[Paper Review] Large shift current, $π$ Zak phase and unconventional nature in Se and Te

Ruihan Zhang, Junze Deng+4 more|arXiv (Cornell University)|Nov 8, 2022

Topological Materials and Phenomena4 citations

TL;DR

This study demonstrates that trigonal selenium and tellurium exhibit unconventional electronic and phononic band structures, characterized by a π Zak phase, obstructed atomic insulator behavior with a nontrivial real-space invariant δ₁@3b = −1, and large shift current in quantum wells. The materials host obstructed surface electronic and phononic modes on the (0001) surface, establishing them as prototypes for dual unconventional behavior in both bands.

ABSTRACT

Recently, unconventional materials (or obstructed atomic insulators) have attracted much attention owing to the unconventional feature of mismatch between Wannier centers and atomic positions. In this paper, we demonstrate that the trigonal selenium and tellurium host an unconventional nature in both electronic and phonon spectra. In electronic band structures, the band representation (BR) decomposition for occupied bands has to contain the essential BR of $A@3b$, and the real-space invariant is $δ_1@3b=-1$. The $π$ Zak phase suggests that the one-dimensional Se/Te chain is a chiral Su-Schrieffer-Heeger chain. The effective magnetism can be induced by $p$ states at ends. More importantly, a large shift current is obtained in Se quantum well. In addtion, in phonon spectra, three sets of phonon bands are well separated and assigned to $B@3b$, $B@3a$, and $A@3b$ BRs, respectively. Thus, the obstructed phonon states are predicted on the (0001) surface. As the prototypes of unconventional materials in both electronic and phonon spectra, our findings could create much interest in the study of obstructed surface electronic and phonon states in these novel materials.

Motivation & Objective

• To investigate the unconventional electronic and phononic band structures in trigonal selenium and tellurium.
• To determine whether these materials host obstructed atomic insulator (OAI) behavior in both electronic and phononic spectra.
• To explore the emergence of topological and nontrivial surface states in both charge and lattice dynamics.
• To quantify the shift current response in Se quantum wells and identify obstructed phonon modes on (0001) surfaces.
• To establish Se and Te as prototypical materials with dual unconventional band structures in electrons and phonons.

Proposed method

• Performed symmetry-based band representation (BR) decomposition using the eBR/aBR workflow to classify occupied electronic and phononic bands.
• Calculated the real-space invariant (RSI) δ₁@3b = −1 to confirm obstructed atomic insulator character in the electronic structure.
• Computed the Zak phase along the c-axis to identify a π Zak phase, indicating a chiral Su-Schrieffer-Heeger (SSH) chain in 1D Se/Te chains.
• Used density functional theory (DFT) with the Quantum ESPRESSO package and IR2PH to compute phonon modes and their irreducible representations.
• Applied the TQC and symmetry-indicator framework to identify obstructed phonon bands and surface modes via BR decomposition of phonon spectra.
• Constructed (0001) and (01̄10) surface slabs to probe surface electronic and phononic states, including in-gap metallic surface bands.

Experimental results

Research questions

• RQ1 Do trigonal Se and Te exhibit unconventional electronic band structures with obstructed Wannier centers?
• RQ2 Is there a nontrivial Zak phase in the 1D Se/Te chain, indicating topological character?
• RQ3 Can large shift current be generated in Se quantum well structures due to spatial separation of electrons and holes?
• RQ4 Are the phonon bands in Se and Te unconventional, with band representations not summing to trivial irreps?
• RQ5 Do obstructed surface phonon modes emerge on the (0001) surface due to band representation mismatch?

Key findings

• The occupied electronic bands in Se and Te are characterized by the essential band representation A@3b, with a nontrivial real-space invariant δ₁@3b = −1.
• The π Zak phase along the c-axis confirms the 1D Se/Te chain as a chiral Su-Schrieffer-Heeger (SSH) chain, supporting topological character.
• A large shift current is predicted in Se quantum wells due to spatial separation of electrons and holes at different interfaces, enabling high photogalvanic response.
• Phonon band representations are decomposed into three distinct sets: B@3b, B@3a, and A@3b, confirming unconventional phononic band structure.
• Obstructed surface phonon modes are predicted to exist in the frequency gap on the (0001) surface, analogous to electronic surface states.
• The magnetic configuration analysis shows that AFM-III is the most stable with J_b = 15.7 meV and J_a = −J_ab = 1.2 meV, consistent with the observed spin ordering.