Abstract
Quantum scars refer to an enhanced localization of the probability density of states in the spectral region with a high energy level density. Scars are discussed for a number of confined pure and impurity-doped electronic systems. Here, we studied the role of spin on quantum scarring for a generic system, namely a semiconductor-heterostructure-based two-dimensional electron gas subjected to a confining potential, an external magnetic field, and a Rashba-type spin-orbit coupling. Calculating the high energy spectrum for each spin channel and corresponding states, as well as employing statistical methods known for the spinless case, we showed that spin-dependent scarring occurs in a spin-coupled electronic system. Scars can be spin mixed or spin polarized and may be detected via transport measurements or spin-polarized scanning tunneling spectroscopy.
Highlights
Wave localization by disorder is a ubiquitous phenomenon widely discussed for quantum [1] and for classical waves [2,3,4] and can be interpreted by scattering and interferences without involving many-body interactions
Scars in wave functions, meaning enhanced localization of the probability density for states in the high energy level density part of the spectrum, were first discussed for non-interacting systems [16,17,18,19,20] and interpreted by analyzing the classical orbits of an electron or waves in various confinements such as chaotic billiards [16,17,18,19,20,21,22,23,24,25,26]; for a discussion, we refer to the book by Heller [27]
The results suggested that scarring occurs for each spin channel individually, causing the spinpolarized probability density to be scarred in the presence of the SOC and magnetic fields
Summary
Wave localization by disorder is a ubiquitous phenomenon widely discussed for quantum [1] and for classical waves [2,3,4] and can be interpreted by scattering and interferences without involving many-body interactions. Scars in wave functions, meaning enhanced localization of the probability density for states in the high energy level density part of the spectrum, were first discussed for non-interacting systems [16,17,18,19,20] and interpreted by analyzing the classical orbits of an electron or waves in various confinements such as chaotic billiards [16,17,18,19,20,21,22,23,24,25,26]; for a discussion, we refer to the book by Heller [27]. We calculated the single particle states in the high energy level density regime and analyzed the spectral properties, as well as spin-dependent perturbation-induced scarring, which was found to be spin-channel selective.
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