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M. Salmhofer

Publications and source records attributed to M. Salmhofer.

7 recordsLinked to original sources
arXiv2023

Triplet superconductivity in the Rashba$^4$ model

The Rashba$^4$ model is a lattice model of interacting fermions with a tight-binding dispersion relation that exhibits four Rashba band crossing points at the same energy. The fermions interact weakly, by an on-site repulsion and an additional nearest-neighbour two-body interaction, which may be attractive or repulsive. We study this model when the Fermi energy is at or close to the band crossings, by a combination of renormalization group flow equations and mean-field theory. We find that the scattering processes between different Rashba points drive superconductivity of an unusual triplet type not found in models with a single Rashba point.

cond-mat.str-el↗
arXiv2016

Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction

The functional renormalization group (RG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated electron systems. In this article, we further develop this method and combine it with mean-field theory to approach multiband systems with spin-orbit coupling, and we apply this to a tight-binding Rashba model with an attractive, local interaction. The spin dependence of the interaction vertex is fully implemented in a RG flow without SU(2) symmetry, and its momentum dependence is approximated in a refined projection scheme. In particular, we discuss the necessity of including in the RG flow contributions from both bands of the model, even if they are not intersected by the Fermi level. As the leading instability of the Rashba model, we find a superconducting phase with a singlet-type interaction between electrons with opposite momenta. While the gap function has a singlet spin structure, the order parameter indicates an unconventional superconducting phase, with the ratio between singlet and triplet amplitudes being plus or minus one on the Fermi lines of the upper or lower band, respectively. We expect our combined functional RG and mean-field approach to be useful for an unbiased theoretical description of the low-temperature properties of spin-based materials.

cond-mat.str-el↗
arXiv2016

Tight-binding Rashba model and statistical field theory

This document contains information supplementary to the article [1], but it is self-contained and can be read independently as a pedagogical review. In the first part, we explain our conventions for the tight-binding description of electronic states on the hexagonal Bravais lattice in two dimensions. We derive the Rashba spin splitting from elementary symmetry conditions, and subsequently construct a minimal tight-binding model which displays Rashba spin splitting near the center of the Brillouin zone. Furthermore, we derive the corresponding symmetry conditions for a two-particle interaction in a second-quantized framework. In the second part, we describe our conventions for the temperature Green functions, in terms of which the renormalization group equations in [1] have been formulated. We also provide a brief summary of the most important definitions and properties of temperature Green functions. [1] G. A. H. Schober, K.-U. Giering, M. M. Scherer, C. Honerkamp, and M. Salmhofer, arXiv:1409.7087.

cond-mat.str-el↗
arXiv2002

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t=-0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder.

cond-mat.str-el↗
arXiv2000

An inversion theorem in Fermi surface theory

We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between the fermions. This theorem gives a physical meaning to the counterterm function K that we use in the renormalization of these models: K can be identified as that part of the self--energy that causes the deformation of the Fermi surface when the interaction is turned on.

math-ph↗
arXiv1999

Breakdown of the Landau-Fermi liquid in Two Dimensions due to Umklapp Scattering

We study the renormalization group flow of the interactions in the two-dimensional t-t' Hubbard model near half filling in a N-patch representation of the whole Fermi surface. Starting from weak to intermediate couplings the flows are to strong coupling with different character depending on the choice of parameters. In a large parameter region elastic Umklapp scatterings drive an instability which on parts of the Fermi surface exhibits the key signatures of an insulating spin liquid (ISL), as proposed by Furukawa et al., rather than a conventional symmetry-broken state. The ISL is characterized by both strong d-wave pairing and antiferromagnetic correlations, however it is insulating due to the vanishing local charge compressibility and a spin liquid because of the spin gap arising from the pairing correlations. We find that the ISL is a consequence of a Fermi surface close to the saddle points at the Brillouin zone boundaries which provides an intrinsic and mutually reinforcing coupling between pairing and Umklapp channels.

cond-mat.str-el↗