Quantum Geometry Explains Anomalous Electrical Effects in Crystals

A groundbreaking study reveals how the geometric curvature of quantum structures in crystals can cause anomalous electrical effects, shedding light on long-standing mysteries in materials science. Researchers from India’s Jawaharlal Nehru Centre for Advanced Scientific Research have demonstrated that lattice vibrations can induce oscillations in the quantum geometry of electrons, leading to observable nonlinear Hall signatures. This discovery opens up new avenues for understanding and characterizing quantum systems, with far-reaching implications for a wide range of materials and excitations.

The article presents a theoretical analysis that demonstrates how the geometric curvature of quantum structures of electrons in crystals can cause anomalous linear and nonlinear electrical Hall effects. This phenomenon has been observed in low-symmetry crystals with narrow electronic band gaps.

The researchers, Bhuvaneswari R, Mandar M Deshmukh, and Umesh V Waghmare, from the Theoretical Sciences Unit at Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India, and their collaborators, have shown that dynamical lowering of crystal symmetry by lattice vibrations results in oscillations in the quantum geometry of electrons. These oscillations have observable nonlinear Hall signatures.

The team’s findings suggest that a vibrational spectroscopy based on Geometry of Quantum Electronic Structure (GQuES) can be used to make specific predictions for the transport and radiative GQuES spectra of 2D materials. This approach is applicable to a wide range of materials and excitations, spanning sub-GHz, THz, and infrared frequencies.

The researchers have demonstrated that when external parameters or fields interacting with a quantum system change slowly along a cyclic path or loop, the quantum energy state time-evolves adiabatically. This process picks up two phase factors: i) the dynamic phase factor determined by the energies of quantum states traversed during the cyclic evolution and ii) an additional factor that depends only on the geometry of quantum states accessed along the loop in the parameter space.

When these parameters correspond to dynamical variables of slow degrees of freedom, the geometric or Berry phases are physically relevant to measurable properties significant to applications. The manifestation of Berry phases is omnipresent and has been realized in diverse phenomena in quantum chemistry, physics, and material science.

In the last two decades, Berry phases and curvature have been shown to govern electronic topology of crystals that defines quantum states of matter like topological insulators, Dirac, and Weyl semimetals. The bending of electronic trajectory in a crystal due to geometric Berry curvature of its quantum electronic structure causes electrical Hall effect even in the absence of external magnetic fields.

The researchers have presented first-principles theoretical analysis that shows how dynamical lowering of crystal symmetry by lattice vibrations results in oscillations in the quantum geometry of electrons. These oscillations have observable nonlinear Hall signatures. The team’s findings suggest that a vibrational spectroscopy based on GQuES can be used to make specific predictions for the transport and radiative GQuES spectra of 2D materials.

The implications of GQuES are significant, as it can be applied to a wide range of materials and excitations, spanning sub-GHz, THz, and infrared frequencies. The approach has the potential to revolutionize our understanding of quantum systems and their behavior under various external conditions.

The researchers have demonstrated that GQuES can be used to make specific predictions for the transport and radiative GQuES spectra of 2D materials. This approach has the potential to be used for materials characterization, allowing scientists to study the properties of quantum systems in real-time.

The researchers have identified several future directions for GQuES, including the development of new experimental techniques and the application of GQuES to a wide range of materials and excitations. The team’s findings suggest that GQuES has the potential to be a powerful tool for understanding quantum systems and their behavior under various external conditions.

In conclusion, the researchers have presented a theoretical analysis that demonstrates how the geometric curvature of quantum structures of electrons in crystals can cause anomalous linear and nonlinear electrical Hall effects. The team’s findings suggest that GQuES has the potential to be a powerful tool for understanding quantum systems and their behavior under various external conditions.