, and crystalline symmetry in driving topological phase transitions.
• To demonstrate experimental tunability of the surface chemical potential in the TCI phase via surface chemical gating, enabling control over VHS energy positions.

Proposed method

• Performed high-resolution angle-resolved photoemission spectroscopy (ARPES) at low and high photon energies to map the surface state band dispersion and Fermi surface topology in Pb₀.₇Sn₀.₃Se.
• Conducted in situ sample cleaving and measurements at 10–300 K under ultra-high vacuum (<1×10⁻¹⁰ torr) to preserve surface integrity and minimize degradation.
• Used low-photon-energy (15–30 eV) and high-photon-energy (~60 eV) ARPES at SRC, SSRL, and ALS beamlines to access different momentum and energy regions of the electronic structure.
• Employed Sn deposition and ARPES measurements at the CASSIOPEE beamline (SOLEIL, France) to probe surface chemical gating effects.
• Performed first-principles density functional theory (DFT) calculations with spin-orbit coupling (SOC) using the projector augmented wave (PAW) method in VASP, including GGA for exchange-correlation effects.
• Constructed an effective surface k·p Hamiltonian model for the (001) surface of Pb₀.₇Sn₀.₃Se to describe the surface band dispersion and spin texture.

Experimental results

Research questions

• RQ1 Can a saddle point singularity emerge in the topological surface states of a TCI, and if so, what is its momentum-space and energy-space signature?
• RQ2 How do van Hove singularities (VHS) in the surface state density of states relate to the topological phase and electronic correlations in Pb₁₋ₓSnₓSe?
• RQ3 To what extent can the surface chemical potential in the TCI phase be tuned, and how does this affect the position and strength of VHS?
• RQ4 What is the role of lattice constant, spin-orbit coupling, and crystal structure (e.g., cubic vs. orthorhombic) in determining the topological phase transition in Pb₁₋ₓSnₓSe?
• RQ5 How does the coexistence of multiple crystal phases (cubic and orthorhombic) at intermediate Sn compositions influence the topological phase diagram?

Key findings

• The ARPES measurements directly reveal a saddle point singularity in the topological surface state band dispersion of Pb₀.₇Sn₀.₃Se, with Fermi surface pockets interconnected in momentum space.
• Momentum-integrated density of states exhibits pronounced peaks at the saddle point energies, confirming the presence of van Hove singularities (VHS) in the topological surface states.
• The surface chemical potential in the TCI phase can be experimentally tuned via surface chemical gating, enabling control over the energy position of the VHS.
• A rich topological phase diagram is established for Pb₁₋ₓSnₓSe, with two distinct phase transitions: one driven by lattice contraction (increasing effective spin-orbit coupling) at x ≈ 0.45, and another by a structural transition to the orthorhombic phase at x ≈ 0.75.
• The system transitions from a non-inverted band gap (~0.15 eV) in PbSe (x=0) to a topological crystalline insulator phase, then to a multi-phase regime, and finally to a large band-gap trivial insulator (gap ~1 eV) in SnSe (x≈1), due to loss of inversion and mirror symmetry in the orthorhombic phase.
• First-principles DFT calculations confirm that the VHS arises from the surface state band structure in the TCI phase, and the k·p model accurately reproduces the observed Dirac-like dispersion and spin texture on the (001) surface.