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Comparison of Two Different Synthesis Methods of Single Crystals of Superconducting Uranium Ditelluride

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Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers.

O Viyuela¹, A Rivas¹, M A Martin-Delgado¹

¹Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.

Physical Review Letters

|August 30, 2014

Summary

We introduce the topological Uhlmann number to classify topological orders in 2D fermionic systems. This invariant reveals novel thermal-topological transitions and phases in insulators and superconductors.

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Area of Science:

Condensed Matter Physics
Quantum Information Theory

Background:

Symmetry-protected topological orders are crucial in condensed matter.
Classifying these orders, especially in fermionic systems, remains a challenge.

Purpose of the Study:

To develop a topological invariant for classifying density matrices of symmetry-protected topological orders.
To investigate thermal topological phases and transitions in 2D fermionic systems.

Main Methods:

Construction of the topological Uhlmann number (n_U) based on the Uhlmann phase.
Computation of phase diagrams for topological insulators and superconductors, incorporating temperature.
Analysis of thermal-topological transitions in models with high Chern numbers.

Main Results:

The topological Uhlmann number (n_U) successfully classifies density matrices.
Novel thermal-topological transitions were discovered between nontrivial phases.
At low temperatures, standard topological phases are recovered as n_U approaches the Chern number.

Conclusions:

The topological Uhlmann number provides a powerful tool for characterizing topological phases.
The study expands understanding of thermal effects on topological order in fermionic systems.