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Register a new userProbing a topological quantum critical point in semiconductor-superconductor heterostructures
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Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.
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A spin-orbit coupled quantum wire, with one end proximate to an s-wave superconductor, can become a topological superconductor, with a Majorana mode localized at each end of the superconducting region. It was recently shown that coupling one end of such a topological superconductor to $two$ normal channels of interacting electrons leads to a novel type of frustration and a quantum critical point when both channels couple with equal strength. We propose an experimental method to access this critical point in a $single$ quantum wire and show its resilience to disorder.
We present a pedagogical review of topological superconductivity and its consequences in spin-orbit coupled semiconductor/superconductor heterostructures. We start by reviewing the historical origins of the notions of Dirac and Majorana fermions in particle physics and discuss how lower dimension
The tunneling junction between one-dimensional topological superconductor and integer (fractional) topological insulator (TI), realized via point contact, is investigated theoretically with bosonization technology and renormalization group methods. For the integer TI case, in a finite range of edge interaction parameter, there is a non-trivial stable fixed point which corresponds to the physical picture that the edge of TI breaks up into two sections at the junction, with one side coupling strongly to the Majorana fermion and exhibiting perfect Andreev reflection, while the other side decouples, exhibiting perfect normal reflection at low energies. This fixed point can be used as a signature of the Majorana fermion and tested by nowadays experiment techniques. For the fractional TI case, the universal low-energy transport properties are described by perfect normal reflection, perfect Andreev reflection, or perfect insulating fixed points dependent on the filling fraction and edge interaction parameter of fractional TI.
Semiconductors in the proximity of superconductors have been proposed to support phases hosting Majorana bound states. When the systems undergo a topological phase transition towards the Majorana phase, the spectral gap closes, then reopens, and the quasiparticle band spin polarization is inverted. We focus on two paradigmatic semiconductor-superconductor heterostructures and propose an all-electrical spectroscopic probe sensitive to the spin inversion at the topological transition. Our proposal relies on the indirect coupling of a time-dependent electric field to the electronic spin due to the strong Rashba spin-orbit coupling in the semiconductor. We analyze within linear response theory the dynamical correlation functions and demonstrate that some components of the susceptibility can be used to detect the nontrivial topological phases.
In metals near a quantum critical point, the electrical resistance is thought to be determined by the lifetime of the carriers of current, rather than the scattering from defects. The observation of $T$-linear resistivity suggests that the lifetime only depends on temperature, implying the vanishing of an intrinsic energy scale and the presence of a quantum critical point. Our data suggest that this concept extends to the magnetic field dependence of the resistivity in the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ near its quantum critical point. We find that the lifetime depends on magnetic field in the same way as it depends on temperature, scaled by the ratio of two fundamental constants $mu_B/k_B$. These measurements imply that high magnetic fields probe the same quantum dynamics that give rise to the $T$-linear resistivity, revealing a novel kind of magnetoresistance that does not depend on details of the Fermi surface, but rather on the balance of thermal and magnetic energy scales. This opens new opportunities for the investigation of transport near a quantum critical point by using magnetic fields to couple selectively to charge, spin and spatial anisotropies.
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