Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1612.06613 · Journal of Physics Communications

Superconductivity in a two-dimensional repulsive Rashba gas at low electron density

Luyang Wang

Published Sep 1, 2017• 2 citations
arXivHTMLPDF

Abstract

We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling at low electron density (namely the Fermi energy E F is lower than the energy E R of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy ( ) decreases, due to two reasons. First, the density of states at increases as . Second, the particle–hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum (or ) channel with Chern number C = 4 (or ), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be ±1 and Majorana zero modes exist in the vortex cores.

DOI
10.1088/2399-6528/aa8215

Related papers

Spin-orbit coupling induced enhancement of superconductivity in a two-dimensional repulsive gas of fermions

Oskar Vafek, Luyang Wang

We study a model of a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling ${\ensuremath{\alpha}}_{R}$ and investigate the superconducting instability using the renormalization-group approach. We find that, in general, superconductivity is enhanced as the dimensionless ratio $\frac{1}{2}m{\ensuremath{\alpha}}_{R}^{2}/{E}_{F}$ increases, resulting in unconventional superconducting states which break time-reversal symmetry.

arXiv:1105.2041•Physical Review B•Nov 3, 2011•16 citations

p -wave superconductivity in weakly repulsive 2D Hubbard model with Zeeman splitting and weak Rashba spin-orbit coupling

Henning G. Hugdal, Asle Sudbø

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ type state for out-of-plane fields, to a nodal $p$-wave-type state for purely in-plane fields.

arXiv:1711.11047•Physical review. B./Physical review. B•Jan 24, 2018•3 citations

Topological States in a One-Dimensional Fermi Gas with Attractive Interaction

Jonathan Ruhman, Erez Berg, Ehud Altman

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to be robust to introducing a finite temperature as long as it is much smaller than the interaction induced single particle gap in the final state of the sweep.

arXiv:1412.3444•Physical Review Letters•Mar 10, 2015•72 citations

Three-dimensional spin–orbit coupled Fermi gases: Fulde–Ferrell pairing, Majorana fermions, Weyl fermions, and gapless topological superfluidity

Xia-Ji Liu, Hui Hu, Han Pu

We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.

arXiv:1411.2993•Chinese Physics B•Apr 30, 2015•16 citations

Intrinsic Second-Order Topological Superconductors with Tunable Majorana Zero Modes

Xiao-Jiao Wang, Yijie Mo, Zhi Wang +2 more

Dirac semimetals, with their protected Dirac points, present an ideal platform for realizing intrinsic topological superconductivity. In this work, we investigate superconductivity in a two-dimensional, square-lattice nonsymmorphic Dirac semimetal. In the normal state near half-filling, the Fermi surface consists of two distinct pockets, each enclosing a Dirac point at a time-reversal invariant momentum ($\textbf{X}=(π,0)$ and $\textbf{Y}=(0,π)$). Considering an on-site repulsive and nearest-neighbor attractive interaction, we use self-consistent mean-field theory to determine the ground-state pairing symmetry. We find that an even-parity, spin-singlet $d_{x^{2}-y^{2}}$-wave pairing is favored as it gives rise to a fully gapped superconducting state. Since the pairing amplitude has opposite signs on the two Dirac Fermi pockets, the superconducting state is identified as a second-order topological superconductor. The hallmark of this topological phase is the emergence of Majorana zero modes at the system's boundaries. Notably, the positions of these Majorana modes are highly controllable and can be manipulated simply by tailoring the boundary sublattice terminations. Our results highlight the promise of nonsymmorphic Dirac semimetals for realizing and manipulating Majorana modes.

cond-mat.supr-conCross-listedarXiv:2512.02775•Dec 3, 2025

Majorana edge modes protected by emergent symmetry in a one dimensional fermi gas

Jonathan Ruhman, Ehud Altman

We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation and the absence of a single particle gap. Majorana zero modes are localized to the interface between a topological region in the middle of the trap and trivial regions at its wings. Unlike the realization of a topological superconductor in proximity coupled nano-wires, the Majorana modes do not carry a quantum number associated with the total fermion parity. Instead, the topological degeneracy is protected by an emergent $Z_2$ symmetry present only at low energies. We discuss the experimental implications of the novel zero modes, as manifest for example in the response to modulation of a local potential near the position of the Majorana bound states. For the range of interaction strength corresponding to Luttinger parameter $12$, on the other hand the zero-mode can be detected as a sharp low frequency response at an energy which generically scales with system size as $1/L^{K/2}$ and is therefore parametrically separated from the phonons.

arXiv:1401.7343•Jan 28, 2014•0 citations
We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling at low electron density (namely the Fermi energy E F is lower than the energy E R of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy ( ) decreases, due to two reasons. First, the density of states at increases as . Second, the particle–hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum (or ) channel with Chern number C = 4 (or ), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be ±1 and Majorana zero modes exist in the vortex cores.
We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction nnn of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning nnn. Moreover, nnn also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ type state for out-of-plane fields, to a nodal ppp-wave-type state for purely in-plane fields.
We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to be robust to introducing a finite temperature as long as it is much smaller than the interaction induced single particle gap in the final state of the sweep.
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.
Dirac semimetals, with their protected Dirac points, present an ideal platform for realizing intrinsic topological superconductivity. In this work, we investigate superconductivity in a two-dimensional, square-lattice nonsymmorphic Dirac semimetal. In the normal state near half-filling, the Fermi surface consists of two distinct pockets, each enclosing a Dirac point at a time-reversal invariant momentum (X=(π,0)\textbf{X}=(π,0)X=(π,0) and Y=(0,π)\textbf{Y}=(0,π)Y=(0,π)). Considering an on-site repulsive and nearest-neighbor attractive interaction, we use self-consistent mean-field theory to determine the ground-state pairing symmetry. We find that an even-parity, spin-singlet dx2−y2d_{x^{2}-y^{2}}dx2−y2​-wave pairing is favored as it gives rise to a fully gapped superconducting state. Since the pairing amplitude has opposite signs on the two Dirac Fermi pockets, the superconducting state is identified as a second-order topological superconductor. The hallmark of this topological phase is the emergence of Majorana zero modes at the system's boundaries. Notably, the positions of these Majorana modes are highly controllable and can be manipulated simply by tailoring the boundary sublattice terminations. Our results highlight the promise of nonsymmorphic Dirac semimetals for realizing and manipulating Majorana modes.
We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation and the absence of a single particle gap. Majorana zero modes are localized to the interface between a topological region in the middle of the trap and trivial regions at its wings. Unlike the realization of a topological superconductor in proximity coupled nano-wires, the Majorana modes do not carry a quantum number associated with the total fermion parity. Instead, the topological degeneracy is protected by an emergent Z2Z_2Z2​ symmetry present only at low energies. We discuss the experimental implications of the novel zero modes, as manifest for example in the response to modulation of a local potential near the position of the Majorana bound states. For the range of interaction strength corresponding to Luttinger parameter 121212, on the other hand the zero-mode can be detected as a sharp low frequency response at an energy which generically scales with system size as 1/LK/21/L^{K/2}1/LK/2 and is therefore parametrically separated from the phonons.