Exploring the effects of crystal symmetry breaking in the transport properties of topological material HgTe

Symmetry plays a central role in determining the electronic and transport properties of condensed matter systems and can give rise to a wide range of topological quantum phenomena. This thesis investigates the influence of crystal symmetry breaking on transport phenomena in three-dimensional HgTe, with a particular focus on nonlinear transport effects and strain-engineered topological phases. Two complementary approaches are explored: the study of nonlinear magnetotransport in compressively strained HgTe and the development of a uniaxial strain platform for tuning topological phases in situ. The first part of the thesis focuses on the nonlinear Hall effect (NHE), a second-order transport response predicted to arise in time-reversal invariant but inversion symmetry-breaking systems through the Berry curvature dipole (BCD). This effect has attracted considerable interest because it enables Hall-like responses without external magnetic fields and may offer potential applications in rectification and low-power electronic devices. However, experimental identification of intrinsic BCD-induced nonlinear transport remains challenging, particularly in narrow-gap systems where extrinsic effects can produce similar nonlinear signatures. Compressively strained three-dimensional HgTe provides an ideal platform for investigating these effects due to its highly tunable band structure, intrinsic inversion asymmetry, and experimentally accessible Weyl semimetal phase. Using electrostatic gating and magnetotransport measurements, the transport properties of a 94 nm thick compressively strained HgTe sample are investigated across different transport regimes, including the Weyl semimetal phase and topological surface state-dominated regimes. Since symmetry considerations forbid the nonlinear Hall response on the (001) surface of cubic crystals under time-reversal symmetry, an in-plane magnetic field is employed to break the relevant rotational symmetry and enable nonlinear transport measurements. The influence of in-plane magnetic fields on the transport properties is studied through anisotropic magnetoresistance (AMR) and planar Hall effect (PHE) measurements. In the Weyl regime, these effects are linked to the chiral anomaly associated with Weyl nodes, while in the topological surface state regime they originate from magnetic-field-induced tilting of the Dirac cones. A major focus of this work is the investigation of irregular magnetotransport fluctuations observed in the surface state regime, which have remained an open experimental question. By considering the effect of Dirac cone tilting on electron transport in the presence of charge puddles, a phenomenological puddle network model is developed. Based on experimentally estimated puddle sizes and distributions in epitaxially grown HgTe, the model successfully reproduces the anomalous magnetotransport fluctuations through tunneling transport between adjacent charge puddles. These findings identify charge puddles as a dominant factor governing transport in narrow-gap systems and demonstrate the significant role of sample inhomogeneity in realistic transport experiments. The same mechanism is further shown to strongly influence nonlinear transport measurements. Nonlinear in-plane magnetotransport experiments reveal that the nonlinear response persists even when the Fermi level is tuned away from the Weyl nodes into electron- and hole-dominated regimes, challenging a purely Berry curvature-related interpretation. Pronounced fluctuations are observed in both longitudinal and transverse nonlinear conductance, closely resembling the fluctuations observed in the linear magnetoresistance. Furthermore, finite nonlinear signals are detected even at zero magnetic field, in contradiction with expectations based solely on crystal symmetry considerations. These observations are explained by nonlinear tunneling transport across charge puddles, which generates harmonic distortion of the applied AC signal. Although weak in magnitude, these nonlinearities become experimentally detectable through higher harmonic lock-in measurements. The results demonstrate that charge puddle-induced tunneling transport can generate measurable nonlinear responses even in the absence of intrinsic band structure effects, thereby complicating the unambiguous identification of Berry curvature-driven nonlinear phenomena in narrow-gap systems. This work therefore highlights the importance of carefully distinguishing intrinsic and extrinsic contributions in nonlinear transport experiments and emphasizes the limitations of theoretical descriptions that neglect realistic sample inhomogeneity. The second part of the thesis investigates symmetry breaking through uniaxial strain engineering. Uniaxial strain provides a direct and highly controllable method for selectively modifying crystal symmetries and tuning topological phases. To study strain-driven topological phase transitions in bulk HgTe, a cryogenic uniaxial strain platform with dynamic in situ strain tuning was used. A piezoelectric pressure-cell-based apparatus enables continuous tuning of a single sample across multiple strain conditions, analogous to tuning with gate voltage or magnetic field. To enable quantitative strain determination during transport measurements, a custom Raman spectroscopy setup was integrated into the low-temperature transport system, allowing simultaneous Raman and transport characterization under uniaxial strain. While the relatively low cleavage energies of CdxHg1−xTe limited the maximum achievable strain before mechanical failure, the developed platform establishes a versatile experimental framework for studying strain-driven transport phenomena and topological phase transitions in quantum materials. Overall, this thesis demonstrates that charge puddle-induced tunneling transport, strongly modulated by in-plane magnetic-field-driven Dirac cone tilting, is a key mechanism governing both linear and nonlinear transport anomalies in HgTe. The work resolves long-standing experimental questions regarding magnetotransport fluctuations in topological surface states and reveals the substantial influence of extrinsic sample inhomogeneity on nonlinear transport measurements. In parallel, the development of a cryogenic uniaxial strain platform with Raman-based strain calibration provides new opportunities for exploring symmetry-controlled topological phase transitions in quantum materials.