Tracing topological phase transitions with X-ray absorption techniques

The atoms of solids, liquids, and gases exhibit very different arrangements and behavior. In solids, atoms are tightly packed in a regular pattern; in liquids, atoms are close together but randomly arranged and with some freedom to move; and in gases, atoms are further apart and can move freely. These features define the conventional phases of matter.

When one enters the quantum world, other phases of matter, which have nothing to do with atomic distribution or mobility, emerge. These are the topological phases. In this realm, some properties of the particles within a material (like atoms or electrons) can become connected through a phenomenon known as long-range entanglement. When a pair of particles is entangled, changing or measuring one of them immediately affects the other, regardless of the distance between them. These particles might be entangled in a complex pattern, spanning the entire system. Different ‘entanglement patterns’ of the material's electrons or other quantum particles define different topological phases. Thus, altering the way particles are entangled, rather than changing their spatial arrangement leads to a phase transition.

Topological states of matter offer the potential to create exotic materials, which can be, for instance, insulators in the bulk but hold conducting states on the surface. In the last years, there has been enormous progress in the development of these modern materials. For example, some topologically non-trivial insulators could be induced by using ultrashort intense lasers. However, these light-induced topological insulators exist only while the laser pulse is on, that is, around several femtoseconds (10^-15 seconds). This imposes a strong requirement to study and characterize them since an ultrafast probe in the femtosecond timescale is needed in order to capture the ultrafast topological phases.

Despite the significant progress in this direction, some challenges remain. For example, angle-resolved photoemission spectroscopy (ARPES) has proved to be effective in probing these topological systems, but it faces a drawback: the shorter the probe pulse duration (and, consequently, the closer for capturing the material’s ultrafast nature), the lower the photoelectron energy resolution.

Recently, a team led by Universidad Autónoma de Madrid, with the collaboration of researchers from ICFO, Dr. Emilio Pisanty, Dr. Alexandre Dauphin and ICREA Prof. Maciej Lewenstein; M. N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences; King’s College London; University of Salamanca; Max Planck POSTECH/KOREA Research Initiative and Condensed Matter Physics Center (IFIMAC), presented a complementary scheme to ARPES in Reports on Progress in Physics Original Research. In a numerical experiment supported by a theoretical model, the team demonstrated that X-ray absorption spectroscopy can directly capture topological phase transitions.

The method employs ultrashort probe pulses that do not suffer from energy resolution reduction. This approach enables further studies of relevant systems for optoelectronics applications, whose investigation had so far been held back by the duration/resolution trade-off.

Topological phase transitions leave an absorption trace

The researchers simulated the action of two ultrashort pulses, separated by a time delay, on a hexagonal boron-nitrate monolayer (hBN). One of them was a linearly-polarized x-ray pulse and the other a circularly-polarized intense infrared pulse. By changing the circular polarization of the latter from left- to right-handed, the absorption of the sample also changed. This dependence enabled them to infer the topological phase of the material.

“Our ultrafast scheme was very sensitive to topological phase transitions. When the topological phase changed, there was a sign imprinted in the absorption spectrum”, explains ICREA Prof. Maciej Lewenstein. “Therefore, this method could be used to study topological phases and identify topological phase transitions within some materials. Now, we need an experimental design to be able to demonstrate it in a real-case scenario.”

Reference:

Juan F P Mosquera et al 2024 Rep. Prog. Phys. 87 117901

DOI: 10.1088/1361-6633/ad889f

Acknowledgements:

J.F.P.M, G.C., M.M., and A.P. acknowledge Comunidad de Madrid through TALENTO grant refs. 2017-T1/IND-5432 and 2021-5A/IND-20959, and the Spanish Ministry of Science, Innovation and Universities & the State Research Agency through grants refs. PID2021-126560NB-I00 and CNS2022-135803 (MCIU/AEI/FEDER, UE), and the ”María de Maeztu” Programme for Units of Excellence in R&D (CEX2023-001316-M), and FASLIGHT network (RED2022-134391-T), and computer resources and assistance provided by Centro de Computación Científica de la Universidad Autónoma de Madrid (FI-2021-1-0032), Instituto de Biocomputación y Física de Sistemas Complejos de la Universidad de Zaragoza (FI-2020-3-0008), and Barcelona Supercomputing Center (FI-2020-1-0005, FI2021-2-0023, FI-2021-3-0019). This publication is based upon work from COST Action NEXT, CA22148 supported by COST (European Cooperation in Science and Technology). M. Malakhov’s work also carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme “Quantum” No. 122021000038-7). E.P. acknowledges Royal Society funding under URF\R1\211390, RF\ERE\210255 and RF\ERE\231081. ICFO and ex-ICFO co-authors acknowledge Europea Research Council AdG NOQIA; MCIN/AEI (PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, Plan National STAMEENA PID2022-139099NB, I00, project funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR” (PRTRC17.I1), FPI); QUANTERA MAQS PCI2019-111828-2); QUANTERA DYNAMITE PCI2022-132919, QuantERA II Programme co-funded by European Union’s Horizon 2020 program under Grant Agreement No 101017733); Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call - Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan - NextGenerationEU within the framework of the Digital Spain 2026 Agenda; Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020); Barcelona Supercomputing Center MareNostrum (FI-2023-3-0024); Funded by the European Union. (HORIZON-CL4-2022-QUANTUM-02-SGA PASQuanS2.1, 101113690, EU Horizon 2020 FETOPEN OPTOlogic, Grant No 899794), EU Horizon Europe Program (This project has received funding from the European Union’s Horizon Europe research and innovation program under grant agreement No 101080086 NeQSTGrant Agreement 101080086 —NeQST); ICFO Internal “QuantumGaudi” project; European Union’s Horizon 2020 program under the Marie Sklodowska-Curie grant agreement No 847648; “La Caixa” Junior Leaders fellowships, La Caixa” Foundation (ID 100010434): CF/BQ/PR23/11980043. A.C. thanks to the Sistema Nacional de Investigación (SNI) de Panama for financial support.