2026/01/31 by Anonymous, Mohamed M. Elsayed, Taras I. Lakoba +1
Materials Science · Mathematics · Physics and Astronomy · #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/6ktq-2nn6
published as Phys. Rev. Research 8, 033128 (2026) · 11 pages, 6 figures
arxiv created 2026/05/17 · openalex publication_date 2026/07/07 · openalex created_date 2026/07/08 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/01
Type-II semi-Dirac fermions in two dimensions have been proposed to describe topologically nontrivial low-energy excitations in titanium/vanadium oxide heterostructures. These quasiparticles appear at the merger of three Dirac cones, resulting in a nonzero Berry phase. We find, by employing Hartree-Fock, renormalization group, and random phase approximation techniques, that the spectrum is very sensitive to long-range electron-electron interactions and can undergo a profound transformation. Our results indicate that at the topological phase boundary, long-range correlations stabilize a hybrid electronic phase displaying both Dirac and type-II semi-Dirac qualities, with physical characteristics exhibiting continuously varying critical exponents as a function of the Fermi energy; for example, Landau levels in a magnetic field vary with the energy scale: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mrow> <a:mo>|</a:mo> </a:mrow> <a:msub> <a:mi>ɛ</a:mi> <a:mi>n</a:mi> </a:msub> <a:msup> <a:mrow> <a:mrow> <a:mo>(</a:mo> <a:mi>B</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mo>|</a:mo> <a:mo>∼</a:mo> <a:mrow> <a:mo>(</a:mo> <a:mi>n</a:mi> <a:mi>B</a:mi> <a:mo>)</a:mo> </a:mrow> </a:mrow> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msup> <a:mo>→</a:mo> <a:msup> <a:mrow> <a:mo>(</a:mo> <a:mi>n</a:mi> <a:mi>B</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mrow> <a:mn>3</a:mn> <a:mo>/</a:mo> <a:mn>4</a:mn> </a:mrow> </a:msup> <a:mo>,</a:mo> <a:mi>n</a:mi> <a:mo>∈</a:mo> <a:msub> <a:mi mathvariant="double-struck">N</a:mi> <a:mn>0</a:mn> </a:msub> </a:mrow> </a:math> . The quasiparticle spectrum evolves, driven by interactions, from anisotropic Dirac dispersion at the lowest energies toward the characteristic type-II semi-Dirac boomerang shape as the energy increases. The corresponding density of states concomitantly varies between linear and power one-third ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>ρ</c:mi> <c:mrow> <c:mo>(</c:mo> <c:mi>ɛ</c:mi> <c:mo>)</c:mo> </c:mrow> <c:mo>∼</c:mo> <c:mrow> <c:mo>|</c:mo> <c:mi>ɛ</c:mi> <c:mo>|</c:mo> </c:mrow> <c:mo>→</c:mo> <c:msup> <c:mrow> <c:mo>|</c:mo> <c:mi>ɛ</c:mi> <c:mo>|</c:mo> </c:mrow> <c:mrow> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mn>3</c:mn> </c:mrow> </c:msup> </c:mrow> </c:math> ). The crossover scale is controlled by the interaction strength <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>α</d:mi> <d:mo>=</d:mo> <d:msup> <d:mi>e</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo>/</d:mo> <d:mrow> <d:mo>(</d:mo> <d:mi>ℏ</d:mi> <d:mi>v</d:mi> <d:mo>)</d:mo> </d:mrow> </d:mrow> </d:math> and the specifics of the effective interacting Hamiltonian.