Ground-state Currents Enable Extraction of Transport Coefficients Without Time-resolved Measurements

Understanding how materials conduct heat and charge, known as their transport properties, usually demands applying external forces and measuring changes over time. However, Felix A. Palm from Université Libre de Bruxelles, Alexander Impertro and Monika Aidelsburger from Ludwig-Maximilians-Universität, along with Nathan Goldman and colleagues, now demonstrate a new method for determining these properties by examining static electrical currents within a material’s fundamental state. The team reveals that by analysing these naturally occurring currents, and exploiting how quickly information travels through the material, they can reconstruct key transport characteristics, including the Hall response, using only a limited number of local measurements. This approach, validated through simulations of specific materials, offers a broadly applicable and scalable technique for probing transport phenomena in engineered matter, even in complex systems and at practical temperatures, and circumvents the need for traditional, dynamic measurements.

This approach bypasses the need for traditional linear response theory, which becomes inaccurate when systems are far from equilibrium. The team demonstrates that these coefficients can be directly obtained by analysing the current flowing through a localized probe coupled to the system of interest. The method involves calculating the ground-state current through a localized impurity and determining how this current changes with applied voltage. Validating this approach with a tight-binding model, the calculations accurately reproduce known transport properties, even in strongly non-equilibrium conditions where traditional methods fail. This technique proves applicable to disordered systems, offering a versatile tool for studying complex materials exhibiting localization effects.

Local Chern Number from Current Correlations

Researchers have developed a novel technique to determine the local Chern number, a measure of topological order, within a material. This method moves beyond global measurements, allowing scientists to map variations in topological properties across a material’s surface. The technique relies on measuring the time-dependent correlation between current operators at different points, revealing information about charge carrier movement and enabling the extraction of a local Hall conductivity, from which the local Chern number can be determined. Extensive testing on the Hofstadter model, a system known for its complex topological phases, demonstrates the method’s accuracy and confirms its reliability. Applying the method to the strongly correlated bosonic Laughlin state further validates its applicability to complex systems.

Static Currents Reveal Hall Response Properties

Scientists have demonstrated a new method for determining a material’s Hall response, a key indicator of its electrical conductivity in magnetic fields, by measuring static ground-state currents. This approach avoids the need for external forcing or time-resolved measurements, simplifying experimental procedures. Researchers established a direct relationship between these static currents and the local Hall response, exploiting the natural decay of correlations within gapped systems. Validating the technique through numerical simulations of a Chern insulator, a material exhibiting unique quantum properties, confirms its accuracy and extends to more complex systems like fractional Chern insulators, which possess intrinsic topological order, and is applicable to mixed states, enabling the investigation of transport at realistic temperatures. The practical implementation requires measurements of only four local currents, further simplifying experimental challenges.