Chiral anomaly is one of the defining properties of Weyl and Dirac fermions. In this thesis, I explore the interest and reasons for studying Weyl and Dirac semimetals in terms of chiral anomaly, along with the hydrodynamic approach. The research covers the fundamentals of hydrodynamics, fluid/gravity duality, and chiral anomaly before diving into the specific properties of Weyl semimetals and the derivation of chiral anomaly in terms of hydrodynamics.

• Download Full Thesis

In this thesis, I explore how hydrodynamics, one of the oldest and most studied branches of classical physics, continues to produce fruitful results in modern physics. The research examines:

• Relativistic Navier-Stokes equations and their applications to quantum systems
• How AdS/CFT correspondence connects string theory to condensed matter physics
• Calculation of transport coefficients such as viscosity/entropy density ratio
• Application of fluid/gravity duality to strongly interacting quantum systems

The mathematical foundations established here provide powerful tools for understanding transport phenomena in complex quantum materials.

The thesis explores Weyl semimetals as a significant topic in condensed matter physics, focusing on:

• Derivation of chiral anomaly from quantum field theory principles
• Mathematical formulation of Berry phase and Berry curvature in band structures
• Topological protection of energy bands and Fermi arcs in Weyl semimetals
• Quantum anomalies and their manifestation in transport phenomena

I analyze how the chiral anomaly leads to unique transport signatures, including negative magnetoresistance that can be observed experimentally in real condensed matter systems.

The core contribution of my thesis is the analysis of how chiral anomaly affects hydrodynamic descriptions of Weyl semimetals:

• Modification of constitutive relations in hydrodynamics due to chiral anomaly
• Calculation of parity-odd kinetic coefficients and their relation to anomaly coefficients
• Derivation of chiral vortical effect and chiral magnetic effect
• Application of these results to understand transport in topological semimetals

This approach provides a powerful framework for understanding anomalous transport in strongly correlated electron systems, with applications extending beyond Weyl semimetals to other quantum materials.

This thesis establishes the connection between holographic hydrodynamics and transport phenomena in Weyl semimetals through the lens of chiral anomaly. While the basic theory of Weyl semimetals is well established, several properties remain to be fully understood:

• Weak anti-localization effects
• Negative magnetoresistance
• Non-saturating magnetoresistance
• Applications to other topological materials

The mathematical tools developed through AdS/CFT correspondence and holographic hydrodynamics have proven valuable for studying transport phenomena in strongly coupled systems, opening paths for future research in quantum materials.