# Carrier-envelope phase effects in graphene

## TL;DR

This paper investigates how the carrier-envelope phase of terahertz pulses influences electron dynamics in graphene, revealing asymmetries in electron momentum distributions and proposing methods for CEP measurement in condensed matter systems.

## Contribution

It introduces a detailed analysis of CEP effects on electron momentum in graphene and demonstrates potential for controlling electron dynamics and measuring CEP using these effects.

## Key findings

- Asymmetric electron momentum distributions depend on CEP.
- Conditions for minimal adiabatic gap influence electron dynamics.
- Potential method for CEP measurement in condensed matter systems.

## Abstract

We numerically study the interaction of a terahertz pulse with monolayer graphene. We observe that the electron momentum density is affected by the carrier-envelope phase (CEP) of the single- to few-cycle terahertz laser pulse that induces the electron dynamics. In particular, we see strong asymmetric electron momentum distributions for non-zero values of the CEP. We explain the origin of the asymmetry within the adiabatic-impulse model by finding conditions to reach minimal adiabatic gap between the valence band and the conduction band. We discuss how these conditions and the interference pattern, emanating from successive non-adiabatic transitions at this minimal gap, affect the electron momentum density and how they are modified by the CEP. This opens the door to control fundamental time-dependent electron dynamics in the tunneling regime in Dirac materials. Also, this control suggests a way to measure the CEP of a terahertz laser pulse when it interacts with condensed matter systems.